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ANALYSIS OF RETRIAL QUEUE WITH TWO WAY COMMUNICATION, WORKING BREAKDOWN AND COLLISION

 B. Somasundaram, G. Archana @ Gurulakshmi, G. Ayyappan

This study examines a two-way communication retrial queue with collision and working breakdown. Retrial incoming calls may interfere with service if the server is busy with primary incoming calls. Arriving primary incoming calls are sent to the orbit while the server is busy or enter for service if the server is discovered to be idle. The server places calls while it is idle. Incoming calls are given high priority, and outgoing calls are given low priority. During regular service, the system may fails at any time. The server will continue to provide service after a breakdown even though at a slower rate rather than shutting down completely. We assume that outgoing calls and service time distributions are modelled in terms of various PH distributions, while incoming calls are assumed to follow a Markovian arrival process (MAP). The matrix-analytic approach will be used to investigate the resulting QBD process in steady state. Some of the performance metrics’ calculations have been figured out. At the end, the results are presented in both numerical and graphical form.

Cite:  B. Somasundaram, G. Archana @ Gurulakshmi, G. Ayyappan ANALYSIS OF RETRIAL QUEUE WITH TWO WAY COMMUNICATION, WORKING BREAKDOWN AND COLLISION. Reliability: Theory & Applications. 2023, September 3(74): 30-43, DOI: https://doi.org/10.24412/1932-2321-2023-374-30-43

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LSA: A LIGHTWEIGHT SYMMETRIC ENCRYPTION ALGORITHM FOR RESOURCE-CONSTRAINED IOT SYSTEMS

Amita Shah, Sanjay Shah, Hiren Patel, Namit Shah

Today, Internet of Things (IoT) systems are being employed in a wide variety of domains, such as education, healthcare, industrial equipment automation, etc. With gigabytes of data being generated and processed by even the average IoT system, securing this generated data is crucial task. It requires a low-cost, high-performance encryption system for constrained IoT systems. The Advanced Encryption Standard (AES) is widely used for many cryptographic domains because of its strong security characteristics. AES is designed for general-purpose symmetric encryption algorithm but there is a need for a lighter algorithm that is specifically tuned for the needs of IoT devices with limited computation capabilities. Aim: This paper is proposing Lightweight Symmetric Algorithm (LSA) as a faster and lighter alternative to the standard AES-128 for IoT applications. The primary objective of its design was to minimize the time and memory usage required for encryption and decryption processes while retaining the strong security characteristics. Method: The research also demonstrates the comparative analysis of LSA and AES based on efficiency and resource usage. It also proves the difficulty of performing a successful brute force attack, confusion and diffusion properties, and avalanche criterion satisfiability are identical for AES and LSA algorithms. Findings: The comparison analysis of LSA and AES suggests a 14.68% lower memory usage for encryption and decryption as well as more than a 50% decrease, on average, in the required time for encryption or decryption of differently-sized files consisting of the same 128 bit data blocks. The comparisons and empirical observations show that AES and LSA are both almost identical in terms of their security characteristics such as the difficulty of performing a successful brute force attack, confusion and diffusion properties, and avalanche criterion satisfiability. Conclusion: The proposed LSA algorithm is compared with various available lightweight cipher technologies with respect to time, memory, and security properties suggests the suitability of LSA for resource constrained IoT devices with strong security requirements.

Cite: Amita Shah, Sanjay Shah, Hiren Patel, Namit Shah LSA: A LIGHTWEIGHT SYMMETRIC ENCRYPTION ALGORITHM FOR RESOURCE-CONSTRAINED IOT SYSTEMS. Reliability: Theory & Applications. 2023, September 3(74): 44-58, DOI: https://doi.org/10.24412/1932-2321-2023-374-44-58

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A STUDY ON THE PROPERTIES OF A NEW EXPONENTIATED EXTENDED INVERSE EXPONENTIAL DISTRIBUTION WITH APPLICATIONS

Sule Omeiza Bashiru

In this paper, a new continuous probability distribution called a new exponentiated extended inverse exponential distribution with four parameters is introduced. The mathematical and statistical properties of the proposed distribution, such as the quantile function, moments, moment generating function, survival function, hazard function, odds function, and reversed hazard function, were studied to understand its nature. The probability density function of the order statistics for this distribution was also obtained. The parameters of the model were estimated using the maximum likelihood method of estimation. The proposed model was applied to two real datasets relating to the relief times of twenty patients receiving an analgesic and the sum of skin folds in 202 athletes collected at the Australian Institute of Sports. The results showed that the new model outperformed its comparators and provides better fit than Topp-Leone exponentiated inverse exponential, Topp-Leone inverse exponential, exponentiated inverse exponential, inverse exponential and exponential distributions.

Cite: Sule Omeiza Bashiru  A STUDY ON THE PROPERTIES OF A NEW EXPONENTIATED EXTENDED INVERSE EXPONENTIAL DISTRIBUTION WITH APPLICATIONS  Reliability: Theory & Applications. 2023, September 3(74): 59-72, DOI: https://doi.org/10.24412/1932-2321-2023-374-59-72

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ON CHANGE-POINT ANALYSIS OF MAXWELL DISTRIBUTION USING BAYESIAN TECHNIQUES

Taiwo M. Adegoke, Oladapo M. Oladoja

This research work focuses on Bayesian inference in this study to detect a change in the rate of a Maxwell distribution model with independent random variables. The paper specifically analyzes a single rate shift and demonstrates how the Bayesian framework can be used to efficiently solve this problem. To produce samples from Maxwell distribution and evaluate the datasets, simulation techniques were used, and the R programming language was used. Although the model looks to be simple, no analytical solutions are available for parameter inference, necessitating the use of approximations. The study emphasizes the Gibbs sampler’s applicability for change-point analysis using a Markovian updating approach. The simulation research findings show that the predicted rate is near to the true value, confirming the consistency and stability of the Bayesian estimator.

Cite: Taiwo M. Adegoke, Oladapo M. Oladoja ON CHANGE-POINT ANALYSIS OF MAXWELL DISTRIBUTION USING BAYESIAN TECHNIQUES. Reliability: Theory & Applications. 2023, September 3(74): 73-80, DOI: https://doi.org/10.24412/1932-2321-2023-374-73-80

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ANALYSIS OF UNCERTAINTY WEIGHTED MEASURES FOR PARETO II DISTRIBUTION

Baria A. Helmy, Amal S. Hassan, Ahmed K. El-Kholy

Extropy is a complimentary dual of Shannon’s entropy, which has many applications. The maximum likelihood and Bayesian approaches are used in this article to explore the weighted extropy and weighted residual extropy of the Pareto type II distribution. Using unified hyper-censoring data, we calculate the maximum likelihood estimation of weighted extropy and its residual measures. Based on symmetric and asymmetric loss functions, Bayesian estimators of weighted extropy and its residual measure are developed based on unified hyper censoring data. To do some complex calculations, Markov chain Monte Carlo methods are used. To test the performance of the estimators, a Monte Carlo simulation study and an illustration using real data sets were carried out. The outcomes of the study showed that as the sample size increases, maximum likelihood and Bayesian estimators of the weighted extropy and its residual measure perform well. Also, Bayesian estimators of the weighted extropy and its residual under the general entropy loss function are superior to the Bayesian estimators under the others in most cases. Theoretical and empirical findings are generally in good agreement.

Cite: Baria A. Helmy, Amal S. Hassan, Ahmed K. El-Kholy ANALYSIS OF UNCERTAINTY WEIGHTED MEASURES FOR PARETO II DISTRIBUTION. Reliability: Theory & Applications. 2023, September 3(74): 81-96, DOI: https://doi.org/10.24412/1932-2321-2023-374-81-96

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ALTERNATE QUADRA SUB - MERGING POLAR FUZZY SOFT GRAPH AND ITS APPLICATION

Anthoni Amali A, J.Jesintha Rosline

Fuzzy graph and Fuzzy soft graph are indispensable computing modules for presenting membership and non - membership values in the world of uncertain situations and incidents. In this research article, we introduce the new module of Alternate Quadra Submerging Polar Fuzzy Soft Graph with four co –ordinates with membership and non – membership values. The aim of this new fuzzy soft graph is to find the single output from different uncertain parametric sets of subjects and events, between the range [-1, 1]. The submerge level of fixed four co ordinates is a tool to find the precise and reliable membership degree values from uncertain problems and outcomes. In this artifact, we also investigate the different types of Alternate Quadra Submerging Polar Fuzzy Soft Graphs, corresponding parametric fuzzy values and submerge membership and non – membership values. We discussed Strong, Complete, Complement and m complement properties of Alternate Quadra Submerging Polar Fuzzy Soft Graphs. We use this fuzzy soft graph in the Analysis of water related diseases to find the result of most and least affected diseases with the symptoms among the hostel students in the same locality. We find the maximum and minimum membership and non - membership value of the water related diseases in an unique way by using this Alternate Quadra Submerging Polar Fuzzy Soft Graph score function values.

Cite: Anthoni Amali A, J.Jesintha Rosline ALTERNATE QUADRA SUB - MERGING POLAR FUZZY SOFT GRAPH AND ITS APPLICATION. Reliability: Theory & Applications. 2023, September 3(74): 97-112, DOI: https://doi.org/10.24412/1932-2321-2023-374-97-112

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WEIGHTED GENERALIZED ENTROPY: PROPRTIES AND APPLICATION

Bilal Ahmad Bhat, M. Sultan Shah, M.A.K Baig

Recently, the measurement of uncertainty has attracted the attention of researchers. In this article, we introduce a new weighted uncertainty measure known as weighted generalized entropy. We also study its dynamic (residual) version which is known as weighted generalized residual entropy. These are length-biased shift-dependent uncertainty measures. It is shown that the proposed dynamic uncertainty measure uniquely determines the survival function. The various significant properties and the relationship with other well-known reliability measures of the proposed dynamic uncertainty measure are also studied. Finally, a real life data set is used to illustrate the usefulness of our proposed uncertainty measures.

Cite: Bilal Ahmad Bhat, M. Sultan Shah, M.A.K Baig WEIGHTED GENERALIZED ENTROPY: PROPRTIES AND APPLICATION . Reliability: Theory & Applications. 2023, September 3(74): 113-120, DOI: https://doi.org/10.24412/1932-2321-2023-374-113-120

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BULK ARRIVAL QUEUEING MODEL WITH SETUP AND M OPTIONAL SERVICE UNDER BERNOULLI VACATION SCHEDULE AND SERVER FAILURE

Binay Kumar

In the present investigation, we consider a bulk queue model with the assumption that the server may stop working due to random failure during any stage of the service. As soon as the server fails, it is immediately sent for repair. The server offers all incoming units the first mandatory service and any one of the optional services as per the unit's requirements. For computation purposes, we assume that the server offers m+1 services, of which the first one is essential and the remaining are optional. The server may take a vacation in accordance with the Bernoulli vacation schedule with probability p as soon as both service phases of a unit are completed. As the system empties, the server idles and needs some time to set up before initiating the next service. In order to analyse the model and derive various steady-state queue length distributions, we incorporated the supplementary variables corresponding to service time, vacation time, and repair time and applied the probability generating function technique to determine the various system state distributions. Using these probability distributions, we derive the explicit form of various performance indices. To discuss the validity of the present model, we obtained some well-known results from the queueing literature as a special case of the present model by setting appropriate parameters. Finally, to analyse the sensitivity of several performance indices, a numerical demonstration is provided.

Cite: Binay Kumar BULK ARRIVAL QUEUEING MODEL WITH SETUP AND M OPTIONAL SERVICE UNDER BERNOULLI VACATION SCHEDULE AND SERVER FAILURE. Reliability: Theory & Applications. 2023, September 3(74): 121-134, DOI: https://doi.org/10.24412/1932-2321-2023-374-121-134

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A NEW FINITE MIXTURE OF PROBABILITY MODELS WITH APPLICATION

K.M. Sakthivel, Vidhya G

In this research, we present an approach to model lifetime data by a weighted three-parameter probability distribution utilizing the exponential and gamma distributions. We have presented some of the essential characteristics such as the shapes of pdf, cdf, moments, incomplete moments, survival function, hazard function, mean residual life, stochastic ordering, and order statistics of the proposed distribution. Furthermore, we also presented the Bonferroni index and Lorenz curve of the proposed distribution. The maximum likelihood approach is used to estimate the parameters of the distribution. Finally, the proposed probability distribution is compared to goodness of fit with Lindley, Akash, exponential, two-parameter Lindley, cubic transmuted Rayleigh, and Exponential-Gamma distributions for the real-time data set.

Cite: K.M. Sakthivel, Vidhya G A NEW FINITE MIXTURE OF PROBABILITY MODELS WITH APPLICATION. Reliability: Theory & Applications. 2023, September 3(74): 135-153, DOI: https://doi.org/10.24412/1932-2321-2023-374-135-153

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A NEW GENERALIZATION OF TWO PARAMETRIC DIVERGENCE MEASURE AND ITS APPLICATIONS

Fayaz Ahmed, Mirza Abdul Khalique Baig

In this communication, we proposed two parametric generalized divergence measures. The well-known divergence measures available in the literature are a particular case of our new proposed divergence measure. We also looked into its monotonic behaviour and characterization results. We applied the proposed measure to some life-time distributions and observed that the deviation has been reduced. We have shown the mortality rate of two different countries based on COVID-19 data sets.

Cite: Fayaz Ahmed, Mirza Abdul Khalique Baig A NEW GENERALIZATION OF TWO PARAMETRIC DIVERGENCE MEASURE AND ITS APPLICATIONS. Reliability: Theory & Applications. 2023, September 3(74): 154-163, DOI: https://doi.org/10.24412/1932-2321-2023-374-154-163

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ESTIMATION OF A PARAMETER OF FARLIE-GUMBEL-MORGENSTERN BIVARIATE BILAL DISTRIBUTION BY RANKED SET SAMPLING

M. R. Irshad, R. Maya, A.I. Al-Omari, Ahmad A. Hanandeh, S. P. Arun

A bivariate version of the Bilal distribution has been proposed in the literature, called the Farlie-Gumbel-Morgenstern bivariate Bilal (FGMBB) distribution. In this article, we have dealt with the problem of estimation of the scale parameter associated with the study variable Z of primary interest, based on the ranked set sample defined by ordering the marginal observations on an auxiliary variable W, when (W, Z) follows a FGMBB distribution. When the dependence parameter f is known, we have proposed the following estimators, viz., an unbiased estimator based on the Stoke’s ranked set sample and the best linear unbiased estimator based on the Stoke’s ranked set sample for the scale parameter of the variable of primary interest. The efficiency comparison of the proposed estimators with respect to the maximum likelihood estimator have been carried out.

Cite: M. R. Irshad, R. Maya, A.I. Al-Omari, Ahmad A. Hanandeh, S. P. Arun ESTIMATION OF A PARAMETER OF FARLIE-GUMBEL-MORGENSTERN BIVARIATE BILAL DISTRIBUTION BY RANKED SET SAMPLING. Reliability: Theory & Applications. 2023, September 3(74): 164-175, DOI: https://doi.org/10.24412/1932-2321-2023-374-164-175

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COST-REVENUE ANALYSIS AND ANFIS COMPUTING OF HETEROGENEOUS QUEUING MODEL WITH A SECOND OPTIONAL SERVICE WITH FEEDBACK UNDER HYBRID VACATION

Divya K, Indhira K

This research article examines an M/M/2 heterogeneous queueing model that provides two services: a mandatory first essential service (FES) and an optional second optional service (SOS). The model incorporates breakdown, feedback, and a hybrid vacation policy. Matrix expressions are structured to evaluate the stationary probability distribution of the number of customers in the system and system performance measures using the matrix-geometric approach (MGA). Additionally, formulas are being developed to estimate the model’s performance indicators. The cost function is being evaluated to determine the best values of the system’s decision variables, and an adaptive neural fuzzy inference system (ANFIS) based on soft computing technology is being utilized to validate the obtained results. Keywords: Markovian queue, Breakdown, Hybrid vacation, Matrix geometric approach, ANFIS.

Cite: Divya K, Indhira K COST-REVENUE ANALYSIS AND ANFIS COMPUTING OF HETEROGENEOUS QUEUING MODEL WITH A SECOND OPTIONAL SERVICE WITH FEEDBACK UNDER HYBRID VACATION. Reliability: Theory & Applications. 2023, September 3(74): 176-195, DOI: https://doi.org/10.24412/1932-2321-2023-374-176-195

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EVALUATION OF RELIABILITY’ INDICES AND CHARACTERISTICS OF THE POWER SYSTEM QUIPMENT AND DEVICES BY NON TRADITIONAL METHOD

Farzaliyev Y.Z., Farhadzadeh E.M.

In the paper considered the research expediency classification of statistical data according to the given varieties of signs. The researching carried out based on modeling of small and multidimensional samples to statistical distribution functions. A discrepancy found in the estimation of the mathematical expectation of the average values of sample implementation, to overcome this inconsistency, a new method for modeling samples of random variables is proposed. It established that the classification in the literature data carried out according to the varieties of signs accepted in the classifiers without control of expediency. The causes of errors arising in the evaluation of Kolmogorov statistics as the largest in absolute deviation are analyzed the deviation between statistical distribution functions of the population and sample using simulation modeling, fiducially intervals and the theory of testing statistical hypotheses. These erroneous calculations with a small number and multidimensionality of sampling implementations double increases of the Type II Error. Finally, the result showed the advantages of the new method in comparison with Kolmogorov’ criterion via checking representativeness of sample.

Cite: Farzaliyev Y.Z., Farhadzadeh E.M.  EVALUATION OF RELIABILITY’ INDICES AND CHARACTERISTICS OF THE POWER SYSTEM QUIPMENT AND DEVICES BY NON TRADITIONAL METHOD. Reliability: Theory & Applications. 2023, September 3(74): 196-205, DOI: https://doi.org/10.24412/1932-2321-2023-374-196-205

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AN ATTRIBUTE CONTROL CHART FOR TIME TRUNCATED LIFE TESTS USING EXPONENTIATED INVERSE KUMARASWAMY DISTRIBUTION

B. Srinivasa Rao, M. Rami Reddy, K. Rosaiah

In this article an attribute control chart is designed for the Exponentiated Inverse kumaraswamy distribution under a time truncated life test by assuming the life-time of the item follow the selected Exponentiated Inverse Kumaraswamy distribution with known parameters. In order to limit the cost of checking the quality of an item in any industrial process with time truncation, this process is much useful. By considering the average number of defective items from a specified lot that are failed before the time limit, the attribute control limits are constructed. The control chart is determined using Binomial distribution based on the Upper and Lower control limits. The functioning of the designed control chart is examined with the average run length (ARL) values. The control chart constants and limits are calculated for specific ARL values with assumed parameters at different sample sizes for an in-control process. These control chart constants are obtained by considering different combinations of parameters of the assumed distribution. With these in-control limits the ARL values are observed by shifting the parameter values. A simulation analysis is developed by taking a specific number of observations in each sample and the average number of failures from each sample is considered as a statistic to establish the execution of the control chart for a specified ARL at a particular shift in parameter. With that statistic of average number of failures from the samples the control chart is prepared. It is observed a specific change in defective number when there is shift in parameter values. The results are illustrated with an example.

Cite: B. Srinivasa Rao, M. Rami Reddy, K. Rosaiah  AN ATTRIBUTE CONTROL CHART FOR TIME TRUNCATED LIFE TESTS USING EXPONENTIATED INVERSE KUMARASWAMY DISTRIBUTION . Reliability: Theory & Applications. 2023, September 3(74): 206-217, DOI: https://doi.org/10.24412/1932-2321-2023-374-206-217

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A TYPE I HALF -LOGISTIC EXPONENTIATED WEIBULL DISTRIBUTION: PROPERTIES AND APPLICATIONS

Olalekan Akanji Bello, Sani Ibrahim Doguwa, Abukakar Yahaya, Haruna Mohammed Jibril

In the area of distribution theory, statisticians have proposed and developed new models for generalizing the existing ones so as to make them more flexible and to aid their application in a variety of fields. In this article, we present a new distribution called the Type I Half-Logistic Exponentiated Weibull (TIHLEtW) Distribution with four positive parameters, which extends the Weibull distribution by two parameters. Some statistical properties of the TIHLEtW distribution, such as explicit expressions for the quantile function, probability weighted moments, moments, generating function, Reliability function, hazard function, and order statistics are discussed. A maximum likelihood estimation technique is employed to estimate the model parameters and the simulation study is presented. The superiority of the new distribution is illustrated with an application to two real data sets. The results showed that the new distribution fits better in the two real data sets amongst the range of distributions considered.

Cite: Olalekan Akanji Bello, Sani Ibrahim Doguwa, Abukakar Yahaya, Haruna Mohammed Jibril A TYPE I HALF -LOGISTIC EXPONENTIATED WEIBULL DISTRIBUTION: PROPERTIES AND APPLICATIONS . Reliability: Theory & Applications. 2023, September 3(74): 218-233, DOI: https://doi.org/10.24412/1932-2321-2023-374-218-233

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ESTIMATION OF RELIABILITY AND LIFETIME OF COMPOSITE OVERWRAPPED PRESSURE VESSELS ADOPING POTENTIAL FAILURES ASSESSMENT AND ACCELERATED TESTS APPROACH

Maryam Gholami Arjenaki, Dr. Mahdi Karbasian, Amin Kazemi Manesh, Mohammadreza Jafari

Aim. Compressed air vessels are responsible for injecting compressed air to the mechanical flying device. It should be noted that the pressure level inside these vessels is very important in conducting all operational stages successfully; therefore, it is of high significance to be assured of the quality of the vessels being used. This study was done in 2017 in order to calculate and estimate the reliability of compressed air vessels in mechanical flying device system with proposing a potential failures assessment and accelerated test approach taking into consideration the current methods. Methods. The paper uses methods of Fault Tree Analysis, Failure Mode & Effect Analysis and Accelerator tests. Initially, the interactions among the components were identified using the Design Structure Matrix in order to design a matrix to help estimate the reliability; consequently, improve equipment performance. Next, failures root recognition was done using Fault Tree Analysis diagram, then, failures reasons prioritization was done using Failure Mode & Effects Analysis tables. Accelerator tests were designed and applied on failure mechanisms such as leakage by pressure on vessels, corrosions on steal head, nipples, O-ring creeping, O-ring ozone cracking and liner chemical degradation. After that, the average of failure rates was calculated within the taking after stage for each test. Within the conclusion, the result of failure rates from the accelerator tests was compared with the result of failure rates from the process approach. Consequently, the most elevated amount of these two approaches was defined as the total failure rate; product reliability and lifetime were calculated utilizing this amount. Results. The following finding were obtained using the proposed methods. When Windy Liner was used, vessel lifetime was six years and half and vessel reliability in ten years was 0/22. Whereas, when Rotational Liner was used, vessel lifetime was eight years and three months and vessel reliability in ten years was 0/3. Conclusion.The approach proposed in the paper allows accelerator degradation test can also be used instead of accelerated test in order to calculate the reliability of failure mechanisms. In the event that high-quality and legitimate O-rings are used, vessel reliability and lifetime can be increased.

Cite: Maryam Gholami Arjenaki, Dr. Mahdi Karbasian, Amin Kazemi Manesh, Mohammadreza Jafari  ESTIMATION OF RELIABILITY AND LIFETIME OF COMPOSITE OVERWRAPPED PRESSURE VESSELS ADOPING POTENTIAL FAILURES ASSESSMENT AND ACCELERATED TESTS APPROACH . Reliability: Theory & Applications. 2023, September 3(74): 234-244, DOI: https://doi.org/10.24412/1932-2321-2023-374-234-244

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CERTAIN RESULTS OF ALEPH- FUNCTION BASED ON NATURAL TRANSFORM OF FRACTIONAL ORDER

Farooq Ahmad, D.K. Jain, Ajjaz Maqbool, Aafaq A. Rather, Maryam Mohiuddin, Priya Deshpande, Madhulika Mishra, Shaikh Sarfaraj

The paper introduces a new type of fractional integral transform called the N-transform of fractional order. This transform is utilized to derive various results for a more generalized function of fractional calculus known as the Aleph-function. The authors present several useful findings and explore the relationship between the N-transform and other existing fractional transforms. Additionally, the paper discusses the relationship between the N-transform of fractional order and other existing fractional transforms. It likely explores how this new transform relates to established transforms in fractional calculus. The authors have also examined special cases or specific examples to further illustrate the applications and properties of the N-transform of fractional order. These cases could involve particular functions or parameter values that offer insight into the behavior of the transform.

Cite: Farooq Ahmad, D.K. Jain, Ajjaz Maqbool, Aafaq A. Rather, Maryam Mohiuddin, Priya Deshpande, Madhulika Mishra, Shaikh Sarfaraj  CERTAIN RESULTS OF ALEPH- FUNCTION BASED ON NATURAL TRANSFORM OF FRACTIONAL ORDER . Reliability: Theory & Applications. 2023, September 3(74): 245-251, DOI: https://doi.org/10.24412/1932-2321-2023-374-245-251

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RELIABILITY TEST PLAN FOR THE POISSON-POWER LINDLEY DISTRIBUTION

Alphonsa George, Dais George

In this article, we introduce a new member to Poisson-X family namely, the Poisson-power Lindley distribution. The statistical as well as the distributional properties of the new distribution are studied. The flexibility of the distribution is illustrated by means of real data sets. We also introduce a reliability test plan for acceptance or rejection of a lot of products submitted for inspection when lifetimes follow the new distribution. The minimum sample size using binomial and Poisson approximations, operating characteristic values and minimum ratios of the true value and the required value of the parameter with a given producer’s risk are also developed with respect to the newly introduced sampling plans. A real data example is also given to illustrate the sampling plan developed.

Cite: Alphonsa George, Dais George RELIABILITY TEST PLAN FOR THE POISSON-POWER LINDLEY DISTRIBUTION. Reliability: Theory & Applications. 2023, September 3(74): 252-268, DOI: https://doi.org/10.24412/1932-2321-2023-374-252-268

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CREATION AND ANALYSIS OF MULTIMODAL EMOTION RECOGNITION CORPUS WITH INDIAN ACTORS

Komal Anadkat, Dr. Hiteishi Diwanji, Dr. Shahid Modasiya, Mihir Mehta

Emotion recognition plays an important role in many real-life application areas of artificial intelligence like human-computer interactions, autism detection, stress and depression detection, measuring mental health, and suicide prevention. Emotion state of a person can be decided by the facial expression, tone of voice, words of speech, and body gestures when they are having a face-to-face conversation. People widely use social media platforms to post their feelings and mood through status. So, the status text can be used to identify the emotional state of a person. Physiological signals (EEG, ECG, and EDA) can identify the emotional state more accurately as people cannot be faked during the data collection but it is difficult to collect data. Many unimodal and multimodal datasets are publicly available but still, there is a strong need to create a multimodal dataset that consists of all the important modalities for the identification of emotional state. In this paper, first, we have reviewed all the available unimodal and multimodal datasets, then in the next section, we discuss the method to prepare the multimodal dataset. The data of four different modalities like facial expressions, audio, social media text, and EEG have been collected from seven different actors of different age groups and of different demographic regions. The dataset is non-spontaneous and contains discrete emotion labels like happy, sad, and angry. The procedure to create a dataset of different modalities include steps like capturing data, pre-processing, feature extraction, and storing to the relevant format. In last, to observe effect of different emotions, analysis of proposed multimodal database is carried out using efficient image, speech and text parameters.

Cite: Komal Anadkat, Dr. Hiteishi Diwanji, Dr. Shahid Modasiya, Mihir Mehta CREATION AND ANALYSIS OF MULTIMODAL EMOTION RECOGNITION CORPUS WITH INDIAN ACTORS . Reliability: Theory & Applications. 2023, September 3(74): 269-283, DOI: https://doi.org/10.24412/1932-2321-2023-374-269-283

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THE EFFICACY OF TRAPEZOIDAL FUZZY NUMBERS AND ITS APPLICATION

Ajjaz Maqbool Dar, Aafaq A. Rather, Rushika Kinjawadekar, Abhay Deshpande, Maryam Mohiuddin, Rashid A. Ganaie, Khursheed Ahmad

Numerous fields, including engineering, agriculture, and management sciences, have been using trapezoidal fuzzy numbers. In this study, we first develop Trapezoidal Fuzzy Number (TFN) and then attempt to formulate a model to handle element uncertainty in order to solve a linear programming problem. Making good decisions will only require this type of approximation.

Cite: Ajjaz Maqbool Dar, Aafaq A. Rather, Rushika Kinjawadekar, Abhay Deshpande, Maryam Mohiuddin, Rashid A. Ganaie, Khursheed Ahmad  THE EFFICACY OF TRAPEZOIDAL FUZZY NUMBERS AND ITS APPLICATION . Reliability: Theory & Applications. 2023, September 3(74): 284-287, DOI: https://doi.org/10.24412/1932-2321-2023-374-284-287

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A NOVEL THREE - PARAMETER VERSION OF THE AILAMUJIA DISTRIBUTION

Idzhar A. Lakibul

In this paper, a novel three - parameter continuous distribution is introduced. This novel distribution is an extented version of the Exponenentiated Ailamujia distribution. This extended version called as Exponentiated Generalized Ailamujia (EGA) distribution. The Exponentiated Generalized class is used to derive the proposed distribution by considering Ailamujia distribution as a baseline distribution. A special case of the EGA distribution called Generalized Ailamujia (GA) distribution is also derived. Properties of the proposed distribution such as moments, mean, variance, harmonic mean, moment generating function, survival function, hazard function, reverse hazard rate, Mills ratio and order statistics are derived. In addition, maximum likelihood approach is used to estimate the proposed distribution parameters. Finally, the proposed distribution is applied to two real datasets and compare with the Exponentiated Ailamujia and the Ailamujia Inverted Weibull distributions. Results reveal that the proposed distribution provides better estimate as compared to the said distributions for the given two real datasets.

Cite: Idzhar A. Lakibul A NOVEL THREE - PARAMETER VERSION OF THE AILAMUJIA DISTRIBUTION. Reliability: Theory & Applications. 2023, September 3(74): 288-298, DOI: https://doi.org/10.24412/1932-2321-2023-374-288-298

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THE EFFICIENCY OF ESTIMATING A POPULATION AVERAGE USING INDEX-TYPE ESTIMATORS IN SEQUENTIAL SAMPLING

Srinivasa Rao Kolli, U.V.Adinarayana Rao, Adilakshmi Siripurapu, Taviti Naidu Gongada

This paper discusses the difficulty of approximating the population average of a variable y by knowledge about a supplementary variable x in the context of two successive (rotation) sampling occasions. The paper proposes a group of exponential-class estimators that includes the regular balanced estimator, produce-class estimator, and proportion-class estimator and suggests that these estimators are superior to existing estimators. The paragraph also mentions that the paper discusses optimal substitute statements and then the implementation of the recommended estimators, which may be important considerations for practical applications of the proposed methods. Finally, an empirical study is mentioned as supporting evidence for the research.

Cite: Srinivasa Rao Kolli, U.V.Adinarayana Rao, Adilakshmi Siripurapu, Taviti Naidu Gongada THE EFFICIENCY OF ESTIMATING A POPULATION AVERAGE USING INDEX-TYPE ESTIMATORS IN SEQUENTIAL SAMPLING . Reliability: Theory & Applications. 2023, September 3(74): 299-307, DOI: https://doi.org/10.24412/1932-2321-2023-374-299-307

299-307

A TWO NON-IDENTICAL UNIT PARALLEL SYSTEM WITH PRIORITY IN REPAIR

Alka Chaudhary, Shivali Sharma

The paper deals with a system composed of two-non identical units (unit-1 and unit-2). Initially both the units are arranged in parallel configuration. Each unit has two possible modes- Normal (N) and Total Failure (F). The first unit gets priority in repair. System failure occurs when both the units stop functioning. A single repairman is always available with the system to repair a totally failed unit and repair discipline is first come, first served (FCFS).If during the repair of a failed unit the other unit also fails, then the later failed unit waits for repair until the repair of the earlier failed unit is completed. The repair times of both the units are exponential distribution with different parameters. Each repaired unit works as good as new. Using regenerative point technique, various important measures of system effectiveness have been obtained.

Cite: Alka Chaudhary, Shivali Sharma A TWO NON-IDENTICAL UNIT PARALLEL SYSTEM WITH PRIORITY IN REPAIR. Reliability: Theory & Applications. 2023, September 3(74): 308-315, DOI: https://doi.org/10.24412/1932-2321-2023-374-308-315

308-315

DEEP LEARNING APPROACH FOR EVENT RECOGNITION IN FIELD HOCKEY VIDEOS

Suhas H. Patel, Dr. Dipesh Kamdar, Dr. D. D. Vyas, Dr. Prakash P. Patel

The objectives of this research are to develop a deep learning approach for event recognition in field hockey videos, construct a dataset that includes important activities in field hockey such as goals, penalty corners, and penalty, and evaluate the performance of the approach using the constructed dataset. By achieving these objectives, the research aims to improve the accuracy and effectiveness of event recognition in the fast-paced and complex domain of field hockey videos. The methods employed in this research involve utilizing a pretrained convolutional neural network (CNN) to train a classifier specifically designed for event recognition in field hockey videos. To facilitate this process, a dataset is constructed, consisting of labeled instances of key activities in field hockey, namely goals, penalty corners, and penalty. The performance of the approach is then evaluated using this carefully prepared dataset, providing insights into the effectiveness and accuracy of the proposed method for event recognition in the context of field hockey videos. The findings of this research reveal that the proposed deep learning approach for event recognition in field hockey videos achieves a remarkable accuracy of 99.47%. This high level of accuracy highlights the effectiveness of the approach in accurately identifying and classifying events in field hockey. Furthermore, the results demonstrate the potential of this approach in various field hockey applications, including performance analysis, coaching, and video replay. The accurate recognition of events opens new possibilities for leveraging field hockey videos for enhanced analysis, coaching strategies, and engaging video presentations. The novelty of this research lies in the introduction of a deep learning approach specifically designed for event recognition in field hockey videos. Unlike traditional methods, this approach leverages the power of deep learning, particularly a pretrained CNN, to improve the accuracy of event recognition. Additionally, the construction of a domain-specific dataset addresses the limitation of existing field hockey datasets and enhances the effectiveness of the approach. The remarkable accuracy achieved in event recognition further emphasizes the novelty and potential of this approach in the field of field hockey video analysis.

Cite: Suhas H. Patel, Dr. Dipesh Kamdar, Dr. D. D. Vyas, Dr. Prakash P. Patel  DEEP LEARNING APPROACH FOR EVENT RECOGNITION IN FIELD HOCKEY VIDEOS . Reliability: Theory & Applications. 2023, September 3(74): 316-332, DOI: https://doi.org/10.24412/1932-2321-2023-374-316-332

316-332

RELIABILITY AND PROFITABILITY ANALYSIS OF UTENSILS MANUFACTURING INDUSTRY WITH EFFECT OF TEMPERATURE AND PREVENTIVE MAINTENANCE

Manisha, Dalip Singh, Kajal Sachdeva, Sheetal

The production stage of the manufacturing process contains numerous subsystems, and the failure of one might have an impact on the entire system. Thus, a manufacturing plant needs to be reliable and well-maintained. This paper examines the profitability and reliability of a production plant for utensils while taking the effect of temperature into account. The plant processes raw materials through several subsystems in series including cutting, pressing, spinning, and polishing & packing. Winter production requires a significant amount of heat which could damage the machinery. As a result, production is low and preventive maintenance is carried out during the winter. For both the summer and winter seasons, many system measures have been assessed. The time distributions have been assumed to be exponential. The model has been analysed using the Markov and Regenerative processes. The production fluctuation between the summer and winter seasons have been illustrated using a numerical example with specific values for the parameters.

Cite: Manisha, Dalip Singh, Kajal Sachdeva, Sheetal RELIABILITY AND PROFITABILITY ANALYSIS OF UTENSILS MANUFACTURING INDUSTRY WITH EFFECT OF TEMPERATURE AND PREVENTIVE MAINTENANCE. Reliability: Theory & Applications. 2023, September 3(74): 333-344, DOI: https://doi.org/10.24412/1932-2321-2023-374-333-344

333-344

ANALYSIS OF A FLEXIBLE GROUP SERVICE MAP\PH\1 QUEUEING MODEL WITH, IMMEDIATE FEEDBACK, BALKING AND RENEGING

G. Ayyappan, S. Kalaiarasi

Queueing models in which the services are provided in groups (or blocks or batches) have found to be very useful in real-world applications and such queues been extensively analysed in the literature. In this paper we see one such group service queueing model with balking, reneging and immediate feedback. The arrival processes is a Markovian arrival , where, the arriving customer may balk the system while the server is idle and the pool is empty. Customers are provided service in groups of varying size from 1 to the fixed constant, say, N. The service time of a batch follows the phase type distribution corresponding to the each size of the group. A group’s service time is taken as the highest of the service times of each customers who make up the group. The group of customers who are dissatisfied with the service then that group will get the service immediately. Here, the feedback of a group is defined as the average of the feedback of each customers who make up the group. During the admission period the customers may renege. We calculated the steady state probabilities by using the matrix geometric method, then, by using it we computed few performance measures. We have studied the busy period and the distribution of waiting time is derived. Results are illustrated with some graphical representations.

Cite: G. Ayyappan, S. Kalaiarasi ANALYSIS OF A FLEXIBLE GROUP SERVICE MAP\PH\1 QUEUEING MODEL WITH, IMMEDIATE FEEDBACK, BALKING AND RENEGING . Reliability: Theory & Applications. 2023, September 3(74): 345-362, DOI: https://doi.org/10.24412/1932-2321-2023-374-345-362

345-362

A STATISTICAL ANALYSIS OF FRACTIONAL FACTORIAL DESIGN USING A FUZZY PROBABILISTIC APPROACH

Sri Devi, P., Pachamuthu, M.

In factorial experiments, treatment combinations increase as the number of factors increases. While handling a large number of factors, many difficulties are encountered. Moreover, mechanical errors like mistaken identification of plots, wrong labeling of treatments, etc., may creep in. To overcome these difficulties, only a fraction of treatment combinations can be tested. This technique is known as fractional replication. The design with fractional replication is known as fractional factorial design (FFD). In FFD, the choice of the fraction of treatment depends on what type of information is sacrificed. Usually, the interactions with higher-order are omitted, and all main effects and two-factor interactions are estimated without loss of information. The procedure for the layout of FFD is closely related to the concept of confounding. The analysis of fractional factorials is similar to the analysis of full factors. FFD is used to reduce treatment combinations by a fraction. FFD plays a significant role when the experiment is too large. When compared to classical designs, FFD yields a cost-benefit relationship. Fuzzy theory is used to deal with the imprecise observations in this design. This paper proposes the statistical analysis of fuzzy fractional factorial design with numerical illustration.

Cite: Sri Devi, P., Pachamuthu, M.  A STATISTICAL ANALYSIS OF FRACTIONAL FACTORIAL DESIGN USING A FUZZY PROBABILISTIC APPROACH . Reliability: Theory & Applications. 2023, September 3(74): 363-373, DOI: https://doi.org/10.24412/1932-2321-2023-374-363-373

363-373

ON THE PROPERTIES OF GENERALIZED RAYLEIGH DISTRIBUTION WITH APPLICATIONS

Sule Omeiza Bashiru, Ibrahim Ismaila Itopa, Alhaji Modu Isa

In this study, a new three-parameter lifetime distribution called the generalized Rayleigh distribution was introduced. The new model is an extension of classical Rayleigh distribution. An extension of density of the generalized Rayleigh distribution was derived from which some of the statistical and mathematical properties were derived. Some mathematical properties of the distribution were presented such as moments, moment generating function, quantile function, survival function, hazard function, reversed hazard function and odd function. The distribution of order statistic was obtained in which the maximum and minimum order statistics were derived. Estimation of the parameters by maximum likelihood method was discussed. Two real-life application of the distribution was presented and the analysis showed the fit and flexibility of the generalized Rayleigh distribution over odd Lindley Rayleigh distribution and Rayleigh distribution. The analysis showed that the generalized Rayleigh distribution is more effective and robust in fitting the data sets.

Cite: Sule Omeiza Bashiru, Ibrahim Ismaila Itopa, Alhaji Modu Isa  ON THE PROPERTIES OF GENERALIZED RAYLEIGH DISTRIBUTION WITH APPLICATIONS . Reliability: Theory & Applications. 2023, September 3(74): 374-386, DOI: https://doi.org/10.24412/1932-2321-2023-374-374-386

374-386

HALF CAUCHY - EXPONENTIAL DISTRIBUTION: ESTIMATION AND APPLICATIONS

K.Jayakumar, Fasna.K

In this paper, we introduce a new two-parameter distribution called the new Half Cauchy – exponential distribution (HCE) for modeling lifetime data. The structural properties of the new distribution are discussed. Expressions for the quantiles, mode, mean deviation, and distribution of order statistics are derived. The model parameters of HCE distribution are estimated by the method of maximum likelihood, method of least square, method of Cramer-von-Mises, and Anderson-Darling methods. The existence and uniqueness of maximum likelihood estimates are proved. The importance of the new distribution is proved empirically by real-life data set.

Cite: K.Jayakumar, Fasna.K HALF CAUCHY - EXPONENTIAL DISTRIBUTION: ESTIMATION AND APPLICATIONS. Reliability: Theory & Applications. 2023, September 3(74): 387-401, DOI: https://doi.org/10.24412/1932-2321-2023-374-387-401

387-401

ANALYSIS OF ENCOURAGED ARRIVAL MULTIPLE WORKING VACATION QUEUING MODEL UNDER THE STEADY STATE CONDITION

Ismailkhan Enayathulla Khan, Rajendran Paramasivam

Businesses typically entice customers with alluring offers and discounts. Encouraged arrivals is the name given to these curious clients. In certain situations, the service offered by queuing models, notably in transportation networks, enables the simultaneous serving of several consumers. In general, closed-form solutions to bulk service queuing models with idle servers are difficult to find. By coordinating the operations at each workstation using the Chapman-Kolmogorov research technique, the main objective of this study is to assess the performance of the car assembly line in order to reduce waiting times. The server is in a busy state, is idle, is regularly busy, and is in a busy state when it breaks down. Performance metrics are being tracked using a multiple working vacation approach. In this study, analysis of encouraged arrival multiple working vacation queuing model under the steady state condition. In this model, we included encouraged arrival. By resolving difference equations and Chapman Kolmogorov balancing equations, the steady state queue size problem is found. Additionally, the server is in the busy, idle state, regular, and breakdown busy states, and performance metrics are conducted. The server was sent for repair and is now completely repaired to avoid the crash at any time. After that, the server continues to offer the service. It is evidently identified that the efficiency level increased while the encouraged arrival is incorporated. The main contribution of this paper is to show the server is in the busy, idle state, regular, and breakdown busy states, and performance metrics efficient level increases. It is found that they offer more efficient results when compared with the Poisson process method

Cite: Ismailkhan Enayathulla Khan, Rajendran Paramasivam ANALYSIS OF ENCOURAGED ARRIVAL MULTIPLE WORKING VACATION QUEUING MODEL UNDER THE STEADY STATE CONDITION . Reliability: Theory & Applications. 2023, September 3(74): 402-407, DOI: https://doi.org/10.24412/1932-2321-2023-374-402-407

402-407

TECHNICAL DEVICE WEAR-OUT PERIOD INFLUENCE ON QUANTITATIVE RISK ASSESSMENT RESULTS

Yuriy D. Kuznetsov, Evgeniy Yu. Kolesnikov

Hazardous production facilities contain numerous technical devices, the reliability assessment of which is a part of quantitative risk assessment. The paper considers the pressure valve as a safety system element of equipment operating under excessive pressure and evaluates its reliability (survival function value) during the operational period. Valve reliability during the wear-out period has been modeled to assess wear-out period influence on this element failure probability. Modeling was carried out by approximating the failure rate tabular values obtained based on statistical data. Approximation was carried out by: a second-degree polynomial, the Weibull distribution law and a power function. Comparison of the obtained quantitative estimates with the element failure probability, calculated without taking into account the wear-out period, showed necessity of wear-out period influence consideration in risk assessment procedure.

Cite: Yuriy D. Kuznetsov, Evgeniy Yu. Kolesnikov  TECHNICAL DEVICE WEAR-OUT PERIOD INFLUENCE ON QUANTITATIVE RISK ASSESSMENT RESULTS . Reliability: Theory & Applications. 2023, September 3(74): 408-415, DOI: https://doi.org/10.24412/1932-2321-2023-374-408-415

408-415

BEHAVIOR ANALYSIS OF WASHING UNIT IN A PAPER PLANT EMPLOYING FUZZY APPROACH

Mamta, Seema Sharma

Aim. The purpose of this research is to employ a fuzzy approach to assess the system behavior of the washing unit in a paper plant using vague, uncertain and inaccurate data. The washing unit is the main operational part of a paper plant for which analysis of system behavior is important to choose an appropriate maintenance strategy. The analysis has been carried out for washing unit of a paper plant situated in northern India. Methods. The proposed approach comprises qualitative and quantitative analysis. In qualitative analysis, the basic arrangement of the washing unit is modelled by Petri Net model. In quantitative analysis, the fuzzy λ-τ approach has been used for analyzing the systems' failure behavior more accurately. Uncertainties in failure/repair data of every subsystem/component of the washing unit are quantified using trapezoidal fuzzy numbers. Results. To assess the performance and failure dynamic behavior of the washing unit quantitatively, six reliability parameters including failure rate, repair time, mean time between failure, expected number of failures, reliability and availability at three different spread levels have been evaluated employing trapezoidal fuzzy numbers. The fuzzified values of these reliability parameters of washing unit have been defuzzified employing center of area defuzzification technique. Further, crisp values and defuzzified values of these parameters using triangular fuzzy numbers have also been obtained. The results obtained by the proposed methodology have been compared with those obtained by fuzzy λ-τ approach based on triangular fuzzy numbers. The information/results obtained through the fuzzy λ-τ approach with trapezoidal fuzzy number are conservative in nature, therefore, these results may be used by system specialist/system analysts for the future plan of implementation. Conclusion. Using this approach, six reliability parameters are evaluated and the trend (increase or decrease) of these reliability parameters is examined for performance analysis of washing unit in a paper plant. Based on these investigations, suitable maintenance policy can be established that will assist maintenance manager/system analysts/engineers in improving system performance by implementing appropriate preventive maintenance procedures. As a result, it will help in achieving a long time system availability and maximizing overall productivity of the paper plant. The implications of this fuzzy reliability approach to industry maintenance and operation planning are quite beneficial.

Cite: Mamta, Seema Sharma BEHAVIOR ANALYSIS OF WASHING UNIT IN A PAPER PLANT EMPLOYING FUZZY APPROACH . Reliability: Theory & Applications. 2023, September 3(74): 416-427, DOI: https://doi.org/10.24412/1932-2321-2023-374-416-427

416-427

THE CONTINUOUS BERNOULLI-GENERATED FAMILY OF DISTRIBUTIONS: THEORY AND APPLICATIONS

Ngozi O. Ubaka, Friday Ewere

The continuous Bernoulli distribution is a one-parameter probability distribution which is useful in analysis on machine learning. A handful of studies has been done to generalize the continuous Bernoulli distribution. In this paper, we introduced a wider extension of the continuous Bernoulli distribution by considering its distribution function as a generator. We referred to the proposed family as the continuous Bernoulli-generated family of distributions. Basic statistical treatments of the proposed family such as the density and cumulative distribution functions, survival and hazard rate functions, quantile, moments, moment generating function, and Renyi entropy are derived. The method of maximum likelihood is employed to estimate the unknown parameters of the family and the asymptotic behaviour of the parameter estimates is investigated via Monte Carlo simulation study. The waiting time (in minutes) of 100 Bank customers and the tensile strength measured in GPa, of 69 carbon fibers data sets formed the basis for real-life data fittings. Results obtained from the fitting of the two data sets when compared with some existing non-nested models revealed that the fittings were in favor of the continuous-Bernoulli Weibull distribution over the rest competing distributions.

Cite: Ngozi O. Ubaka, Friday Ewere  THE CONTINUOUS BERNOULLI-GENERATED FAMILY OF DISTRIBUTIONS: THEORY AND APPLICATIONS . Reliability: Theory & Applications. 2023, September 3(74): 428-441, DOI: https://doi.org/10.24412/1932-2321-2023-374-428-441

428-441

A NEW EXPONENTIAL TYPE RATIO ESTIMATOR FOR THE POPULATION MEAN IN SYSTEMATIC SAMPLING

Ayed AL e’damat, Khalid Ul Islam Rather

Utilizing auxiliary information effectively in sample surveys can enhance the accuracy of estimations by capitalizing on the relationship between the main variable under study and the auxiliary variable. Estimators such as ratio, product, exponential, and regression estimators are frequently employed either during the estimation process, the design phase, or both. In everyday situations, it is common to incorporate information from one or two auxiliary variables to improve the precision of estimators. Auxiliary information has been in practice in sampling theory since the advent of modern sample surveys. Information on auxiliary variable having high correlation with the variable under study is quite useful in improving the sampling design. Cochran (1940) used the highly positively correlated study and auxiliary variable to propound the ratio estimator. Product estimator requires a high negative correlation between study and auxiliary variable. By reviewing the literature, it is concluded that applying the auxiliary information enhances the efficiencies of the estimators for estimating any parameter under consideration. So it is well established fact that the use of auxiliary variable technique improves the estimation process for target population. It is also noticed that ratio method of estimation is relatively simple and one of the commonly used methods of estimation. Due to limitations in terms of time and cost, sample surveys are often preferred over census surveys for collecting primary data. In these sample surveys, the ratio, product, and regression estimators are frequently employed to estimate the mean or other parameters of interest for the variable under study. To assess their efficiency, these estimators are compared based on their approximate mean squared errors. In this paper we proposed an exponential ratio type estimator for the estimation of finite population mean under systematic sampling. The mean square error of the proposed estimator is computed up to the first order of approximation and we find proposed estimator is efficient as compared to other existing estimators. Furthermore this theoretical result is supported by numerical examples as well.

Cite: Ayed AL e’damat, Khalid Ul Islam Rather A NEW EXPONENTIAL TYPE RATIO ESTIMATOR FOR THE POPULATION MEAN IN SYSTEMATIC SAMPLING . Reliability: Theory & Applications. 2023, September 3(74): 442-449, DOI: https://doi.org/10.24412/1932-2321-2023-374-442-449

442-449

FAILURE RATE ESTIMATION BY WEIBULL DISTRIBUTION IN A STOCHASTIC ENVIRONMENT: APPLICATION TO THE HEMODIALYSIS MACHINE

Sofiene Fenina, Souheyl Jendoubi, Faker Bouchoucha,

This paper presented a study of the failure rate by introducing the effect of influencing variables. These variables have a random effect which depends on the external environment of the system. There are a multitude of variables and their modeling is difficult. The perturbation, to the failure rate, caused by external factors, has a direct impact on the time scale by the acceleration (or deceleration) of the degradation of the system. Therefore, the adopted methodology consists in introducing a perturbation on the Weibull parameters and studying its effect on the failure rate. Weibull parameters are considered random variables with a Gaussian distribution. The failure rate formulation in a random environment is offered through Weibull distribution. A case study of the hemodialysis machine is offered to illustrate the proposed approach and validate the results. The simulations presented show the failure rate statistics for different configurations of the Weibull distribution. The validation of the results was done using Monte Carlo simulations.

Cite: Sofiene Fenina, Souheyl Jendoubi, Faker Bouchoucha,  FAILURE RATE ESTIMATION BY WEIBULL DISTRIBUTION IN A STOCHASTIC ENVIRONMENT: APPLICATION TO THE HEMODIALYSIS MACHINE . Reliability: Theory & Applications. 2023, September 3(74): 450-463, DOI: https://doi.org/10.24412/1932-2321-2023-374-450-463

450-463

ROBUST CLASSIFICATION USING MINIMUM REGULARIZED COVARIANCE DETERMINANT ESTIMATOR

R Muthukrishnan, Surabhi S Nair

The association between a categorical variable and a group of interconnected factors is the main objective of the classification procedure. The linear discriminant analysis (LDA) aims to provide a method for classifying populations and dividing up forthcoming observations among the groups that have already been identified. Under the suppositions of normality and homoscedasticity, the LDA produces the best discriminant rule for two or more groups. Outliers have a significant impact on the parameters of the LDA, mean, and covariance matrix. Robust methods are resistant to outliers. This paper explores the robust methods, namely the Minimum Covariance Determinant (MCD) estimator and Minimum Regularized Covariance Determinant (MRCD) estimators in the context of discriminant analysis under real environments. The MCD technique is used to estimate the location and dispersion matrix using the subset of the given size that has the lowest sample covariance determinant. Its fundamental problem is that it doesn’t provide a reliable result when the features/dimension is greater than the size of the subset. As a result, the MRCD method is employed and the efficiency is studied by computing the Apparent Error Rate (AER). In this paper, an attempt has been made to review the existing theory and methods of RLDA.

Cite: R Muthukrishnan, Surabhi S Nair  ROBUST CLASSIFICATION USING MINIMUM REGULARIZED COVARIANCE DETERMINANT ESTIMATOR . Reliability: Theory & Applications. 2023, September 3(74): 464-470, DOI: https://doi.org/10.24412/1932-2321-2023-374-464-470

464-470

DESIGN OF MULTIPLE DEPENDENT STATE SAMPLING PLAN USING ZECH DISTRIBUTION WITH APPLICATION TO REAL LIFE DATA

Sunday J. Adeyeye, Ademola J. Adewara, Rao S. Gadde, Kayode S. Adekeye, Adedayo F. Adedotun,  Lawrence O. Aako

In this work, a multiple dependent state sampling plan, which is an inspection procedure that determines whether an attribute is conforming or non-conforming to a specific requirement, in which the decision criterion for each lot dictates whether to accept the lot; reject the lot; or conditionally accept or reject the lot based on the disposition of future related lots, is introduced. This plan has some advantages over other acceptance sampling plans, like increased efficiency, improved ability to discriminate between acceptable and non – acceptable lots or batches, flexibility in designing the sampling process, and improved cost-effectiveness. To reject a lot, the plan made use of the properties of the sampled current and preceding lots. The study aims to reduce the average sampling number by using a non-linear optimization problem that is subjected to some constraints. With regards to a life test that is truncated in time, the product’s median life was used for the proposed sampling plan assuming that the lifetime of the product follows Zech distribution. The usage of median life was necessitated because Zech distribution is an asymmetric distribution with longer tail to the right. Two points on the operating characteristic curve were used for the proposed sampling plan and the following parameters were found; number of preceding lots which is required for deciding if the current lot should be accepted or rejected, the size of the sample, rejection number, and acceptance number. For different shape parameters, we constructed tables for various combinations of consumers’ and producers’ risks. A real example was provided which showed that a multiple dependent state sampling plan is a good sampling plan for fitting the datasets. Comparing the proposed plan with a single sampling plan, the results reveal that the proposed plan is more effective at securing the consumer and the producer with less inspection. The approach introduced in this study provides an ample opportunity for the manufacturers to reduce the cost and time of inspection by having the sample size reduced without compromising the decision-making accuracy. By implementing the findings of this study, the consumers are confident that their hard-earned money is not used to purchase sub-standard goods.

Cite: Sunday J. Adeyeye, Ademola J. Adewara, Rao S. Gadde, Kayode S. Adekeye, Adedayo F. Adedotun,  Lawrence O. Aako  DESIGN OF MULTIPLE DEPENDENT STATE SAMPLING PLAN USING ZECH DISTRIBUTION WITH APPLICATION TO REAL LIFE DATA . Reliability: Theory & Applications. 2023, September 3(74): 471-481, DOI: https://doi.org/10.24412/1932-2321-2023-374-471-481

471-481

MULTIBAND COMPACT MICROSTRIP PATCH ANTENNA FOR WIRELESS COMMUNICATION APPLICATIONS

Dr.Shahid Modasiya, Dr.Balvant Makwana, Anil Poriya

In this paper, a multiband compact microstrip patch antenna for different communication frequencies has been presented. The proposed design of the microstrip patch antenna consists of a slotted patch, a quarter-wave feed line, and a ground with a cross-edge slot. The antenna can operate from 2.1 GHz to 3.4 GHz with a bandwidth of 1.3 GHz; this band corresponds to applications such as Mobile WiMax (2110 MHz-2200 MHz, 2300 MHz-2400 MHz, 2500 MHz-2690 MHz), Bluetooth (2400 MHz-2497 MHz), and RFiD. (2400 MHz -2483 MHz). The higher band, 4.7 GHz to 7.4 GHz, covers C-band, WLAN, and sub-6GHz 5G applications and has a gain factor of about 2.15 dB. The antenna is fabricated, and measurements of the radiation pattern and return loss are made. The comparison of observed results with those from simulations reveals excellent symmetry. Furthermore, the 70× 40 mm2 size of the proposed antenna makes it appropriate for use in lower 5G bands.

Cite: Dr.Shahid Modasiya, Dr.Balvant Makwana, Anil Poriya MULTIBAND COMPACT MICROSTRIP PATCH ANTENNA FOR WIRELESS COMMUNICATION APPLICATIONS . Reliability: Theory & Applications. 2023, September 3(74): 482-491, DOI: https://doi.org/10.24412/1932-2321-2023-374-482-491

482-491

DETECTION OF CERVICAL CANCER RISK FACTORS IN VENEZUELA USING DECISION TREE ALGORITHM

Oladapo M. Oladoja, Taiwo M. Adegoke

Cervical cancer, a threat to female existence is one of major cancer affecting women in the developing countries of the world. Several factors are responsible which humans didn™t take cognizance of. These factors are numerous and can at times be difficult to explain using linear regression because it can™t handle many dummy variables that are not necessary to create qualitative predictors. This study uses decision trees to classify and identify the major risk factors causing cervical cancer in women depending on their age since it closely mirrors human decision making than the classical regression approach. A regression tree was constructed from the training data using recursive binary splitting. There was a minimum number of observations required for each terminal node before it stopped. Then cost complexity pruning to the large tree in order to obtain a sequence of best sub trees was applied. By using decision trees as building blocks, we can construct more powerful predictions for decision trees, bagging, random forests, and boosting. 858 cervical cancer patients were observed using 34 risk factor attributes from University Hospital of Caracas, Venezuela. Using classification trees, 14.22% of errors are produced during training. Based on the test data set, 91.5% of the predictions are correct. Based on the data set’s pruned data, 91.75% of the observations can be classified correctly. Test predictions generated by this model are within 67 years of the true median age of patients, based on regression trees. Bagging and Random forest show improvement on the regression trees by setting a reduced mean square error. There are four most significant variables among all trees examined by the random forest, including age at first sexual intercourse, number of pregnancies, number of sexual partners, and hormonal contraceptives. The same goes for boosting, as a result of the relative influence statistics.

Cite: Oladapo M. Oladoja, Taiwo M. Adegoke DETECTION OF CERVICAL CANCER RISK FACTORS IN VENEZUELA USING DECISION TREE ALGORITHM. Reliability: Theory & Applications. 2023, September 3(74): 492-500, DOI: https://doi.org/10.24412/1932-2321-2023-374-492-500

492-500

ASSESSMENT OF WATER QUALITY USING MULTIVARIATE TECHNIQUES

Olamiji T. Onafowokan, Kazeem O. Obisesan, Oladapo M. Oladoja

When deciding if water is suitable for a particular usage, its quality ”which includes its chemical, physical, and biological characteristics” is referred to. The quality of the water is influenced by many natural and human influences. Despite being in equilibrium, the natural ecosystem and water quality would certainly be disturbed by any large changes in the water quality. In order to assess the levels of water pollution in the Asejire and Eleyele reservoirs, this study conducted a Physico-chemical analysis of the two reservoirs. It also used multivariate techniques to identify the causes of water pollution in the two reservoirs under investigation, used a generalized linear model to analyze the variability in turbidity levels, and suggested regulatory solutions to address water pollution in the two reservoirs under study. In Ibadan, which has a population of about four million, the two main sources of pipe-borne water are the Eleyele and Asejire reservoirs. Between January 2003 and August 2019, water samples were taken from both locations and analyzed for 13 Physico-chemical parameters using the Principal Component Analysis and Cluster Analysis for feature extraction and finally a Generalized Linear model for prediction. Basic Tables and descriptive plots, Principal Component Analysis, Factor Analysis, and Generalized Linear Models were employed. Results: In the Asejire and Eleyele reservoirs, respectively, the PCA yields 5 significant main components explaining 76.56% and 60.97% of the variance, while the FA yields 5 significant major components explaining 94.90% and 79.97%. A generalized linear model (GLM) was used to study the variability in turbidity level, and the results indicate that two parameters ”Iron and Silicon” in the Asejire reservoir are crucial for understanding turbidity variation and four ”Colour, Alkaline, Silica, and Solids ”contribute significantly to turbidity in the water level in the Eleyele Reservoir. With the exception of dissolved oxygen from either reservoir (Eleyele or Asejire) and iron from Eleyele Reservoir, many metrics in Asejire are within SON and WHO acceptable limits. This suggests that the water in the Eleyele reservoir is more contaminated than the Asejire reservoir.

Cite: Olamiji T. Onafowokan, Kazeem O. Obisesan, Oladapo M. Oladoja ASSESSMENT OF WATER QUALITY USING MULTIVARIATE TECHNIQUES. Reliability: Theory & Applications. 2023, September 3(74): 501-513, DOI: https://doi.org/10.24412/1932-2321-2023-374-501-513

501-513

ON SOME STATISTICAL PROPERTIES AND APPLICATIONS OF THREE-PARAMETER SUJATHA DISTRIBUTION

Hosenur Rahman Prodhani, Rama Shanker

In this paper some important statistical properties of three-parameter Sujatha distribution including descriptive measures based on moments, reliability properties, mean deviations, stochastic ordering and Bonferroni and Lorenz curves have been discussed. The estimation of parameters using maximum likelihood estimation has been discussed. Finally, the goodness of fit of the distribution has been presented for two real lifetime datasets and compared with several one and two-parameter well- known lifetime distributions.

Cite: Hosenur Rahman Prodhani, Rama Shanker  ON SOME STATISTICAL PROPERTIES AND APPLICATIONS OF THREE-PARAMETER SUJATHA DISTRIBUTION . Reliability: Theory & Applications. 2023, September 3(74): 514-527, DOI: https://doi.org/10.24412/1932-2321-2023-374-514-527

514-527

ANALYSIS OF MMAP/PH/1 CLASSICAL RETRIAL QUEUE WITH NON-PREEMPTIVE PRIORITY, SECOND OPTIONAL SERVICE, DIFFERENTIATE BREAKDOWNS, PHASE TYPE REPAIR, SINGLE VACATION, EMERGENCY VACATION, CLOSEDOWN, SETUP AND DISCOURAGEMENT

G. Ayyappan, G. Archana @ Gurulakshmi

A single server retrial queueing model with non-preemptive priority was examined in this research. The arrival of priority consumers follow a marked Markovian arrival pattern, and both high priority and low priority service times are according to phase type distribution. Matrix analytic method are used to examine the steady state analysis of this model. Various system performance measures, cost analysis and busy period analysis also examined in this model. In additionally, by using some system performance measures we provide the numerical illustration with numerically and graphically.

Cite: G. Ayyappan, G. Archana @ Gurulakshmi ANALYSIS OF MMAP/PH/1 CLASSICAL RETRIAL QUEUE WITH NON-PREEMPTIVE PRIORITY, SECOND OPTIONAL SERVICE, DIFFERENTIATE BREAKDOWNS, PHASE TYPE REPAIR, SINGLE VACATION, EMERGENCY VACATION, CLOSEDOWN, SETUP AND DISCOURAGEMENT. Reliability: Theory & Applications. 2023, September 3(74): 528-551, DOI: https://doi.org/10.24412/1932-2321-2023-374-528-551

528-551

EXPONENTIAL - POISSON DISTRIBUTION IN RELIABILITY ACCEPTANCE SAMPLING PLAN FOR LIFE TESTING

Dr. V.Kaviyarasu, A.Nagarajan

Statistical Quality Control is an important field in production and maintenance of quality product in manufacturing environments. Reliability sampling plans (RSP) were widely employed in the sectors of manufacturing to monitor the quality of products in order to safe guard the producer as well as the consumer also the experimental costs and time can be saved. This article is developed on the reliability sampling plan when the evaluating life of the product is set to be truncated at pre-determined time follows Exponential-Poisson (EP) distribution. The probability of acceptance criteria for the single sampling is designed to achieve the lowest sample size for such proposed two parameter probability distribution with the corresponding decision rule. This study is conducted to design plan parameters on the basis of desired quality levels such as Acceptable Reliability Quality Level (ARQL), Indifference Reliability Quality Level (IRQL) and Rejectable Reliability Quality Level (RRQL). This study computes the median life for the specified producer's risk, its OC curve is provided along with the minimum ratio values. Furthermore, it determines the minimum size of the samples and the acceptance number. Table values have been obtained and provided for single sampling plan. Additionally, suitable examples are provided to conduct a study on a real time situations.

Cite: Dr. V.Kaviyarasu, A.Nagarajan EXPONENTIAL - POISSON DISTRIBUTION IN RELIABILITY ACCEPTANCE SAMPLING PLAN FOR LIFE TESTING . Reliability: Theory & Applications. 2023, September 3(74): 552-559, DOI: https://doi.org/10.24412/1932-2321-2023-374-552-559

552-559

CHARACTERIZATION OF POISSON TYPE LENGTH BIASED EXPONENTIAL CLASS SOFTWARE RELIABILITY GROWTH MODEL AND PARAMETER ESTIMATION

Rajesh Singh , Kailash R. Kale , Pritee Singh

The authors of this study set out to build a software reliability growth model (SRGM). Software reliability is a crucial attribute that has to be quantified and evaluated. In most cases, software errors happen at unpredictable times. In this article, the failure intensity of the single parameter length-biased exponential class SRGM has been characterized taking into account the Poisson process of the incidence of software faults. The parameters of the proposed SRGM under investigation are the scale parameter (theta1) and the total number of failures (theta1). It is considered that the experimenter may have previous knowledge of the parameters from past or earlier experiences in the form of gamma priors. The posterior probability may be obtained by combining the prior probability with the likelihood of the data, and Bayes estimators can then be suggested.

Cite: Rajesh Singh , Kailash R. Kale , Pritee Singh  CHARACTERIZATION OF POISSON TYPE LENGTH BIASED EXPONENTIAL CLASS SOFTWARE RELIABILITY GROWTH MODEL AND PARAMETER ESTIMATION . Reliability: Theory & Applications. 2023, September 3(74): 560-567, DOI: https://doi.org/10.24412/1932-2321-2023-374-560-567

560-567

POWER WEIGHTED SUJATHA DISTRIBUTION WITH PROPERTIES AND APPLICATION TO SURVIVAL TIMES OF PATIENTS OF HEAD AND NECK CANCER

Rama Shanker, Kamlesh Kumar Shukla

In this paper a power weighted Sujatha distribution, which includes power Sujatha distribution, weighted Sujatha distribution and Sujatha distribution as particular cases, has been proposed. Its statistical properties including behavior of density function, moments, hazard rate function, and mean residual life function have been discussed. Estimation of parameters has been discussed using the method of maximum likelihood. A simulation study has been presented to know the performance of maximum likelihood estimates of parameters. Application of the proposed distribution have been explained with a real lifetime data relating to patients suffering from head and neck cancer and goodness of fit shows quite satisfactory fit.

Cite: Rama Shanker, Kamlesh Kumar Shukla  POWER WEIGHTED SUJATHA DISTRIBUTION WITH PROPERTIES AND APPLICATION TO SURVIVAL TIMES OF PATIENTS OF HEAD AND NECK CANCER . Reliability: Theory & Applications. 2023, September 3(74): 568-581, DOI: https://doi.org/10.24412/1932-2321-2023-374-568-581

568-581

A STUDY ON STATISTICAL PROPERTIES OF A NEW CLASS OF Q-EXPONENTIAL-WEIBULL DISTRIBUTION WITH APPLICATION TO REAL-LIFE FAILURE TIME DATA

N. Sundaram, G. Jayakodi

This article introduces a new four-parameter probability distribution called the q-Exponential-Weibull distribution based on the q-Exponential-G family of distribution. The proposed new distribution has to decrease and increase failure rates which are more common in reliability scenarios and can be used instead of Weibull and the exponential distribution. It also includes some sub-models like q-Exponential-Exponential, q-Exponential-Rayleigh, Exponential-Weibull, Exponential-Exponential and Exponential-Rayleigh lifetime distributions. Various Mathematical and statistical Properties are investigated, which include Limiting behavior, Moments and Moment Generating functions, Quantile function and Order Statistics. The Maximum Likelihood estimator is used for estimating the model parameters. This new distribution is compared with other lifetime distributions using different kinds of real-life failure time data.

Cite: N. Sundaram, G. Jayakodi A STUDY ON STATISTICAL PROPERTIES OF A NEW CLASS OF Q-EXPONENTIAL-WEIBULL DISTRIBUTION WITH APPLICATION TO REAL-LIFE FAILURE TIME DATA . Reliability: Theory & Applications. 2023, September 3(74): 582-595, DOI: https://doi.org/10.24412/1932-2321-2023-374-582-595

582-595

RELIABILITY ACCEPTANCE SAMPLING PLAN FOR ONE PARAMETER POLYNOMIAL EXPONENTIAL DISTRIBUTION

Anumita Mondal, Sudhansu S. Maiti

In this study, we construct a reliability acceptance sampling inspection plan to decide whether to accept or reject a lot of products where the One Parameter Polynomial Exponential (OPPE) family of distributions governs the lifetimes. The OPPE distribution has infinite support. To utilise finite support, it has transformed into its unit form, i.e. having the support (0, 1). The design of the plan, Operating characteristic curve, and Sampling procedure are discussed. Determination of the plan parameters using an algorithm is stated. The optimal sample size is determined to protect the consumer’s confidence level. Two simplest particular choices of the OPPE family - the exponential and the Lindley are chosen as examples, and optimal plan parameters are tabulated and compared. The plan is executed with three real-life data sets.

Cite: Anumita Mondal, Sudhansu S. Maiti RELIABILITY ACCEPTANCE SAMPLING PLAN FOR ONE PARAMETER POLYNOMIAL EXPONENTIAL DISTRIBUTION. Reliability: Theory & Applications. 2023, September 3(74): 596-609, DOI: https://doi.org/10.24412/1932-2321-2023-374-596-609

596-609

TWO-CLASSES FOR REGRESSION TYPE OF ESTIMATORS FOR THE RATIO OF TWO POPULATION MEANS IN TWO-PHASE SAMPLING IN THE PRESENCE OF NON-RESPONSE FOR STRATIFIED POPULATION

Manish Mishra, B. B. Khare, Sachin Singh

Utilizing the auxiliary information in stratified population, in the current study, we have discussed two classes for the regression type of estimators to estimate the ratio of two population means in the presence of non-response with the unknown population mean of the auxiliary variable. To estimate the unknown value of the population mean of auxiliary variable, we have used two-phase sampling method. For the suggested classes of estimators, we have considered two situations for the use of auxiliary information along with the non-response in the study variable such as incomplete information on the study variable and incomplete information on the corresponding units of the auxiliary variable and in another situation we have considered incomplete information on the study variable and complete information on the auxiliary variable. To estimate the non-response in study variable and auxiliary variables, we have used the Hansen and Hurwitz method of sub-sampling from the non-respondents. For the suggested classes of estimators, some members have been recognized. Using large sample approximation, the expressions for bias and mean square error have been derived for the suggested classes. The optimum values of the constants involving in the expression of mean square error have also been calculated. Mean square errors of the Suggested classes are found to be equal in theoretical study and real data study. An empirical study has been conducted with the help of a real data set (The Primary Census Abstract-2011 published by the Office of the Registrar General & Census Commissioner, India.) in order to compare the proposed classes of estimators with the conventional estimator for the different rates of non-response and different choices of sub-sampling fraction. The Suggested classes are found to be most efficient with respect to the conventional estimator for the different rates of non-response and different choices of sub-sampling fraction in empirical study.

Cite: Manish Mishra, B. B. Khare, Sachin Singh TWO-CLASSES FOR REGRESSION TYPE OF ESTIMATORS FOR THE RATIO OF TWO POPULATION MEANS IN TWO-PHASE SAMPLING IN THE PRESENCE OF NON-RESPONSE FOR STRATIFIED POPULATION. Reliability: Theory & Applications. 2023, September 3(74): 610-620, DOI: https://doi.org/10.24412/1932-2321-2023-374-610-620

610-620

DISTRIBUTIONAL PROPERTIES OF ORDER STATISTICS AND RECORD STATISTICS FROM ERLANG-TRUNCATED EXPONENTIAL FAMILY OF DISTRIBUTION AND ITS CHARACTERIZATIONS

Imtiyaz A. Shah

Erlang Truncated Exponential Distributions are characterized by distributional properties of order statistics. These characterizations include known results for ordinary order statistics based on two non-adjacent order statistics coming from two independent Erlang truncated exponential distributions. Using this method and compared with an efficient recent method given, three examples of real lifetime data-sets are analyzed by that deals with non-random samples. Such type of examples predicts the accumulative new cases per million foe infection of the new COVID-19. Corollaries for Pareto and power function distributions are also derived.

Cite: Imtiyaz A. Shah DISTRIBUTIONAL PROPERTIES OF ORDER STATISTICS AND RECORD STATISTICS FROM ERLANG-TRUNCATED EXPONENTIAL FAMILY OF DISTRIBUTION AND ITS CHARACTERIZATIONS. Reliability: Theory & Applications. 2023, September 3(74): 621-630, DOI: https://doi.org/10.24412/1932-2321-2023-374-621-630

621-630

ESTIMATION OF FRECHET PARAMETERS WITH TIME-CENSORED DATA IN ACCELERATED LIFE TESTING UTILISING THE GEOMETRIC PROCESS

Abdul Kalam, Cheng Weihu, Ahmadur Rahman, Mohammad Ahmad

The geometric process (GP) has been applied to estimate constant stress accelerated life testing for the Frechet failure item with time-censored data. A geometric process (GP) is developed by the failure time of tested items when stress levels are constantly rising. The estimates of the various parameters are calculated using the maximum likelihood estimation procedure. The asymptotic variance of estimates is obtained using a Fisher information matrix. The asymptotic variance is then used to calculate the distribution parameter asymptotic interval values. The statistical properties and confidence intervals of the required parameters are then illustrated using a simulation technique.

Cite: Abdul Kalam, Cheng Weihu, Ahmadur Rahman, Mohammad Ahmad ESTIMATION OF FRECHET PARAMETERS WITH TIME-CENSORED DATA IN ACCELERATED LIFE TESTING UTILISING THE GEOMETRIC PROCESS. Reliability: Theory & Applications. 2023, September 3(74): 631-641, DOI: https://doi.org/10.24412/1932-2321-2023-374-631-641

631-641

RELIABILITY ANALYSES OF AN INDUSTRIAL SYSTEM BASED ON HERMITE POLYNOMIAL AND 2-PARAMETER WEIBULL

Anas Sani Maihulla, Michael Khoo Boon Chong, Ibrahim Yusuf

The current study aims to assess the structure's reliability using stochastic Hermite surface methodology. This approach uses series expansion of standard normal random variables to model uncertainty. (i.e., polynomial chaos expansion). The coefficients of the polynomial chaos expansion are found through stochastic collocation, which only requires a few performance function evaluations. After determining the order of the polynomial and its coefficients, first order methods calculates the reliability index. To demonstrate the applicability of the suggested based reliability analysis, failure rates were used and the duration for the evaluated were set to be 360 days. Numerical result are provided on monthly basics. On the other hand, to achieve our goal, we proposed the 2-parameter modified Weibull distribution. The simulation was performed using Maple software. The evaluation for each subsystem was displayed in the result and analyses section. The conclusion, however, draws a broad conclusion about the study.

Cite: Anas Sani Maihulla, Michael Khoo Boon Chong, Ibrahim Yusuf  RELIABILITY ANALYSES OF AN INDUSTRIAL SYSTEM BASED ON HERMITE POLYNOMIAL AND 2-PARAMETER WEIBULL . Reliability: Theory & Applications. 2023, September 3(74): 642-648, DOI: https://doi.org/10.24412/1932-2321-2023-374-642-648

642-648

COMPLETELY RANDOMIZED DESIGN IN FUZZY OBSERVATIONS

Kirthik VairaMariappan A, Manigandan P

The real world is vague, unclear and full of ambiguity, and are inevitable. The classical statistics disregards the extreme, aberrant, uncertain values, and hence a new appropriate tool had to surface. The Analysis of Variance (ANOVA) method is used to compare the response variable's means between several groups that are specified by the factor variable. Another method of data analysis offered by ANOVA is one that is based on statistics and is experimental design-driven, or Design of Experiment (DOE). In DOE, there are single and two-factor experimental designs depending on, observing the effect of number of factor(s) on output variable as a primary interest. Among all the single factor experimental designs, Completely Randomized Design (CRD) is the simplest and flexible design. In this design, treatments are randomly allocated to the experimental units over the entire experimental material. Each treatment is repeated to increase the efficiency of the design. CRD is more appropriate to use when the data is homogenous. The objective that deals with the preparation and analysis of experiments is experimental design. The treatments are apportioned to the exploratory units at random in the fully randomized experimental design. When the observed data are fuzzy observations rather than precise numerical values, the CRD is expanded in this study. In this paper, an innovative Triangular Fuzzy Number (TFN) in the fuzzy Completely Randomized Design (FCRD) analysis statistical method for evaluating CRD model hypotheses on fuzzy data is presented. To convert the fuzzy totally randomized design model into two crisps CRD models using the suggested way, and then convert to lower and upper models are used in fuzzy hypothesis. Determine the fuzzy hypothesis for the fuzzy CRD model based on the hypotheses of the two crisp CRD models using the decision rules. The fuzzy test appears to be a competitive tool in circumstances with ambiguous data, particularly linguistic ambiguity because it is more adaptable than the conventional test of significance. This paper presents and illustrates a novel fuzzy triangular number-based approach to fuzzy CRD analysis. This paper also explores how flexible a CRD may be when handling uncertain elements. This study provides an example of a new method for fuzzy CRD analysis employing TFN.

Cite: Kirthik VairaMariappan A, Manigandan P COMPLETELY RANDOMIZED DESIGN IN FUZZY OBSERVATIONS . Reliability: Theory & Applications. 2023, September 3(74): 649-658, DOI: https://doi.org/10.24412/1932-2321-2023-374-649-658

649-658

A COLD STANDBY SYSTEM WITH IMPERFECT SWITCH AND PREVENTIVE MAINTENANCE: A STOCHASTIC STUDY

R.K. Bhardwaj, Purnima Sonkar

The aim of this paper is to develop a probabilistic model for a cold standby system that consists of an imperfect switching device and a servicing facility. The model aims to address the issue of unexpected random failures of the switch by implementing preventive maintenance measures. The system has two identical units. It starts with one unit in active operation and another unit in cold standby mode. In standby mode the unit remains in perfect state. No failure is allowed in standby mode. As the operating unit fails, the standby unit needs to be switched into operation, to keep the system working. A servicing facility is present in the system to perform necessary servicing related tasks. The servicing facility referred to as the server, also takes care of all necessary remedial activities like preventive maintenance and repairs. The switch used as switching mechanism to place the standby unit into operation may found imperfect when needed. Similarly, the server too can fail while doing job. A preventive maintenance scheme is used for the switch whereas treatment is given to server. The method of semi-Markov process and regenerative point technique is used for model developing and solving, respectively. The expressions are derived to determine different system performance measures such as mean time to system failure, availability, busy period, expected number of preventive maintenances and the profit. The distributions of random time elapsed in repairs, replacements, preventive maintenances and treatments are general. This study highlights the usefulness of switch’s preventive maintenance in long run. To study the asymptotic behavior of the system model, all the expressions for system performance measures are obtained in steady state. A simulation study is conducted using a presumed data set and assuming a Weibull probability distribution. The numerical results are shown in tabular form. The simulation results serve to highlight the significance of preventive maintenance for the switch. The findings of the paper can provide guidelines to the people engaged in designing, framing and implementing standby switching systems in real applications.

Cite: R.K. Bhardwaj, Purnima Sonkar  A COLD STANDBY SYSTEM WITH IMPERFECT SWITCH AND PREVENTIVE MAINTENANCE: A STOCHASTIC STUDY . Reliability: Theory & Applications. 2023, September 3(74): 659-670, DOI: https://doi.org/10.24412/1932-2321-2023-374-659-670

659-670

MOVING BLOCK BOOTSTRAP METHOD WITH BETTER ELEMENTS REPRESENTATION FOR UNIVARIATE TIME SERIES DATA

Kayode Ayinde, James Daniel, Akinola Adepetun, Olusegun S. Ewemooje

Bootstrap method was initially used to determine accuracy measures for sample estimates of independent and identical distributions (i.i.d.). In order to apply bootstrap method to time-dependent data, blocking technique is introduced to preserve serial correlation of the original time series data. In the past, resampling techniques for time-dependent data were implemented using Non-overlapping Block Bootstrap (NBB) method but its dichotomous block arrangement restricts the number of blocks. As a result, improvement becomes necessary. Although the Moving Block Bootstrap (MBB) method improves upon NBB with regard to many more blocks, it introduces an uneven representation of the time series elements which eventually influences its accuracy. In this paper, an innovative method called Moving Block Bootstrap Method with better element Representation (MBBR) is developed to ensure that the time series elements within the block are better represented with minimum number of elements. To compare MBB and MBBR, simulated studies were carried out on some set time series data following each classes of Autoregressive Moving Average (ARMA) model with different parameters, sample sizes and standard deviation using Root Mean Squared Error (RMSE) and Mean Absolute Error (MAE). Results show that by improving the representation of time series data in the blocking arrangement, the accuracy of the proposed method (MBBR) consistently outperforms the existing one (MBB) and thus, provides more efficient estimates of the dependent variable.

Cite: Kayode Ayinde, James Daniel, Akinola Adepetun, Olusegun S. Ewemooje MOVING BLOCK BOOTSTRAP METHOD WITH BETTER ELEMENTS REPRESENTATION FOR UNIVARIATE TIME SERIES DATA . Reliability: Theory & Applications. 2023, September 3(74): 671-688, DOI: https://doi.org/10.24412/1932-2321-2023-374-671-688

671-688

RELIABILITY AND SENSITIVITY ANALYSIS OF A SYSTEM WITH CONDITIONAL AND EXTENDED WARRANTY

Kajal Sachdeva, Gulshan Taneja, Amit Manocha

System reliability and maintenance cost are the most crucial and decisive factors influencing consumers’ buying behaviour. The manufacturer attempts to address the consumer concern by offering a warranty in accordance with the reliability of the system and maintenance costs. This study aims to examine the stochastic behaviour of a single unit system operating in three different time frames, namely normal, extended and expired warranty time duration. The system user can prolong the normal warranty period at an extra cost. This prolonged warranty is termed an ‘Extended Warranty’. However, the manufacturer provides a warranty on a system with certain conditions. If the failures are covered under the warranty conditions, the repair/replacement is done free of cost; otherwise, all charges are borne by the system user. Markov and regenerative processes are used to derive the system’s reliability and other performability measures. Time distributions used in the study are taken as arbitrary. The profit function for the manufacturer and the user is formulated and analysed. Sensitivity analysis for system availabilities in different time zones and profit functions is also done. Numerical examples for exponential, Weibull and Erlang time distributions are discussed to illustrate the derived measures.

Cite: Kajal Sachdeva, Gulshan Taneja, Amit Manocha RELIABILITY AND SENSITIVITY ANALYSIS OF A SYSTEM WITH CONDITIONAL AND EXTENDED WARRANTY. Reliability: Theory & Applications. 2023, September 3(74): 689-707, DOI: https://doi.org/10.24412/1932-2321-2023-374-689-707

689-707

ANALYZING LOAD SHARING SYSTEM RELIABILITY: A MODIFIED WEIBULL DISTRIBUTION APPROACH

Santosh S. Sutar, Chandrakant G. Gardi, Somnath D. Pawar

Load sharing systems have the ability to distribute the workload among its components. For analyzing a two component parallel load sharing system, the accelerated failure time (AFT) based model with component lifetimes as linear failure rate distribution have been recently proposed in the literature. In the present study, the component lifetimes are assumed to follow a modified Weibull distribution, which is the generalization of many standard lifetime distributions such as exponential, Weibull, Rayleigh, and linear failure rate. The use of modified Weibull distribution leads to a new family of bivariate distributions for ordered random variables. We have also looked into the associated inference techniques for the proposed model. In order to evaluate the effectiveness of the suggested estimating approaches, we conducted a simulation study. In order to provide a practical application and better understanding, we carefully examine a dataset related to motors.

Cite: Santosh S. Sutar, Chandrakant G. Gardi, Somnath D. Pawar ANALYZING LOAD SHARING SYSTEM RELIABILITY: A MODIFIED WEIBULL DISTRIBUTION APPROACH. Reliability: Theory & Applications. 2023, September 3(74): 708-724, DOI: https://doi.org/10.24412/1932-2321-2023-374-708-724

708-724

RANDOMIZED BLOCK DESIGN IN FUZZY ENVIRONMENTS

A. Kirthik VairaMariappan, Manigandan Palanisamy

On the basis of the statistics, ANOVA also provides a method of data analysis that is motivated by consideration of the experimental design or Design of Experiment (DOE). Experimental design plays an essential part in statistical analysis and data interpretation. One factor of criteria forms the basis of a one-way classification. Two factors or two criteria form the basis of two-way classification. Innovations and creations require experimentation as their foundation. Replication, randomization, and local control are the three fundamental tenets of experimental designs, which are used to determine the cause and effect of interactions. The error of any treatment can be isolated and any number of treatments may be omitted from the analysis without complicating it. The data provided in this study are vague and need an extended version of the RBD to investigate these vague observations. The simplest of all designs based on the principles of randomization and replication are Completely Randomized Designs (CRD). When the experimental materials aren't uniform in some circumstances. Divide the experimental region into smaller, homogeneous blocks in RBD. The treatment is applied at random to each block, and each block is reproduced. Since uncertainty is a common feature of all real-world issues and denotes fuzziness and unpredictability, Randomized Block Design has long been widely used in the agricultural and industrial sectors. It is therefore impossible to avoid using statistical RBD analysis with fuzzy observations. The objective of this study was to develop the problem of a Randomized Block Design (RBD) test for Triangular Fuzzy Numbers (TFN) is discussed in this paper. However, in a scenario that is actual, the underlying relationship is not a clear-cut function of a particular form; it has some ambiguity or imprecision. The estimated numbers are very similar to the actual ones. This approach may generally be used for any real-time triangle fuzzy number calculation. In this proposed methodology, it is obvious that if the value of the observed fuzzy test statistics is similar to real numbers in the testing crisp hypotheses, then fuzzy RBD is very sensitive for making the determinations as to whether to accept or reject the fuzzy null hypotheses and also debates the application of the method for example.

Cite: A. Kirthik VairaMariappan, Manigandan Palanisamy  RANDOMIZED BLOCK DESIGN IN FUZZY ENVIRONMENTS . Reliability: Theory & Applications. 2023, September 3(74): 725-733, DOI: https://doi.org/10.24412/1932-2321-2023-374-725-733

725-733

A NEW CLASS OF SIN-G FAMILY OF DISTRIBUTIONS WITH APPLICATIONS TO MEDICAL DATA

Laxmi Prasad Sapkota, Pankaj Kumar And Vijay Kumar

This article is dedicated to the study of the new class of distributions and one of its particular members. Based on the ratio of CDF G(x) and 1+G(x) of the baseline distribution, we have developed the new trigonometric family of distributions by transforming the sine function, and we named it the new class sin-G (NCS-G) family of distributions. The general properties of the suggested family of distributions are provided. Using the inverted Weibull distribution as a baseline distribution, we have introduced a member of the suggested family having a reverse-j or increasing, or inverted bathtub-shaped hazard function. Some statistical properties of this NCS-IW distribution are explored. The associated parameters of the new distribution are estimated through the MLE method. To assess the estimation procedure, we conducted a Monte Carlo simulation and found that even for small samples, biases and mean square errors decreased as the size of the sample increased. Two real medical data sets are considered for the application of the NCS-IW distribution. Using some criteria for model selection and goodness of fit test statistics, we empirically proved that the suggested model performs better than six other existing models (most of which have more parameters).

Cite: Laxmi Prasad Sapkota, Pankaj Kumar And Vijay Kumar A NEW CLASS OF SIN-G FAMILY OF DISTRIBUTIONS WITH APPLICATIONS TO MEDICAL DATA. Reliability: Theory & Applications. 2023, September 3(74): 734-750, DOI: https://doi.org/10.24412/1932-2321-2023-374-734-750

734-750

STUDY OF THE FUNCTIONING OF A MULTI-COMPONENT AND MULTI-PHASE QUEUING SYSTEM ON THE EXAMPLE OF A VEHICLE REPAIR ENTERPRISE

M.D. Katsman, V.I. Matsiuk, V.K. Myronenko

The purpose of the work is to build, on the basis of multi-component and multi-phase models of queuing systems (QS), mathematical models of maintenance and repair of vehicles by repair enterprises to increase the efficiency of their use. Results. The article considers multi-component and multi-stage mathematical models of QSs with the distribution of the arrival flow simultaneously between the system components, which consist of a certain number of service channels and waiting places in the queue. The same service channels can have different performance depending on the type of customers which they serve. Customers go through several stages of service and waiting. Considered are service of customers without a lack of time to stay in the service channel and waiting and with a lack of such time. The service process in the QS of each component consists of several (ke) stages with the corresponding duration, the full-service period will be equal to the sum of such time intervals. Stage durations have certain probability distributions with appropriate parameters, then the total duration of the service process will have a generalized Erlang distribution with parameters of probability distributions of stages of order ke. The number of components and their parameters correspond to the similar characteristics of the production divisions of the repair enterprise. The study of the effectiveness of the repair enterprise operation as a multi-component and multi-stage QS consists in determining the probability of service and the probability of failure of QS components and the system as a whole, the number of service channels, the number of customers in components, the number of customers in component queues, the duration of maintenance of customers in components and the system, the duration of being customers in queues of components and QSs, duration of stay of requirements in QSs and duration of customer waiting in QS queues. The model is implemented using Any Logic University Researcher. The AnyLogic University Researcher development environment allowed to combine the principles of system dynamics with the paradigms of agent and discrete-event modeling. In addition, thanks to the built-in Java SE compiler, a library of ready-made solutions is available, including generators of random variables, which significantly expands the possibilities of developing and implementing experiments. In particular, experiments on optimization (relative to a defined criterion), sensitivity of the model, stability of the model, etc. are available.

Cite: M.D. Katsman, V.I. Matsiuk, V.K. Myronenko  STUDY OF THE FUNCTIONING OF A MULTI-COMPONENT AND MULTI-PHASE QUEUING SYSTEM ON THE EXAMPLE OF A VEHICLE REPAIR ENTERPRISE . Reliability: Theory & Applications. 2023, September 3(74): 751-767, DOI: https://doi.org/10.24412/1932-2321-2023-374-751-767

751-767

MATHEMATICAL MODELING OF AVERAGE WEIGHTED RENYI’S ENTROPY MEASURE

Savita, Rajeev Kumar

A weighted entropy measure of information is provided by a probabilistic experiment whose basic events are described by their objective probabilities and some qualitative (objective or subjective) weights. Weighted entropy has also been applied to equity the amount of information and degree of homogeneity related with a partition of data in classes. These measures have tremendous applications and are found to be quite helpful in many fields. In the present paper, a new weighted Renyi’s entropy measure is proposed for the discrete distributions when probabilities are unknown and weights are known. The various characteristics of the measure are investigated. The measure is also studied taking into a particular case. In the last, numerical computation and graphical analysis is also done. Based on the graphical analysis, it is concluded that the proposed measure varies with values of weights and is concave in nature. The developed weighted information measure is useful for the discrete distribution when probabilities are unknown and weights are known.

Cite: Savita, Rajeev Kumar  MATHEMATICAL MODELING OF AVERAGE WEIGHTED RENYI’S ENTROPY MEASURE . Reliability: Theory & Applications. 2023, September 3(74): 768-775, DOI: https://doi.org/10.24412/1932-2321-2023-374-768-775

768-775

REDUCTION IN WAITING TIME OF SINGLE SERVER MARKOVIAN QUEUING ENCOURAGED ARRIVAL MODEL

Ismailkhan Enayathulla Khan, Rajendran Paramasivam

There are several other methods for improving efficiency in a control chart. The use of a control chart alone is not advised. Other process improvement methods should always be used in addition to control charts. To trace the evolution of a process variable across time, use a control chart. The variable is applicable to all industries, including service, manufacturing, non-profit, and healthcare. It illustrates how a process variable changes over time and provides information on the kinds of variations that deal with ongoing improvement. Having a solid understanding of variation is necessary for effective control chart usage. Queuing models with constant or variable sizes are extensively used in the modeling of road and transport systems, sophisticated information and computer systems, and inventory replenishment systems. The control chart technique helps in tracking the performance of these queues, because of the single-server Markovian queue with encouraged arrival (SSMQEA model) the company which is running with fewer customers can increase the number of customers and hence the company finance level increase also this SSMQEA method will improve the points in share market. The major measurable performance characteristics of any queuing system are average queue length and average waiting time. Control limits are defined in this study for the M[X]/M/1 encouraged arrival queuing model where the batch size follows a geometric distribution. To highlight its uses, numerical observations are also included. Little' s law is also satisfied.

Cite: Ismailkhan Enayathulla Khan, Rajendran Paramasivam REDUCTION IN WAITING TIME OF SINGLE SERVER MARKOVIAN QUEUING ENCOURAGED ARRIVAL MODEL . Reliability: Theory & Applications. 2023, September 3(74): 776-784, DOI: https://doi.org/10.24412/1932-2321-2023-374-776-784

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THEORY AND APPLICATIONS OF THE ALPHA POWER TYPE II TOPP-LEONE- GENERATED FAMILY OF DISTRIBUTIONS

Jacob C. Ehiwario, John N. Igabari, Peter E. Ezimadu

This paper introduces a composition of two single parameter generalized family of distributions: the alpha power transform and type II Topp-Leone-G families of distributions. Some basic mathematical treatments of the family of distributions are studied. The parameter estimates of the proposed family of distributions are derived via maximum likelihood estimation method and a Monte Carlo simulation study was conducted to examine the asymptotic behaviour of the parameter estimates of sub-model belonging to the proposed family of distributions. To illustrate the applicability of the proposed family of distributions in real world data fittings, two data sets consisting of the daily recovery and mortality rates of Covid-19 patients in Nigeria, from May 1 to June 30, 2020, was employed. The APTIITLK distribution arising from the proposed family of distributions, alongside with some bounded non-nested distributions was used to fit the two data sets and results obtained from the analysis clearly revealed that the APTIITLK distribution outperformed all the non-nested distributions used in fitting the two data sets. Some informative graphical plots for goodness of fit test were investigated to further validate the flexibility of the APTIITLK distribution over the competing distributions.

Cite: Jacob C. Ehiwario, John N. Igabari, Peter E. Ezimadu THEORY AND APPLICATIONS OF THE ALPHA POWER TYPE II TOPP-LEONE- GENERATED FAMILY OF DISTRIBUTIONS . Reliability: Theory & Applications. 2023, September 3(74): 785-807, DOI: https://doi.org/10.24412/1932-2321-2023-374-785-807

785-807

NOVEL DISTRIBUTION FOR MODELING UNCENSORED AND CENSORED SURVIVAL TIME DATA AND REGRESSION MODEL

Adubisi O. D., Adubisi C. E.

This work proposes a new one-parameter model titled the type II Topp Leone half logistic (TIITLHL) model which is characterized by an increasing and decreasing hazard rate function quite dependent on the shape parameter. Some structural properties and basic functions used in reliability analysis are derived. Simulations are carried out for both uncensored and censored samples. The uncensored simulation results indicated that the estimators perform quite well in producing good parameter estimates at finite sample sizes. However, the Anderson Darling estimator (ADE) average estimate tend to the true parameter value faster than other methods with minimum bias. More so, simulation based on censored samples using different censoring proportions showed that the bias, MSE and MRE values decrease as the sample size increases for the different censoring proportions. Two uncensored and censored datasets from the medical and environmental sciences were analysed to show the relevance, flexibility and adaptability of the TIITLHL model, and the new model achieved the best performance when compared with six other competing lifetime models. In addition, the log-TIITLHL regression model constructed and compared with two existing models showed that this model will be a useful option in survival investigation.

Cite: Adubisi O. D., Adubisi C. E. NOVEL DISTRIBUTION FOR MODELING UNCENSORED AND CENSORED SURVIVAL TIME DATA AND REGRESSION MODEL. Reliability: Theory & Applications. 2023, September 3(74): 808-824, DOI: https://doi.org/10.24412/1932-2321-2023-374-808-824

808-824

MOVING AVERAGE AND DOUBLE MOVING AVERAGE CONTROL CHARTS FOR PROCESS VARIABILITY USING AUXILIARY INFORMATION

Vikas Ghute, Sarika Pawar

The memory type control charts based on auxiliary information have been introduced in the literature for improved monitoring of the process parameters for normally distributed process. In this paper, we design moving average and double moving average control charts based on auxiliary information for efficient monitoring the shifts in the process variability. Regression estimator of process variance in the form of auxiliary and study variables is considered to construct charting statistics for the proposed charts. The average run length (ARL) and standard deviation of run length (SDRL) performance of the proposed charts is investigated using simulation study and is compared with the originally proposed Shewhart control charts based on auxiliary information and without auxiliary information. The proposed auxiliary information based moving average and double moving average charts are found to be efficient for monitoring the process variance of normally distributed process. An illustrative example based on simulated data set is provided to show the implementation of the proposed charts in detecting shifts in the process standard deviation.

Cite: Vikas Ghute, Sarika Pawar  MOVING AVERAGE AND DOUBLE MOVING AVERAGE CONTROL CHARTS FOR PROCESS VARIABILITY USING AUXILIARY INFORMATION . Reliability: Theory & Applications. 2023, September 3(74): 925-840, DOI: https://doi.org/10.24412/1932-2321-2023-374-925-840

925-840

A NEW ZERO-INFLATED COUNT MODEL WITH APPLICATIONS IN MEDICAL SCIENCES

Zehra Skinder, Peer Bilal Ahmad, Na Elah

Inflated models are used whenever there are too many frequencies at a given count. In this regard, Poisson moment exponential distribution and a distribution to a point mass at zero are used to create a zeroinflated model namely Zero-Inflated Poisson Moment Exponential Distribution. Its distributional and reliability characteristics are investigated in some detail. A simulation exercise is undertaken to evaluate the effectiveness of the maximum likelihood estimators. The adaptability of the suggested distribution is demonstrated using three real datasets from various domains (e.g., vaccine adverse events, medical science data, epileptic seizure counts). The suggested distribution and the Poisson moment exponential distribution are distinguished by using the two different test procedures.

Cite: Zehra Skinder, Peer Bilal Ahmad, Na Elah A NEW ZERO-INFLATED COUNT MODEL WITH APPLICATIONS IN MEDICAL SCIENCES. Reliability: Theory & Applications. 2023, September 3(74): 841-855, DOI: https://doi.org/10.24412/1932-2321-2023-374-841-855

841-855