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On the TeSU-G family of distributions applied to life data analysis
Idzhar A. Lakibul, Bernadette F. Tubo Department of Mathematics and Statistics Mindanao State University -Iligan Institute of Technology Iligan City, Philippines idzhar.lakibul@g.msuiit.edu.ph, bernadette.tubo@g.msuiit.edu.ph
This paper derives distributions from the U-quadratic and the T-X family of distributions labeled as the T-extended Standard U-quadratic.G family of distributions or simply, TeSU-G family. In particular, the TeSU-Weibull distribution (TeSU-W) is explored with respect to some statistical properties such as its limiting distribution, moment, mean and variance and moment generating function. Also, the statistical properties of the TeSU-Exponential distribution (TeSU-E) which is a special case of the TeSU-W are also derived. The Weibull and Exponential distributions are mostly used in life data analysis because of its ability to adapt to different situations. Moreover, the formula for the median is derived via a proposed algorithm. Simulation study is conducted to verify the performance of the ML estimates of the TeSU-W distribution for varied sample sizes. Further, real life data analysis reveals that derived extended distribution can provide a better fit than several well-known distributions.
Keywords: U-quadratic distribution, T-X family of distributions, Weibull distribution
Cite: Idzhar A. Lakibul, Bernadette F. Tubo On the TeSU-G family of distributions applied to life data analysis. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-24-38 |
24-38 |
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EXPONENTIATED ADYA DISTRIBUTION: PROPERTIES AND APPLICATIONS
Rashid A. Ganaie, D. Vedavathi Saraja Department of Statistics, Annamalai University, Tamil nadu, India rashidau7745@gmail.com, sarajayoganand@gmail.com
Aafaq A. Rather Symbiosis Statistical Institute, Symbiosis International (Deemed University), Pune-411004, India
Mahfooz Alam Department of Statistics, Faculty of Science and Technology, Vishwakarma University, Pune, India
Aijaz Ahmad Department of Mathematics, Bhagwant University, Ajmer, India
Arif Muhammad Tali Department of Mathematics, Sharda University, Noida, India
Rifat Nisa Department of Statistics, Cluster University, Srinagar, Kashmir, India
Berihan R. Elemary Department of Statistics and Insurance, Faculty of Commerce, Damietta University-34511, Egypt
In this article, we introduce a new generalization of Adya distribution known as Exponentiated Adya distribution. We have also derived and discussed its different statistical properties. The Exponentiated Adya distribution has two parameters (scale and shape). The different structural properties of the proposed distribution have been obtained. The maximum likelihood estimation technique is also used for estimating the parameters of the proposed distribution. Finally, a real lifetime data set is used for examining the superiority of the proposed distribution.
Keywords: Exponentiated distribution, Adya distribution, Order statistics, Entropies, Reliability analysis, Maximum likelihood Estimation.
Cite: Rashid A. Ganaie, Aafaq A. Rather, D. Vedavathi Saraja, Mahfooz Alam, Aijaz Ahmad, Arif Muhammad Tali, Rifat Nisa, Berihan R. Elemary EXPONENTIATED ADYA DISTRIBUTION: PROPERTIES AND APPLICATIONS. Reliability: Theory & Applications. 2023, June 2(73): 39-49. https://doi.org/10.24412/1932-2321-2023-273-39-49 |
39-49 |
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A REVIEW ON QUANTILE FUNCTIONS, INCOME DISTRIBUTIONS, AND INCOME INEQUALITY MEASURES
Ashlin Varkey, Haritha N Haridas Farook College (Autonomous), Department of Statistics, Kozhikode, 673632, Kerala, India. ashlinvarkey@gmail.com, haritasuhas@gmail.com
The modeling of income data has originated a century ago with the work of Vilfredo Pareto. Since then several authors have added immense literature about income distributions and income inequality measures. In the present paper, we have pointed out some recent works in income distributions and income inequality measures. Recently the potential of the quantile function has been discussed in parallel with the distribution function for modeling reliability and income data. So we have also included some quantile functions existing in the literature and their potentiality to model income data in the review. We derived the Lorenz curve, Gini index, Pietra index, Bonferroni index, Bonferroni curve, and Zenga curve for six distributions and checked the model adequacy of three distributions using real income data.
Keywords: Income distribution, Income Inequality measures, Quantile based reliability models, Quantile function, Distribution function.
Cite: Ashlin Varkey, Haritha N Haridas A REVIEW ON QUANTILE FUNCTIONS, INCOME DISTRIBUTIONS, AND INCOME INEQUALITY MEASURES. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-50-62 |
50-62 |
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THE EXTENDED ERLANG TRUNCATED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATION TO STATISTICAL PREDICTION PROBLEM
Imtiyaz A. Shah Department of Community Medicine (Bio Statistics), Sher-I-Kashmir Institute of Medical Sciences, Srinagar (J&K) India
The Erlang Truncated (ETE) distribution is modified and the new lifetime distribution is called the Extended Erlang Truncated Exponential (EETE) distribution. Some statistical and reliability properties of the new distribution functions have been characterized based on two non-adjacent generalized and dual generalized order statistics. Moreover, we show that these characterization properties provide a beneficial strategy to predict future events, which are based on past or current events and on an arbitrary distribution function. A characterization in statistics is a specific distributional property of a statistic that uniquely identify related parametric family of distributions. In statistical applications, the researchers usually want to verify whether the data that they are dealing with belong to a certain family of DFs. Therefore, the researchers have to rely on a characterization of the assumed distribution and check if the corresponding conditions are satisfied.
Keywords: Generalized order statistics, Dual generalized order statistics, Dilation Characterization of distributions, Point prediction
Cite: Imtiyaz A. Shah THE EXTENDED ERLANG TRUNCATED EXPONENTIAL DISTRIBUTION: PROPERTIES AND APPLICATION TO STATISTICAL PREDICTION PROBLEM. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-63-72 |
63-72 |
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INTERVAL PATTERN RECOGNITION IN RELATION TO INFORMATION ABOUT THE TREATMENT OF COVID 19 IN PATIENTS WITH BLOOD DISEASES
G.Tsitsiashvili Russia, 690041, Vladivostok, Radio street 7, Institute for Applied Mathematics Far Eastern Branch of Russian Academy Sciences
V. Nevzorova, A.Talko Russia, 690002, Vladivostok, 2 Ostryakova Ave., Pacific State Medical University, nevzorova@inbox.ru, talkang92@mail.ru
M. Osipova Russia, 690002, Vladivostok, FEFU Campus 10 Ajax Bay, Russky Island, Far Eastern Federal University, Russia, 690041, Vladivostok, Radio street 7, Institute for Applied Mathematics Far Eastern Branch of Russian Academy Sciences
Since the problem of coronavirus infection, especially in vulnerable groups, remains relevant in the healthcare system, it is necessary to recognize the risk of fatal events during the treatment of patients from COVID-19. Patients with hemoblastosis are exposed to a more severe course of coronavirus infection than the general population, as well as an increased risk of fatal events. The aim of our study was to determine the effect of signs on the risk outcomes of fatal events among patients with diseases of the blood system, both of a tumor and non-tumor nature. According to the values of the signs, it was necessary to recognize survivors and those who died during treatment from COVID-19. The method of interval pattern recognition was chosen due to the presence of big data, it is described in detail in the article. The patients were broken down by gender and age. The signs that significantly affect the forecast according to the developed algorithm were identified. This is especially evident in groups of men and women with malignant diseases of the blood system over the age of 60 years. In these groups, a positive outcome of treatment is detected due to the presence of a large set of uninformative signs. This phenomenon is closely related to the tasks of technical gerontology.
Keywords: interval pattern recognition, big data, informative signs, technical gerontology, coronavirus infection, hemoblastosis, tumor.
Cite: G.Tsitsiashvili, V. Nevzorova, A.Talko, M. Osipova INTERVAL PATTERN RECOGNITION IN RELATION TO INFORMATION ABOUT THE TREATMENT OF COVID 19 IN PATIENTS WITH BLOOD DISEASES. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-73-78 |
73-78 |
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STUDY OF OPERATING MODES OF SMALL HPSS' HYDROELECTRIC UNITS EQUIPPED WITH SYNCHRONOUS GENERATOR
L.H. Hasanova, H.S. Aliyev Azerbaijan Technical University, Baku, Azerbaijan AZ1073, 25 Hussein Javid pros. gasanovalg@mail.ru, hikmetaliyev@aztu.edu.az
M.M. Musayev Azerbaijan Scientific-Research and Designed-Prospecting Institute of Energetics Baku, Azerbaijan AZ1012, Aven. H.Zardabi-94
A universal analytical expression is obtained for the power of hydraulic turbines of small hydropower plants such as Francis, Pelton and Kaplan with fixed blades as a function of water flow. This expression allows us to predict the generation of active power of each of the turbines, depending on the adjusted water flow rate, which varies in the seasonal, monthly and daily periods of the year. It also allows you to solve the inverse problem, when it is necessary, depending on the load schedule dictated by the electrical system to which these small hydroelectric power stations are connected, to regulate the amount of water flow by changing the opening angles of the guiding devices of the hydraulic turbines. Studies on the proposed mathematical model containing a synchronous generator with electromagnetic excitation coupled to a Francis hydraulic turbine with a 60% change in water flow from q=1 (r.u) to q=0.4 (r.u). The value of the required active power of a small hydroelectric power station, i.e. power output of the generator will jam (either by the dispatcher, or by the value of the load schedule), i.e. it is an input value, and as the output value of the controller is the opening angle of the guiding apparatus of the turbine.
Keywords: small hydropower plants, Francis turbine, Pelton turbine, axial turbines, synchronous generator with electromagnetic excitation, electrical grid.
Cite: L.H. Hasanova, H.S. Aliyev, M.M. Musayev STUDY OF OPERATING MODES OF SMALL HPSS' HYDROELECTRIC UNITS EQUIPPED WITH SYNCHRONOUS GENERATOR. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-79-86 |
79-86 |
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A COMPOUND OF GAMMA AND SHANKER DISTRIBUTION
Mousumi Ray Department of Statistics, Assam University, Silchar, India
Rama Shanker Department of Statistics, Assam University, Silchar, India
This paper considers a new lifetime distribution called Gamma-Shanker distribution which is a compound of Gamma and Shanker distribution. Many important properties of the suggested distribution including its shape, Inverse moments, hazard rate function, reversed hazard rate function, quantile function and stress-strength reliability have been discussed. The estimation of its parameters has been discussed using maximum likelihood estimation. Goodness of fit of the proposed distribution has been explained with two examples of real lifetime data from biomedical sciences and it shows that the proposed distribution gives much closure fit over the considered distributions
Keywords: Lifetime distribution, Statistical Properties, Stress-strength reliability, Maximum Likelihood estimation, Goodness of fit.
Cite: Mousumi Ray, Rama Shanker A COMPOUND OF GAMMA AND SHANKER DISTRIBUTION. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-87-99 |
87-99 |
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DIFFERENT ESTIMATION METHODS FOR TOPP-LEONE-(A) MODEL: INFERENCE AND APPLICATIONS TO COMPLETE AND CENSORED DATASETS
Adubisi O. D. Department of Mathematics and Statistics, Federal University Wukari, Nigeria
Adubisi C. E. Department of Physics, University of Ilorin, Nigeria.
This work proposes a new two-parameter model, titled Topp-Leone (A) model. The main benefit of the new model is that it has an inverted bathtub shaped curve, increasing and decreasing hazard rate function quite dependent on the shape parameter. Its structural properties including the ordinary moments, quantiles, probability weighted moment, median, entropy and order statistics are derived. More so, the survival, failure rate, reversed failure rate and cumulative failure rate functions are also derived. Six classical estimation methods are discussed for estimating the parameters of the new model. Monte Carlo experiments and real datasets analyses are conducted to examine the classical estimators performance of this model. Finally, the usefulness of the Topp-Leone (A) model demonstrated with different applications to complete and type-II right censored data proves its more flexible when compared to well-known models in statistical literature.
Keywords: (A)-model, Censoring, Estimation methods, Simulation, Topp-Leone-G class
Cite: Adubisi O. D., Adubisi C. E. DIFFERENT ESTIMATION METHODS FOR TOPP-LEONE-(A) MODEL: INFERENCE AND APPLICATIONS TO COMPLETE AND CENSORED DATASETS. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-100-117 |
100-117 |
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RELIABILITY AND AVAILABILITY ANALYSIS OF AN 8-STEP AUTO UNIT MANUFACTURING PROCESS HAVING A FAULT IN MAINTENANCE
Surabhi Sengar G. B. Pant University of Agriculture and Technology, Pantnagar (India)
Human plays a vital role in the manufacturing process of a product during the planning, design, assembly, production, and maintenance phase. This paper presents a systematic method of determining the reliability and availability of an 8-step auto unit manufacturing system taking into consideration the case of occurring human error during maintenance. The whole process involves eight major units as Combustion engine, power train unit, fuel feed unit, fuel injection unit, drain or exhaust unit, engine cooling unit, brake unit, and body frame. With the failure of any of these units, the whole process can fail. Also, a constant failure rate and a general repair time are taken into the consideration for each operative unit that makes up the process. The integral differential equations were generated based on Markov modeling of the process and solution derived by considering repair time distribution using the Laplace transform. Calculations of different reliability aspects like process availability, mean time to failure steady-state nature, and profit analysis are done using supplementary variable technique and copula methodology.
Keywords: Reliability, Availability, Failure probability, Supplementary variable technique, Markov model, Human error.
Cite: Surabhi Sengar RELIABILITY AND AVAILABILITY ANALYSIS OF AN 8-STEP AUTO UNIT MANUFACTURING PROCESS HAVING A FAULT IN MAINTENANCE. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-118-128 |
118-128 |
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ESTIMATION OF A PARAMETER OF FARLIE-GUMBEL-MORGENSTERN BIVARIATE BILAL DISTRIBUTION BY RANKED SET SAMPLING
M. R. Irshad Cochin University of Science and Technology, Kochi-22, Kerala.
R. Maya University College, Trivandrum-695 034.
A.I. Al-Omari Yarmouk University, Irbid 21163, Jordan.
Ahmad A. Hanandeh Yarmouk University, Irbid 21163, Jordan.
S. P. Arun University Library, Research Centre, University of Kerala, Trivandrum-695 034
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 defned by ordering the marginal observations on an auxiliary variable W, when (W, Z) follows a FGMBB distribution. When the dependence parameter . is known, we have proposed the following estimators, viz., an unbiased estimator based on the StokeÒs ranked set sample and the best linear unbiased estimator based on the StokeÒs ranked set sample for the scale parameter of the variable of primary interest. The effciency comparison of the proposed estimators with respect to the maximum likelihood estimator have been carried out.
Keywords: Farlie-Gumbel-Morgenstern bivariate Bilal distribution, Concomitants of order statis≠tics, Ranked set sampling, Best linear unbiased estimator
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, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-129-140 |
129-140 |
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PROCESS MODELING AND NUMERICAL INVESTIGATION OF VENEER CUTTING SYSTEM OF A PLYWOOD PLANT WITH STOCHASTIC APPROACH
Dr. Subhash Malik, Dr. Narendra Kumar, Er. Sudhir Kumar Maharishi Markandeshwar University, Mullana, India, Technology Education & Research Integrated Institutions, Kurukshetra, India subhashmalik604@gmail.com, narendraip005@gmail.com, sudhirtamak@gmail.com
Present paper covers performance modelling and performability evaluation of a veneer-cutting system of plywood manufacturing industry. The performability is evaluated as a function of availability. In this system the different subsystems are connected in hybrid mode. Markovian Approach was used for developing the process modeling of the subsystems and to evaluate the performability of said system. MATLAB software was used to perform the numerical computations as well as simulation of results. The current work examines the impact of varied failure rates and repair rates on the long-term availability of the system. A Particle Swarm Optimization (PSO) based technique was used to optimize the results. A Decision Support System (DSS), which can be helpful for making strategic decisions on financial investments in managing the maintenance priorities, spare part management, and human resource requirements, among other things, has been recommended based on the numerical investigation..
Keywords: Availability, DSS, Maintenance, Markov Chain, PSO, RAM Tools
Cite: Subhash Malik, Narendra Kumar, Er. Sudhir Kumar PROCESS MODELING AND NUMERICAL INVESTIGATION OF VENEER CUTTING SYSTEM OF A PLYWOOD PLANT WITH STOCHASTIC APPROACH. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-141-153 |
141-153 |
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A NEW CONTROL CHART FOR PROCESS DISPERSION BASED ON RANKED SET SAMPLING
Chandrakant Gardi, Vikas Ghute Department of Statistics Punyashlok Ahilyadevi Holkar Solapur University, Solapur (MS), India chandrakant.gardi@gmail.com, vbghute_stats@rediffmail.com
In this paper, we propose a new control chart based on Downton's estimator (D) for monitoring the process dispersion using ranked set sampling design and runs rules. The performance of the proposed control chart is compared with the originally proposed D chart based on simple random sampling method when underlying process distribution is normal and non-normal. The average run length is used to evaluate the performance of the proposed control chart. It is observed that the proposed control chart is efficient in detecting shifts in process dispersion as compared with the chart using simple random sampling method. The performance of the proposed chart is further investigated using runs rules. The efficiency of the designed runs rules RSS-D chart is compared with its existing counterparts and is found to be superior.
Keywords: Control chart, Average run length, Process dispersion, Ranked set sampling, Runs rules, Downton estimator.
Cite: Chandrakant Gardi, Vikas Ghute A NEW CONTROL CHART FOR PROCESS DISPERSION BASED ON RANKED SET SAMPLING. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-154-166 |
154-166 |
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MODELING THE RELIABILITY OF TRANSPORT UNDER EXTREME CONDITIONS OF OPERATION AS A QUEUING SYSTEM WITH PRIORITIES
M.D. Katsman The Joint-Stock Company of Railway Transport of Ukraine "Ukrzaliznytsia", Kyiv, Ukraine
V.I. Matsiuk National University of Life and Environmental Sciences of Ukraine, Kyiv, Ukraine
V.K. Myronenko State University of infrastructure and technologies, Kyiv, Ukraine
The article presents a simulation model of a queuing system (QS) with a queue and relative priority, which can be used to manage the reliability of transport systems under resource constraints. The developed simulation model combines agent and discrete-event simulation principles and allows studying queuing systems in terms of establishing regularities: probabilities (service, failure, push≠out), time delays (waiting in a queue, under service), queue sizes, order of queue formation upon arrival of consumers of different priority. As a result of the research, dependencies were obtained for the probability of servicing higher priority consumers depending on the intensities of their arrival and service; probabilities of servicing lower priority consumers depending on the intensity of service and servicing of higher priority consumers; the probability of "pushing out" lower priority consumers from the QS by higher priority consumers depending on service intensities and the arrival of high priority consumers.
Keywords: transport system, agent modeling, simulation modeling, queuing systems, absolute priority, arrival and service intensity, service and push-out probabilities, consumer service probabilities
Cite: M.D. Katsman, V.I. Matsiuk, V.K. Myronenko MODELING THE RELIABILITY OF TRANSPORT UNDER EXTREME CONDITIONS OF OPERATION AS A QUEUING SYSTEM WITH PRIORITIES. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-167-179 |
167-179 |
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SINGLE SAMPLING PLANS FOR VARIABLE INSPECTION BASED ON BIRNBAUM - SAUNDERS DISTRIBUTION
Saranya C R Assistant Professor, Department of Statistics Mar Ivanios College, Thiruvananthapuram 695 015, INDIA
Vijayaraghavan R Professor & Head, Department of Statistics Bharathiar University, Coimbatore 641 046, INDIA
Sathya Narayana Sharma K Assistant Professor, Department of Mathematics Vellore Institute of Technology, Vellore 632 014, INDIA
Sampling inspection by the method of variables is a well-known category of product control in which the discretion of acceptance or rejection is made hinge on some specific rule, which is framed according to the measurement of a quality characteristic under study. In this scenario, the quality feature under study is considered a continuous random variable that can be demonstrated using any continuous type statistical distribution. Birnbaum - Saunders distribution is a continuous probability distribution, which is having numerous applications in various fields. Application of Birnbaum - Saunders distribution is considered in this paper for establishing acceptance sampling inspection plans for variables based on the examination of units from a single sample. Numerical illustrations are given to demonstrate the application of proposed sampling plan. In addition, the results of numerical illustrations are explained with the help of simulated data.
Keywords: Sampling inspection plans, variable sampling, Birnbaum -Saunders distribution, non≠normality, skewness.
Cite: Saranya C R , Vijayaraghavan R, Sathya Narayana Sharma K SINGLE SAMPLING PLANS FOR VARIABLE INSPECTION BASED ON BIRNBAUM Ö SAUNDERS DISTRIBUTION. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-180-190 |
180-190 |
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OPTIMAL SPARE-SWITCHING TIMES IN SERIES SYSTEMS UNDER A GENERAL FRAMEWORK
Hamideh Jeddi Department of Statistics, Ferdowsi University of Mashhad, Iran
Mahdi Doostparast Department of Statistics, Ferdowsi University of Mashhad, Iran
Spares are commonly used to improve system performances. They are allocated to original components during system missions. The optimal allocations depend on system confgurations and lifetimes of components and spares. Various methods for fnding optimal allocations have been proposed in the literature. For sake of brevity, lifetimes of components are commonly assumed to be independent. This paper deals with series systems, a common confguration, under a general setting, i.e. component lifetimes are dependent and heterogeneous. Moreover, the spare is also allowed to switch among original components to impose more fexibility for spare managements. This allowance occurred usually in network servers and electrical generators which manage by a dispatching center. Explicit expressions for system reliability functions are derived in detail. Since system lifetimes are random phenomena, stochastic orders are utilized for comparison purposes. Various illustrative examples are also given.
Keywords: Allocation; Reliability; Stochastic orders; Redundancy; Switching.
Cite: Hamideh Jeddi, Mahdi Doostparast OPTIMAL SPARE-SWITCHING TIMES IN SERIES SYSTEMS UNDER A GENERAL FRAMEWORK. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-191-199 |
191-199 |
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DESIGNING OF ACCEPTANCE SAMPLING PLAN BASED ON PERCENTILES FOR TOPP-LEONE GOMPERTZ DISTRIBUTION
SJayalakshmi Assistant Professor, Department of Statistics, Bharathiar University Coimbatore -641 046
Aleesha A Research Scholar, Department of Statistics, Bharathiar University Coimbatore -641 046
Acceptance sampling is a statistical technique used to inspect the quality of a batch of products. An acceptance sampling plan under which sampling inspection is performed by conducting life test upon the sampled products is termed as reliability sampling plan. In this paper, a single acceptance sampling plan based on percentile is presented for Topp-Leone Gompertz (TL-G) distribution when the life test is truncated at a pre-specified time. The minimum sample size necessary to ensure the specified life percentile is obtained under a given consumerÑs risk. The operating characteristic values (and curves) of the sampling plans as well as the producerÒs risk are presented.
Keywords: Acceptance sampling plan, Percentiles, Topp-Leone Gompertz (TL-G) distribution, Operating characteristic values, ProducerÑs risk, Minimum sample size
Cite: SJayalakshmi, Aleesha A DESIGNING OF ACCEPTANCE SAMPLING PLAN BASED ON PERCENTILES FOR TOPP-LEONE GOMPERTZ DISTRIBUTION. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-200-206 |
200-206 |
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BAYESIAN AND CLASSICAL ESTIMATIONS OF TRANSMUTED INVERSE GOMPERTZ DISTRIBUTION
T. M. Adegoke, K.O. Obisesan, O. M. Oladoja Department of Mathematics and Statistics, First Technical University, Ibadan, Nigeria. taiwo.adegoke@tech-u.edu.ng, obisesan.olalekan@tech-u.edu.ng, oladapo.oladoja@tech-u.edu.ng
G.K. Adegoke Department of Computer Science, Nasarawa State University,Keffi, Nigeria.
In this article, the use of the transmuted inverse Gompertz distribution in modeling lifetime data is investigated particularly in cases where standard probability distributions are not able to properly handle complex datasets. The quadratic rank transmutation map scheme is utilized to obtain the distribution. The study explores several characteristics of the transmuted inverse Gompertz model, including the estimation of parameters through classical approaches such as maximum likelihood estimation, least-squares estimation, Crammer-Von Misses estimation, and maximum product spacing estimation. Additionally, the Bayesian techniques is used under different loss functions, such as the Linex loss function, square error loss function, and general entropy loss function. The estimates obtained from both classical and Bayesian techniques are evaluated using simulation. To illustrate the potential benefits of the transmuted inverse Gompertz model, a dataset on the strength of aircraft window glass is employed. The results obtained from the application of the new distribution to the real-life dataset demonstrate that it yields superior fits in comparison to other well-known distributions. The studyÒs findings suggest that the transmuted inverse Gompertz model can provide a useful alternative for modeling lifetime data. The research offers valuable insights into the distributionÒs properties and estimation techniques, as well as its superiority over other commonly used distributions. The new model can contribute to the development of more accurate and efficient models for analyzing lifetime dataset. Overall, the study highlights the importance of exploring new statistical models and techniques to improve data analysis and decision-making
Keywords: Classical method, Bayesian method, Posterior distribution, Loss functions, Transmuted inverse Gompertz distribution.
Cite: T. M. Adegoke, K.O. Obisesan, O. M. Oladoja, G.K. Adegoke BAYESIAN AND CLASSICAL ESTIMATIONS OF TRANSMUTED INVERSE GOMPERTZ DISTRIBUTION. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-207-222 |
207-222 |
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ON THE BAYESIAN MODELING OF ROAD ACCIDENTS DUE TO VEHICLE TYPE IN OYO STATE NIGERIA
Oladapo M. Oladoja, K.O. Obisesan, Sururat A. Adebayo, T. M. Adegoke Department of Mathematics and Statistics, First Technical University, Ibadan, Nigeria . oladapo.oladoja@tech-u.edu.ng, obidairo@gmail.com, sururatadeboyin@gmail.com, taiwo.adegoke@tech-u.edu.ng
Transportation plays an important role in the day to day activities of human race. Road, rail, water and air are the four major forms of transportation in Nigeria. Road transportation is the most common means of movement in Oyo State and this has raise the likelihood of the occurrence of road traffic accident even posing a serious problem that needs serious attention. Road traffic accidents would Continually increase if tangible efforts are not made to tackle is problem. In Oyo state, the epicenter of the western Nigeria, road transportation is the most popular means of transportation. Of concern is the accidents recorded daily on the roads. This study takes into account the series of accidents caused on the state roads due to vehicle types. Seven vehicle types were considered due to the data available. Bayesian Model Averaging (BMA), a variable selection approach, was used to handle uncertainty in the model selection process. Several classical approach like time series have been used in analysing road accidents but few had explored the Bayesian approach via BMA route. A uniform model prior was used with a numeric g-prior to improve the predictive performance. The trend of accidents were observed for a period of 15 years from (2006 -2020). 78% of the models were visited and using the Posterior Inclusion Probability results (99.546%), it was seen that the accidents that occurred via private cars was the predominant. It is the most important in modeling vehicle type accidents in Oyo State Nigeria. Also, accidents for 2023 and 2024 were predicted using the posterior predictive distribution. It is imperative for concerned authorities (Federal Road Safety Corps amongst others) in the state to look into the issue of private car owners in the state.
Keywords: Bayesian Model Averaging, Posterior Inclusion Probability, Predictive, Trend, Transportation, Private Cars
Cite: Oladapo M. Oladoja, K.O. Obisesan, Sururat A. Adebayo, T. M. Adegoke ON THE BAYESIAN MODELING OF ROAD ACCIDENTS DUE TO VEHICLE TYPE IN OYO STATE NIGERIA. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-223-232 |
223-232 |
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THE APPLICATION OF QUEUEING THEORY FOR MAXIMIZING SYSTEM SIZE USING ENCOURAGED ARRIVAL
S. Immaculate, P. Rajendran Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, India -632014. immaculate.s@vit.ac.in, prajendran@vit.ac.in
Customers are frequently drawn in by lucrative deals and discounts offered by businesses. These interested customers are referred to as encouraged arrivals. The major goal of this study is to evaluate the performance of the automobile assembly line in order to decrease waiting time by coordinating the activities at each workstation using stopwatch time study approach. The novelty of this research is to convert poisson arrival to encouraged arrival with some discounts (like.,10%, 20%). The queuing problem is represented by the notation M/M/1:FCFS/./.in Kendall's notation. It is a single channel, multi-server service with infinite system capacity and an infinite number of calling population. Data concerning the system's encouraged arrival and service distribution were established. These data were used to calculate the system performance parameter. The finding of the study was used to predict the system's performance and effectiveness and to make logical recommendations for possible future improvements. According to the results, it is possible to conclude that increasing the level of automation reduces part waiting time, decreasing the cost of waiting. When compared to the poisson arrival system, the size of the Markovian encouraged arrival queuing system is in creased as shown in the table. LittleÒs lawis verified that systemsize and queue size is same as in length. Little's law is used to predicts lead time based on production rate and work-in≠process. Here it is verified as shown in table.
Keywords: Encouraged arrival, Assembly Line, Queuing Analysis, Stopwatch time study, Steady state Solution.
Cite: S. Immaculate, P. Rajendran THE APPLICATION OF QUEUEING THEORY FOR MAXIMIZING SYSTEM SIZE USING ENCOURAGED ARRIVAL. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-233-243 |
233-243 |
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RELIABILITY ANALYSIS OF THIN -WALLED PRESSURE VESSELS USING ADVANCED FIRST ORDER SECOND MOMENT (AFOSM) METHOD
K. Sunitha, T. Sumathi Uma Maheshwari, M. Tirumala Devi Department of Mathematics, Kakatiya University, Warangal, Telangana, India-506009 kadiresunitha79@gmail.com, tsumathiuma@gmail.com, oramdevi@yahoo.com
Pressure vessels are highly used in commercial purposes and industries such as boiling, softening and hot water storing tanks. Pressure vessels are subjected to its internal and external pressure. In this paper, thin-walled pressure vessels are taken for analysis. Pressure, radius, thickness and strength of the material are considered as random variables. The random variables follow normal distribution. The reliability index of the pressure vessel made with different materials such as 6061 aluminum alloy and SA 516 70 stainless steel has been found. Reliability analysis has been done for the pressure vessel by using AFOSM with MATLAB. It is observed that strength of the materials influences more on reliability of the vessels.
Keywords: Thin-walled cylinder, reliability, stress, strength, normal distribution, pressure, thickness, inner radius of cylinder, mean, variance.
Cite: K. Sunitha, T. Sumathi Uma Maheshwari, M. Tirumala Devi RELIABILITY ANALYSIS OF THIN -WALLED PRESSURE VESSELS USING ADVANCED FIRST ORDER SECOND MOMENT (AFOSM) METHOD. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-244-252 |
244-252 |
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WEIGHTED INTERVENED EXPONENTIAL DISTRIBUTION AS A LIFETIME DISTRIBUTION
Vilayat Ali Bhat, Sudesh Pundir Department of Statistics, Pondicherry University, Kalapet, Puducherry-605014, INDIA vilayat.stat@gmail.com, sudeshpundir19@gmail.com
This study proposes and investigates the weighted intervened exponential distribution, which is demonstrated as a generalized extension of the intervened exponential distribution. The form of the weighted intervened exponential distribution is obtained by considering a specifc non-negative weighted function. The probability density function and cumulative density function of the proposed model are given, and its generalized form of reliability function and the hazard rate function is also derived. By choosing a different set of parametric values, the graphical demonstrations of the probability density function of weighted intervened exponential distribution are given where it acquires different curve shapes. The weighted intervened exponential distribution density function is then further studied in the limited form as a special case called the length-biased intervened exponential distribution. Along with the distribution of order statistics, stochastic ordering, stress-strength reliability, and entropy measure, several distributional and reliability aspects of the length-biased intervened exponential distribution are derived. For estimating the unidentifed parameters of the length-biased variant, the most suggested approach known as the maximum likelihood estimation technique is implemented. To explore the behavior of the parameter estimates for various sample sizes, a sample data generation technique is required to carry out the process. Since the quantile function of the length biased intervened exponential distribution is not in closed form. So, the alternative data generation algorithm is employed which is known as the acceptance-rejection algorithm technique, and a Monte-Carlo simulation study is done. The absolute average bias and mean square error of the estimated parameters of the length-biased version model are calculated and it is noticed that both the calculated measures decrease simultaneously on increasing the sample size. In order to determine if the model is appropriate, a real-life time-to-event data set is examined as an example, and length biased distribution is juxtaposed with several other common available lifetime distributions for comparison purposes.
Keywords: Acceptance-rejection algorithm; Entropy; Weighted intervened distribution; Monte Carlo simulation
Cite: Vilayat Ali Bhat, Sudesh Pundir WEIGHTED INTERVENED EXPONENTIAL DISTRIBUTION AS A LIFETIME DISTRIBUTION. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-253-266 |
253-266 |
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TRADE CREDIT FINANCING SCHEME ON RETAILERÒS ORDERING QUANTITY FOR IMPERFECT QUALITY ITEM WITH LEARNING EFFECTS AND STOCKING STRATEGIES
A. R. Nigwal, , L. Sharma Department of Mathematics, Ujjain Engineering College, Ujjain, 456010, Madhya Pradesh India,
U. K. Khedlekar, N. Gupta Department of Mathematics and Statistics, Dr. Harisingh Gour Vishwavidyalaya, Sagar, 470003, Madhya Pradesh, India, (A Central University)
TodayÒs life is a age of modern life, and in the modern life for any kind of business setup, customer service, pricing, stocking strategies and trade credit fnancing schemes are effective, essential and survival parameters to grow the business. In this paper, we have developed, an economical order quantity model for imperfect quality product by considering retailerÒs stock sensitive demand of product under trade credit fnancing policy. Further in this paper we have studied the Learning effect on screening process on every batch of imperfect quality product. Under the trade credit fnancing scheme, we have considered that, the supplier proposes to the retailer, a fxed credit time period for payment and retailer also offers to his customers to a fxed credit time period of payment. Finally an appropriate total proft function per unit time has been derived under the various trade credit fnancing periods of payment including various expenditure and other related parameters. A sensitivity analysis has been done to verify the optimum results and also a numerical example has been given to verify the modelÒs outputs.
Keywords: Learning Effect, Stocking, Imperfect quality items, Trade credit policy. Screening process
Cite: A. R. Nigwal, U. K. Khedlekar, N. Gupta, L. Sharma TRADE CREDIT FINANCING SCHEME ON RETAILERÒS ORDERING QUANTITY FOR IMPERFECT QUALITY ITEM WITH LEARNING EFFECTS AND STOCKING STRATEGIES. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-267-285 |
267-285 |
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A NOVEL METHOD TO GENERATE A FAMILY OF BATHTUB-SHAPED FAILURE RATES FROM A FAMILY OF UPSIDE DOWN BATHTUB-SHAPED FAILURE RATES AND VICE-VERSA
R.L. Giri, Subarna Bhattacharjee Department of Mathematics, Ravenshaw University, Cuttack-753003, Odisha, India rajiblochan.giri@gmail.com, subarna.bhatt@gmail.com
Suchandan Kayal, S. K. Misra Department of Mathematics, National Institute of Technology Rourkela, Odisha, India 4 Department of Mathematics, KIIT University, Bhubaneswar, Odisha, India suchandan.kayal@gmail.com, satyamisra05@gmail.com
It is indeed a matter of great signifcance for system engineers and scientists to derive new classes of lifetime distributions for providing a better statistical model which will ft a given lifetime data set. It is known that many real time data have varied characteristics and can be modeled by distributions with bathtub and upside down bathtub failure rates viz., Weibull, Modifed Weibull, Inverse Weibull. This paper proposes a method which generates a family of distributions having bathtub (BT)-shaped failure rate from a distribution having upside down bathtub (UBT)-shaped failure rate and vice-versa. The proposed method is validated with the help of a few statistical distributions. The closure properties of the proposed model under various reliability operations are studied.
Keywords: Aging phenomenon, hazard rate, bathtub-shaped failure rate, upside down bathtub≠shaped failure rate.
Cite: R.L. Giri, Subarna Bhattacharjee, Suchandan Kayal, S. K. Misra A NOVEL METHOD TO GENERATE A FAMILY OF BATHTUB-SHAPED FAILURE RATES FROM A FAMILY OF UPSIDE DOWN BATHTUB-SHAPED FAILURE RATES AND VICE-VERSA. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-289-297 |
286-297 |
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AN APPROACH FOR ASSESSMENT OF RELIABILITY INDICES CONSIDERING OMISSION OF FIXED REPAIR TIME FOR ELECTRIC TRACTION SYSTEM APPLYING MONTE CARLO SIMULATION
Aditya Tiwary Department of Fire Technology & Safety Engineering, IPS Academy, IES, Indore (M.P) India
Assessment of numerous reliability indices is essential when availability and unavailability of supply in any electric power system is talked about. The reliability index which are very important for overall performance of any complex engineering system are mean up time, mean down time and unavailability. In this paper, assessment of various reliability indices for the electric traction system is done based on Monte Carlo simulation. If an engineering system fails then its repair is required to be performed at proper time interval. Omission of a threshold value of fixed repair time will not have so much impact on the overall reliability of the engineering system taken together. Electric traction system is very important as it is utilized for operation of passenger trains and freight trains across a large rail network throughout the continents. In view of above, modified values of mean up time, mean down time and unavailability have been obtained accounting fixed repair time omission for the electrical traction system taken under consideration.
Keywords: Monte Carlo simulation, Electric traction system, Mean up time, Repair time, Reliability indices.
Cite: Aditya Tiwary AN APPROACH FOR ASSESSMENT OF RELIABILITY INDICES CONSIDERING OMISSION OF FIXED REPAIR TIME FOR ELECTRIC TRACTION SYSTEM APPLYING MONTE CARLO SIMULATION. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-298-306 |
298-306 |
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BAYESIAN INTERVAL ESTIMATION FOR THE PARAMETERS OF POISSON TYPE LENGTH BIASED EXPONENTIAL CLASS MODEL
Rajesh Singh, Preeti A. Badge Department of Statistics, S. G. B. Amravati University, Amravati, India rsinghamt@hotmail.com, preetibadge10@gmail.com
Pritee Singh Department of Statistics, Institute of Science, Nagpur, India
In this research paper, two sided Bayesian interval is proposed for Poisson type length biased exponential class software reliability growth model. The failure intensity function, mean time to failure function and likelihood function are derived. Bayesian interval estimation has been done for the parameters using non informative priors. The performance of proposed Bayesian interval is obtained by using Monte Carlo simulation technique. Average length and coverage probability of Bayesian interval for the parameters are calculated. From the obtained intervals it is concluded that Bayesian interval of parameters perform better for appropriate choice of execution time and certain values of parameters.
Keywords: Length biased exponential distribution, Non informative priors, Software reliability growth model (SRGM), Bayesian interval, average length, coverage probability.
Cite: Rajesh Singh, Preeti A. Badge, Pritee Singh BAYESIAN INTERVAL ESTIMATION FOR THE PARAMETERS OF POISSON TYPE LENGTH BIASED EXPONENTIAL CLASS MODEL. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-307-314 |
307-314 |
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RESILIENCE OF A TELECOMMUNICATIONS NETWORK SUBJECTED TO CORRELATED GEOGRAPHICAL FAILURES
Dora Jimenez Universidad Adolfo Ibanez.
Abigail Medina Universidad de Carabobo
Due to the COVID-19 pandemic, the way in which routine activities are carried out changed, taking a leading role telecommunications networks, it is important to evaluate their operation, service interruption and progressive deterioration, especially those generated by natural disasters, we have focused on earthquakes. Venezuela is a seismic country, being vulnerable to economic and human losses caused by this disaster. Many of the infrastructures that are used by both public and private institutions may not follow the current laws on earthquake-resistant structures. We seek to evaluate the damage by correlated geographic faults produced by earthquakes in a telecommunications network using probabilistic seismic risk analysis.
Keywords: reliability, seismic, simulation
Cite: Dora Jimenez1 and Abigail Medina RESILIENCE OF A TELECOMMUNICATIONS NETWORK SUBJECTED TO CORRELATED GEOGRAPHICAL FAILURES. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-315-326 |
315-326 |
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A NEW ZERO-TRUNCATED DISTRIBUTION AND ITS APPLICATIONS TO COUNT DATA
Na Elah, Peer Bilal Ahmad, Muneeb Ahmad Wani Department of Mathematical Sciences, Islamic University of Sciene & Technology-192122, Kashmir naaelashah@gmail.com, bilalahmadpz@gmail.com, wanimuneeb163@gmail.com
Numerous disciplines, including engineering, public health, sociology, psychology, and epidemiology, are particularly interested in the analysis and modelling of zero truncated count data. As a result, we suggest a novel and straightforward structural model in this study called zero truncated new discrete distribution. We examine its statistical properties including probability mass function, cumulative function, and moments. The parametric estimation of the zero-truncated new discrete distribution is explained by Maximum Likelihood Estimation method and, to investigate its performance, a simulation study is proposed. The importance of the distribution is evaluated using two real-world data sets as well as one simulated data set and the model comparison is made on the basis of AIC and BIC criterions.
Keywords: truncation, zero-truncated distribution, simulation maximum likelihood estimation, goodness-of-ft
Cite: Na Elah, Peer Bilal Ahmad, Muneeb Ahmad Wani A NEW ZERO-TRUNCATED DISTRIBUTION AND ITS APPLICATIONS TO COUNT DATA. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-327-339 |
327-339 |
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USE OF TRIBODIAGNOSTICS IN PRACTICE
Pavol Mikus, Alena Breznicka Faculty of Special Technology, Alexander Dubcek University of Trencin, Ku kyselke 469,91106,Trencin,Slovakia pavol.mikus@tnuni.sk, alena.breznicka@tnuni.sk
Tribodiagnostics deals with the problems of lubrication, friction and analysis of oils in technical fluids. Based on the results of parameter monitoring and chemical analysis of the oil, it is possible to determine the impending failure of the entire system very accurately. Today, this relatively young field of technical diagnostics is gradually becoming very viable and its results are fully in line with classical vibroacoustic diagnostics or thermodiagnostics. It is used in all mechanical systems containing oil systems. This is one of the methods of non-disassembly technical diagnostics, which is based on the knowledge that the lubricant after a certain period of use in the lubrication system reflects the condition of the equipment and the conditions in which this equipment was operated.
Keywords: Tribodiagnostics, lubrication fluid, oil, friction
Cite: Pavol Mikus, Alena Breznicka USE OF TRIBODIAGNOSTICS IN PRACTICE. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-340-347 |
340-347 |
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MOMENTS PROPERTIES OF CONCOMITANTS OF GENERALIZED ORDER STATISTICS FROM FGMTBM EXPONENTIAL DISTRIBUTION
Mustafa Kamal Department of Basic Sciences, College of Science and Theoretical Studies, Saudi Electronic University, KSA
Nayabuddin Faculty of Public Health and Tropical Medicine, Jazan University, KSA
Intekhab Alam Department of Management St. Andrews Institute of Technology & Management Gurugram, Haryana, India
Ahmadur Rahman Department of Statistics and O.R., Aligarh Muslim University, India
Abdul Salam Department of Epidemiology, Faculty of Public Health and Tropical Medicine, Jazan University, KSA
Shazia Zarrin Uttaranchal Unani Medical College and Hospital, Haridwar, India
Concurrent or induced order statistics are produced when individuals in a random sample are ordered in compliance with the corresponding values of some other random sample. Concomitants are most helpful when k(n) individuals are to be chosen using a selection technique based on their X-values. The relevant Y-values are then used to reflect how well a characteristic has performed. In this paper, concomitants of generalized order statistics (GOS) from Farlie Gumbel Morgenstern type bivariate moment (FGMTBM) exponential distribution are obtained. Additionally, distribution function (df) and probaility density function (pdf) r-th generalized order statistics and a joint pdf of r-th and s-th GOS were also obtained. Furthermore, we provide the minimum variance linear unbiased estimator (MVLUE) of the position and scale parameters of the concomitants of the k-th upper record values and order statistics for the distribution under consideration. Finally, an implementation of the suggested methodology has been taken into account.
Keywords: Generalized order statistics, Concomitants, Record Values, FGMTBM exponential distribution, Single and Product Moments, Minimum variance linear unbiased estimator.
Cite: Mustafa Kamal, Nayabuddin, Intekhab Alam, Ahmadur Rahman, Abdul Salam, Shazia Zarrin MOMENTS PROPERTIES OF CONCOMITANTS OF GENERALIZED ORDER STATISTICS FROM FGMTBM EXPONENTIAL DISTRIBUTION. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-348-358 |
348-358 |
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PROJECT CHARACTERISTICS WITH TRIANGULAR FUZZY NUMBER
Adilakshmi Siripurapu Dept. of Basic Scienceand Humanities, VignanÒsInstitute of Information Technology (A), Duvvada, Visakhapatnam, AP, India
Ravi Shankar Nowpada Dept. of Mathematics, Institute of Science, GITAM (Deemed to be University), Visakhapatnam, AP, India
The Critical Path Method (CPM) is required to plan, organize, and arrange for major project networks. A clear estimate of the time duration will help in the successful execution of the CPM. However, the time duration cannot be precisely specified in real life. As a result, there is always uncertainty about the duration of activities, leading to the invention of the fuzzy critical path method. This study proposes a simple method for critical path analysis and project characteristics in a project network with a triangular fuzzy number. Furthermore, this study defines the most critical path and the relative path degree of criticality, both theoretically valid and practical. The suggested method can determine the critical path, project characteristics and critical degree of an activity as shown by an example discussed in some earlier studies. The proposed approach is very simple to apply and does not require knowing the explicit form of the membership functions of the fuzzy activity times.
Keywords: Activity duration, critical degree, critical path method, project characteristics, triangular fuzzy number,
Cite: Adilakshmi Siripurapu, Ravi Shankar Nowpada PROJECT CHARACTERISTICS WITH TRIANGULAR FUZZY NUMBER. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-359-369 |
359-369 |
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RELIABILITY FACTORS OF SOFTWARE FOR MICROPROCESSOR PROTECTIONS
M. I. Uspensky Institute for Socio-Economic & Energy Problems of the North of FRC Komi Science Center, Ural Branch, Russian Academy of Sciences, Syktyvkar, Russia
The features of the program functioning reliability that are typical for critical applications operating in real mode for microprocessor protections are considered. Among the main characteristics of the relay protection functioning are reliability indicators. With the transition to the execution of such protections on a microprocessor-based basis, in addition to hardware reliability, it became necessary to characterize its operation by software reliability. The importance of the solve tasks in the operation process refers it to programs used in safety-critical software and operating in real mode. This, in turn, tightens the requirements for their reliability evaluation. Comparative analysis made it possible to assess the generality of the considered reliability factors for the functioning of the application software under consideration. At the same time, we were able to highlight some of the features that are typical for the implementation of relay protection on microprocessors. An example of such an assessment is given, showing that despite all the difficulties of complete testing for microprocessor protection programs the software erroneous contribution still amounts to 2.5% of the total contribution. It is shown that microprocessor protection programs are related to programs of critical applications operating in real mode, which makes it possible to use the experience and characteristics of such software in solving relay protection challenges. Nevertheless, some features are given that are specific for relay protection based on a microprocessor. Further tasks are defined.
Key words: safety-critical software, microprocessor relay protection, software reliability.
Cite: M. I. Uspensky RELIABILITY FACTORS OF SOFTWARE FOR MICROPROCESSOR PROTECTIONS. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-370-375 |
370-375 |
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ANALYSIS OF M[X1], M[X2]/G1, G2/1 RETRIAL QUEUE WITH PRIORITY SERVICES, DIFFERENTIATE BREAKDOWN, REPAIR, SYNCHRONIZED RENEGING AND OPTIONAL VACATION
G. Ayyappan, S. Nithya Department of Mathematics Puducherry Technological University Puducherry-605014, India ayyappan@ptuniv.edu.in, nithyamouttouraman@gmail.com
This study deals with the steady-state analysis of single-server retrial non-preemptive priority queue with differentiate breakdown, repair, synchronized reneging and optional vacation. For this purpose, two categories of customers are considered, priority and ordinary customers, who arrive as per Poisson arrival process. The server consistently affords single service for these customers based on general distribution. The server randomly fails while providing service to the customer. Hard failure and soft failure are the two kinds of system failure. Hard failure is defined as an equipment failure that requires a repairman with specialized knowledge to be physically present, which is a time-consuming process. Whereas soft failure is defined as failure caused by events rather than physical condition and is usually resolved rebooting the system. Ordinary customers may renege the orbit if the server is engaged or unavailable. Furthermore, once the service of all priority customers is completed by the server, the server goes for a vacation or becomes idle. In this study, we used probability generating function and supplementary variable technique to solve the Laplace transforms of time-dependent probabilities of system states. Finally, we evaluated performance measures and expressed the results in numerical values.
Keywords: Batch arrivals; Priority queues; Differentiate Breakdown; Optional Vacation; Synchronized Reneging
Cite: G. Ayyappan, S. Nithya ANALYSIS OF M[X1], M[X2]/G1, G2/1 RETRIAL QUEUE WITH PRIORITY SERVICES, DIFFERENTIATE BREAKDOWN, REPAIR, SYNCHRONIZED RENEGING AND OPTIONAL VACATION. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-376-391 |
376-391 |
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MUlTI-COMPONENT CONDITIONAL STRESS-STRENGTH PARAMETER
Kavoos Khorshidian Department of Statistics, Faculty of Science, Shiraz University, Shiraz, Iran
Morteza Taheri Saif Abad Department of Statistics, Faculty of Science, Shiraz University, Shiraz, Iran
There are situations in which the experimenter has some information about the components of the operating system and he/she wants to use this information for better assessment or operating of the underlying system. In such cases the notion of conditional probability may help the operator to use that information and improve his/her task. In the present study this notion has been examined, and some conditional stress-strength parameters have been introduced for s of k systems. The multi-component conditional stress-strength parameter (MCCSSP) and its maximum likelihood estimator have been calculated when the strength and stress random variables are exponentially distributed. In the case of having extra information about the parameters, a closed form has been derived for the Bayes estimator of MCCSSP and has been calculated by using an algorithm together with Monte Carlo method. For the case of non-exponential stress or strengths, the nonparametric estimator of the defined parameter has also been derived. Finally, some simulation study on the MLE and Bayes estimator, as well as real data analysis for nonparametric estimators have been done to verify the analytic results.
Keywords: Conditional Reliability, Exponential Distribution, Maximum Likelihood Estimator, Multi-Component Systems, Stress-Strength Parameter
Cite: Kavoos Khorshidian, Morteza Taheri Saif Abad MUlTI-COMPONENT CONDITIONAL STRESS-STRENGTH PARAMETER. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-392-405 |
392-405 |
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BAYESIAN ANALYSIS OF ARMA AND BSTS MODELS FOR COVID-19 DATA USING R AND STAN
Muhammed Navas T, Athar Ali Khan Department of Statistics and Operations Research Aligarh Muslim University, Aligarh-202002, India navasmku@gmail.com, atharkhan1962@gmail.com
This study compares the performance of Bayesian ARIMA and BSTS models for COVID-19 data using Bayesian approach. Many studies in the literature have compared the BSTS model and classical ARIMA models for infectious disease modelling, and the BSTS model performs well. Apart from the literature, this study is trying to prove the Bayesian ARIMA model gives a better result than the BSTS model. This study uses a different modelling and model comparison method to compare widely used autoregressive integrated moving average (ARIMA) models with their Bayesian structural time series (BSTS) models for COVID-19 data using the Bayesian approach. It is essential to find the order of the ARIMA model before doing bayesian analysis. We find the order of the ARIMA model using measurement LOO information criteria , using the Hamiltonian Montecarlo algorithm and rstan estimate the parameters of ARIMA and BSTS models for COVID-19 data. Furthermore, compare both models using Looic and Waic values; Bayesian ARIMA models outperform in this study.
Keywords: BSTS, COVID-19, ARIMA, MCMC, LOOIC, WAIC, Stan
Cite: Muhammed Navas T, Athar Ali Khan BAYESIAN ANALYSIS OF ARMA AND BSTS MODELS FOR COVID-19 DATA USING R AND STAN. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-406-416 |
406-416 |
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ANALYSIS OF PROJECTED PROFIT IN AN M/M/K ENCOURAGED ARRIVAL QUEUEING MODEL USING CHI-SQUARE TEST
V. Narmadha, P. Rajendran Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore, Tamil Nadu 632014, India. narmadha.v@vit.ac.in, prajendran@vit.ac.in
Nowadays, queues be seen in fast food restaurants and in all service-based businesses. This study is a mathematical analysis of such business firms with the help of Queueing Theory . The discounts and promotions entice customers to the firm and in this study such attracted customers are referred to as Encouraged Arrivals. The Chi-square test is used to determine the kind of encouraged arrival pattern that adheres to the data observed from a fastfood outlet. We introduce the encouraged arrivals in an M/M/k queueing model for the analysis of performance metrics. The performance metrics of the various encouraged arrival patterns are compared and the ideal one is chosen for the firm. The economic analysis shows that with encouraged arrivals, the cost associated with the time lost due to waiting is reduced gradually with increasing number of servers. Thus the firm increases its projected profit with encouraged arrivals. This study helps the entrepreneurs to decide the kind of discounts that would attract the customers simultaneous ly improving the firmÒs profit. Little's lawis also verified.
Keywords: Encouraged Arrivals (ea.), Promotions, Expenses, Chi-square test, Frequency, Degrees of freedom (Dof),LittleÒs formula (LF).
Cite: V. Narmadha, P. Rajendran ANALYSIS OF PROJECTED PROFIT IN AN M/M/K ENCOURAGED ARRIVAL QUEUEING MODEL USING CHI-SQUARE TEST. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-417-428 |
417-428 |
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MOMENTS OF GENERALIZED RECORD VALUES FROM MODIFIED FRECHET DISTRIBUTION AND ITS CHARACTERIZATION
Zaki Anwar, Rafiqullah Khan Department of Statistics and Operations Research, Aligarh Muslim University, Aligarh-202002, India zakistats@gmail.com, aruke@rediffmail.com
Abdul Nasir Khan School of Mathematics and Statistics, MIT World Peace University, Pune-411038, India zakistats@gmail.com, aruke@rediffmail.com
The aim of this paper is to introduce the relations for moments and characterizing results for the newly introduced modified Frechet distribution based on generalized record values. Here, we used an ordered random variable approach like generalized record values for generating the results. We have established the recurrence relations for single and product moments of generalized record values from modified Frechet distribution. These relations are also deduced for the lower record values and some specific distributions, which are the special cases of modified Frechet distribution. Further, the characterization results for this distribution have been established by using recurrence relations for single and product moments and conditional expectation of a function of generalized record values and truncated moments.
Keywords: Order statistics, generalized record values, modified Frechet distribution, single moments, product moments, recurrence relations and characterization.
Cite: Zaki Anwar, Abdul Nasir Khan, Rafiqullah Khan MOMENTS OF GENERALIZED RECORD VALUES FROM MODIFIED FRECHET DISTRIBUTIONAND ITS CHARACTERIZATION. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-429-440 |
429-440 |
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PROFITABILITY ANALYSIS OF A FOOD INDUSTRIAL SYSTEM HAVING MAKE-AND-PACK PRODUCTION STRATEGY WITH PRIORITY BASIS REPAIR
Monika, Garima Chopra Department of Mathematics, University Institute of Engineering & Technology, Maharshi Dayanand University, Rohtak, Haryana, India monika.dhull8@gmail.com, garima.chopra@gmail.com
The present investigation is concerned with the profitability analysis of a food industrial system where production is based on the make-and-pack strategy. The system is assumed to have two subsystems: first subsystem is for making while the second is for packing the product so formed. As per the gathered information about the production procedure in the food industrial plant, the priority of repair is given to the making subsystem over the packing subsystem. Here, failure of either subsystem leads to a complete breakdown of the system. Also, two types of failures are considered in the packing subsystem i.e. minor failures and major failures. Two kinds of repairers (operator and fitter) are appointed to tackle the failures in the subsystems. For minor and major failures in the packing subsystem, the operator and fitter respectively are responsible for repairs. However, any failure in making subsystem is repaired by the combined efforts of the operator and fitter. Reliability characteristics such as mean time to system failure (MTSF), system availability, and expected busy period of the repair persons are studied by employing the semi-Markov process and regenerative point technique. The system profitability is graphically analyzed concerning to failure rates of both subsystems.
Keywords: make-and-pack production process, priority basis repair, regenerative point technique, semi-Markov process
Cite: Monika, Garima Chopra PROFITABILITY ANALYSIS OF A FOOD INDUSTRIAL SYSTEM HAVING MAKE-AND-PACK PRODUCTION STRATEGY WITH PRIORITY BASIS REPAIR. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-441-455 |
441-455 |
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HYBRID AND BLIND WATERMARKING FRAMEWORK FOR PRIVACY PROTECTION AND CONTENT AUTHENTICATION OF DIGITAL MULTIMEDIA
Swati J. Patel Ph.D. Scholar, Information Technology Department, Gujarat Technological University, Ahmedabad, India
Dr. Mehul C. Parikh Associate Professor, Information Technology Department, L.D.College of Engineering, Ahmedabad, India
Nowadays, due to inexpensive and conveniently available internet access at the fingertip, the illegitimate sharing of digital multimedia i.e. image, audio, and video is becoming a universal and significant threat. Illegal transmission of digital multimedia through the internet creates an issue of authentication and copyright protection; hence, piracy protection is a vital need for protecting digital media. Digital watermarking is a method of preventing digital theft in which additional information, known as a watermark, is inserted into digital multimedia. This technology was originally designed for still photos, but it has subsequently been expanded to include additional multimedia artifacts such as audio and video, due to its countless use in today's era. Digital watermarking is an effective method of limiting piracy and providing authenticity and copyright ownership to digital content. Watermarking can be performed either in the spatial or in the transform domain. In this paper, a hybrid digital video watermarking technique for copyright protection, data security, and content authentication of multimedia, based on Discrete Wavelet Transform, Discrete Cosine Transform, and Singular Value Decomposition is presented. The authenticity of the content has been ensured by embedding a watermark in the transform domain, while copyright protection has been provided by a strong watermark. The experimental results show that the proposed schemes achieve a PSNR greater than 51 dB on average, which illustrates that the proposed method gives excellent performance for robustness, authentication, and security. A comparison of the proposed framework to various cutting-edge techniques illustrates its e.ectiveness and superiority.
Keywords: Digital Video Watermarking, Robustness, Imperceptible, Authentication, Copyright Protection, Discrete Wavelet Transform, Discrete Cosine Transform, Singular Value Decomposition
Cite: Swati J. Patel, Mehul C. Parikh HYBRID AND BLIND WATERMARKING FRAMEWORK FOR PRIVACY PROTECTION AND CONTENT AUTHENTICATION OF DIGITAL MULTIMEDIA. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-456-465 |
456-465 |
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EMPIRICAL STUDY ON ROBUST REGRESSION ESTIMATORS AND THEIR PERFORMANCE
Lakshmi R, Dr.Sajesh TA Department of Statistics, St. Thomas College (Autonomous), Thrissur 680001, University of Calicut lakshmi.nss19@gmail.com, sajesh.t.abraham@gmail.com
Regression Analysis is statistical technique to model data. But the presence of outliers and influential points affect data modelling and its interpretation. Robust regression analysis is an alternative choice to this. Here we made an attempt to study different robust estimators and propose a new robust reweighted Sn covariance based regression estimator. We have evaluated the performance empirically and the simulation study shows our proposed estimator is preferable to OLS and other robust regression estimators in terms of the MSE criteria. Also, proposed robust Sn covariance regression estimator produce outperforming results for regression equivaraince and breakdown criterion. Robustness of the proposed estimator is proved empirically. The proposed method is innovatively used to model fluid data. R software is used for simulation and study.
Keywords: robust Sn regression, influential observations, modelling, data analysis,
Cite: Lakshmi R, Sajesh TA EMPIRICAL STUDY ON ROBUST REGRESSION ESTIMATORS AND THEIR PERFORMANCE. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-466-478 |
466-478 |
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RATIO ESTIMATOR OF POPULATION MEAN USING A NEW LINEAR COMBINATION UNDER RANKED SET SAMPLING
Khalid Ul Islam Rather Division of Statistics and Computer Science, SKUAST-Jammu, India.
Showkat Maqbool Department of Statistics, University of Kashmir, Srinagar 190006, J&K, India
Saba Riyaz, T. R. Jan 1,4 Division of AGB, FVSC & AH, SKUAST-K, Shuhama, J&K, India Saba.riyaz.syed@gmail.com, drtrjan@gmail.com
Ranked set sampling is an approach to data collection originally combines simple random sampling with the field investigator's professional knowledge and judgment to pick places to collect samples. Alternatively, field screening measurements can replace professional judgment when appropriate and analysis that continues to stimulate substantial methodological research. The use of ranked set sampling increases the chance that the collected samples will yield representative measurements. This results in better estimates of the mean as well as improved performance of many statistical procedures. Moreover, ranked set sampling can be more cost-efficient than simple random sampling because fewer samples need to be collected and measured. The use of professional judgment in the process of selecting sampling locations is a powerful incentive to use ranked set sampling. This paper is devoted to the study, we introduce an approach to the mean estimators in ranked set sampling. The amount of information carried by the auxiliary variable is measured with the on populations and samples and to use this information in the estimator, the basic ratio and the generalized exponential ratio estimators are as an improved form of a difference cum exponential ratio type estimator under the ranked set sampling in order to estimate the population mean of study variate Y using single auxiliary variable X. The expressions for the mean squared error of propose estimator under ranked set sampling is derived and theoretical comparisons are made with competing estimators. We show that the proposed estimator has a lower mean square error than the existing estimators. In addition, these theoretical results are supported with the aid of some real data sets using R studio. Therefore, Under RSS architecture, a better difference cum exponential ratio type estimator has been suggested. The estimator's mathematical form has been developed, and its efficiency requirements have been developed in relation to various already-existing estimators from the literature. By imputing various values for the constants used in the creation of our proposed estimator, we also provide several specific situations of our estimator.
Keywords: mean squared error, auxiliary variable, median, coefficient of variation, kurtosis
Cite: Saba Riyaz, Khalid Ul Islam Rather, Showkat Maqbool, T. R. Jan RATIO ESTIMATOR OF POPULATION MEAN USING A NEW LINEAR COMBINATION UNDER RANKED SET SAMPLING. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-479-485 |
479-485 |
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COMBINED REDUNDANCY OPTIMIZATION FOR A SYSTEM COMPRISING OPERATIVE, COLD STANDBY AND WARM STANDBY UNITS
Lalji Munda Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana, India
Gulshan Taneja Department of Mathematics, Maharshi Dayanand University, Rohtak, Haryana, India
The company or industry can increase system reliability and provide stress-free operation by adding redundant equivalent subsystems to the active unit. The warm standby system is accessible if the operational unit malfunctions, and the cold standby system can take over. This paper aims to analyze a system comprised of one operative unit, cold standby unit, and one warm standby unit. Cold standby is activated to become warm standby when the operative unit fails, and warm standby becomes operational immediately. A minor defect causes the warm standby unit to fail, whereas a major fault causes the operational unit to fail. Such systems are used by many businesses, sectors, and facilities to prevent operational and reputational losses. Cut-off values for the failure rate, activation rate, revenue cost, and cost per repairman visit have been calculated to determine when the system is profitable. Various system performance measures have been defined by using the Markov process and regeneration point method.
Keywords: Cold Standby, Profit Analysis, Redundancy, Warm Standby
Cite: Lalji Munda, Gulshan Taneja COMBINED REDUNDANCY OPTIMIZATION FOR A SYSTEM COMPRISING OPERATIVE, COLD STANDBY AND WARM STANDBY UNITS. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-486-497 |
486-497 |
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A TWO-STATE FEEDBACK RETRIAL QUEUEING SYSTEM HAVING TWO HETEROGENEOUS PARALLEL SERVERS AND IMPATIENT CUSTOMERS
Neelam Singla Department of Statistics, Punjabi University, Patiala-India
Harwinder Kaur University School of Business, Chandigarh University, Gharuan, Mohali-India
Objective: In the present paper we consider a two-state retrial queueing system with feedback having two heterogeneous parallel servers and impatient customers. Transient state probabilities for exact number of arrivals and departures from the system will be obtained when both, one or none of the servers is busy. Numerical and graphical solutions will also be obtained. Methods: The difference-differential equations governing the system are solved recursively, Laplace transform is then used to obtain the transient state probabilities for exact number of arrivals and departures from the system. Findings: Time dependent probabilities are obtained when both, one and none of the servers is busy. Numerical and Graphical solutions are also obtained using MATLAB programming. Novelty: In past research, models considered arrivals and departures from the orbit whereas in present model arrivals and departures from the system are studied along with the concept of feedback. Applications: This type of model is implemented in computer systems.
Cite: Neelam Singla, Harwinder Kaur A TWO-STATE FEEDBACK RETRIAL QUEUEING SYSTEM HAVING TWO HETEROGENEOUS PARALLEL SERVERS AND IMPATIENT CUSTOMERS. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-498-512 |
498-512 |
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ANALYSIS OF A NON-IDENTICAL COMPONENT-STRENGTHS SYSTEM BASED ON LOWER RECORD DATA
Amal S. Hassan Doaa M. Ismail, Heba F. Nagy Faculty of Graduate Studies for Statistical Research, Cairo University, Giza, 12613, Egypt. amal52_soliman@cu.edu.eg, doaa22ismail@gmail.com, heba_nagy_84@cu.edu.eg
In engineering applications and reliability literature, stress-strength models play a crucial role. The goal of this study is to develop more accurate stress-strength models by addressing the reliability estimation in multi-component systems with non-identical component strengths and stress. In the context of lower record values, the system's reliability is assessed using both classical and Bayesian approaches. In classical estimation, the maximum likelihood estimator of the reliability function is constructed, and a simulation study based on measurements of precision is used to assess the behavior of various estimates. The Bayesian estimators of reliability under general entropy, logarithmic and precautionary loss functions are computed. The suggested Bayesian estimates are calculated using the Markov Chain Monte Carlo method through a simulation study because there is no one particular way to do it. We found through simulated research that the accuracy of measurements decreases as the number of records rises. The theoretical results are validated using an example from actual data sets.
Keywords: Exponentiated Pareto model; Lower record data; Bayesian inference; General entropy loss function.
Cite: Amal S. Hassan, Doaa M. Ismail, Heba F. Nagy ANALYSIS OF A NON-IDENTICAL COMPONENT-STRENGTHS SYSTEM BASED ON LOWER RECORD DATA. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-513-528 |
513-528 |
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OPTIMAL SOFTWARE RELIABILITY PREDICTION USING CRITERIA WEIGHTS UNDER FUZZY DECISION≠MAKING APPROACH
H. D. Arora, Anjali Naithani, Surbhi Gupta Department of Mathematics, Amity Institute of Applied sciences, Amity University Uttar Pradesh, Noida, U.P., India hdarora@amity.edu, anathani@amity.edu, sgupta11@amity.edu
Multi Criteria Decision Making techniques often face the challenge of determining criteria weights. The weights of criteria can significantly impact the outcomes of the decision-making process. Therefore, it is crucial to pay close consideration to the objectivity characteristics of criteria weights. Many weighting methods were discussed by various authors and utilized to solve various decision≠making complications in Analytical Hierarchy Process (AHP), Entropy method, Weighing Score Method (WSM), Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS), Best worse method (MWM), VlseKriterijumska Optimizacija I Kompromisno Resenje (VIKOR), Criteria Importance Through Intercriteria Correlation (CRITIC) method, ELECTRE, etc. This research article gives an overview of various weighting strategies that can be used in multi-criteria optimization and proposes a novel approach to determine criteria weights using Pythagorean fuzzy sets to handle uncertainties inthe decision makerÒs preferencesforallocating software reliability. The comparative analysis shows that the proposed weighting method has the advantage of being simple and straightforward in comparison to the existing weighting methods. The evaluation confirms that this novel approach is effective enough to determine objective weights.
Keywords: Criteria Weights, software reliability, MCDM, Entropy, AHP, Pythagorean fuzzy number
Cite: H. D. Arora, Anjali Naithani, Surbhi Gupta OPTIMAL SOFTWARE RELIABILITY PREDICTION USING CRITERIA WEIGHTS UNDER FUZZY DECISION-MAKING APPROACH. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-529-544 |
529-544 | |||
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STRESS-STRENGTH RELIABILITY MODEL UNDER MULTIVARIATE NORMAL SETUP AND ITS APPLICATIONS
Anirban Goswami Regional Research Institute of Unani Medicine, Patna, Bihar
Babulal Seal Department of Mathematics and Statistics, Aliah University, Kolkata, West Bengal
We often see that in a system, the energy is supplied to the system by p1 sources and its consumed through p2 sources and the sources are linearly dependent with vector a' and b'. The overall representation of the two sets are related to vectors a and b, such that they are approximated by a'x and b'y as in principal component analysis. In this article, a stress strength reliability model R= Pr(a'x > b'y), when x and y are distributed dependently multivariate normal distribution is proposed, with a and b are two known vectors. MVUE and MLE of R are obtained. Through simulation studies, their performances are compared using different measures. The two-sided confidence intervals and lower bounds of R are obtained through exact and asymptotic distribution of maximum-likelihood estimators and using bootstrap procedure. Through simulation studies, the performances of these confidence intervals are empirically checked using their coverage and the accuracy. In this study, we proposed to choose the optimal sample size for an experiment assures an adequate power and level. Finally, we applied these interval estimators to a real data set.
Keywords: Stress-strength, Principal component, Maximum Likelihood Estimator (MLE), Minimum Variance Unbiased Estimator (MVUE), Confidence Intervals.
Cite: Anirban Goswami, Babulal Seal STRESS-STRENGTH RELIABILITY MODEL UNDER MULTIVARIATE NORMAL SETUP AND ITS APPLICATIONS. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-545-564 |
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GENERALIZATION OF LENGTH BIASED WEIGHTED GENERALIZED UNIFORM DISTRIBUTION AND ITS APPLICATIONS
Jismi Mathew Department of Statistics, Vimala College (Autonomous), Thrissur, Kerala, India
In this article, a generalization of length biased weighted generalized uniform distribution called Marshall Olkin length biased weighted generalized uniform distribution is introduced and studied. Some of the statistical properties of the new distribution such as hazard rate function, compounding, quantile function, moments, Renyi and Shannon entropies are discussed. The maximum likelihood estimation of the model parameters is done and a simulation study is conducted for confirming the validity of the estimates and also introduced a minification process with respect to the model and explored its sample path behaviour for different combinations of parameters. Further, the stress strength analysis is carried out and the estimate of the reliability is obtained based on a simulation study.
Keywords: Entropy, Length biased weighted generalized uniform distribution, Maximum likelihood method, Order statistics, Quantiles, Stress strength analysis.
Cite: Jismi Mathew GENERALIZATION OF LENGTH BIASED WEIGHTED GENERALIZED UNIFORM DISTRIBUTION AND ITS APPLICATIONS. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-565-578 |
565-578 | |||
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A NOVEL METHOD FOR SOFTWARE BUG REPORT ASSIGNMENT
Lukasz Chmielowski Nokia Solutions and Networks sp. z o.o., Poland Wroclaw University of Science and Technology, Poland
Pavlo Konstantynov Nokia Solutions and Networks sp. z o.o., Poland pavlo.konstantynov.ext@nokia.com
Ryszard Luczak Nokia Solutions and Networks sp. z o.o., Poland
Michal Kucharzak Nokia Solutions and Networks sp. z o.o., Poland Wroclaw University of Science and Technology, Poland
Robert Burduk Wroclaw University of Science and Technology, Poland
During the development of software and electronic devices, it is inevitable to make mistakes. In large, developed companies, assigning a request to the right development team or even a department is not an easy task. Often, the creation of software bug reports and assignment to groups is also formalized by appropriate processes. The paper presents a novel method of software bug report assignment to a group of developers or analysts. A specifc usage of organizational structure at the company is a key component of the proposed approach. There are presented results from real use application including both machine learning predictions and human decisions. Human predictions are not independent, the issues are raised as to why comparing the results of machine learning models with those of humans may be inappropriate and what factors infuence human decisions. The work also covers conclusive research about potential benefts of the application of automated assignment of bug reports.
Keywords: Software bug assignment, Software bug triaging, Software bug report, Software bug, Text analysis
Cite: Lukasz Chmielowski, Pavlo Konstantynov, Ryszard Luczak, Michal Kucharzak, Robert Burduk A NOVEL METHOD FOR SOFTWARE BUG REPORT ASSIGNMENT. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-579-588 |
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A NEW TWO PARAMETRIC GENERALIZED DIVERGENCE MEASURE AND ITS RESIDUAL
Fayaz Ahmed Department of Statistics, University of Kashmir, Srinagar, India
Mirza Abdul Khalique Baig Department of Statistics, University of Kashmir, Srinagar, India
In this research article, we proposed a new two-parametric divergence measure and developed its weighted version. We also looked at its properties and specific cases with examples and also obtained some results and bounds for new two prametric weighted generalized divergence measure. With the aid of a numerical example that determine the distribution function and also studied some inequality for the new proposed divergence measure. The known divergence measure is the particular case of our proposed measure. The proposed measure uniquely characterized the distribution function using the proportional hazard rate model (PHRM). Its residual function is also being worked on.
Keywords: characterization result, Divergence measure, distribution function, proportional hazard rate model, Residual function.
Cite: Fayaz Ahmed, Khalique Baig A NEW TWO PARAMETRIC GENERALIZED DIVERGENCE MEASURE AND ITS RESIDUAL. Reliability: Theory & Applications. 2023, June 2(73): 24-38. https://doi.org/10.24412/1932-2321-2023-273-589-598 |
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