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K.B. KORDONSKY. EDUCATOR AND RESEARCHER (1917-1999)
Andronov, A. Transport and Telecommunication Institute, Riga, Latvija, aleksander.andronov1@gmail.com
Shestakov, V. Riga Technical University, Institute of Aeronautics, Riga, Latvija,
The article is about Khaim Borisovich Kordonsky (Tula, Russia, 1919 - Boston, USA, 1999) - Soviet mathematician, Doctor of Technical Sciences, Professor at the Riga Red Banner Institute of Civil Aviation Engineers; specialist in the field of probability and reliability theory, leader of the development of the first computer system for making aircraft schedules, Honoured Scientist of the Latvian SSR, Laureate of the State Prize of the Latvian SSR. Kordonsky's entire scientific and teaching career is connected with RCIIGA. He is one of the founders of reliability theory and the author of the first monograph on the application of probability theory to solving real-world problems. The book "Applications of Probability Theory in Engineering" was published in 1963 and was reviewed by Academician Yuri Vladimirovich Linnik, the greatest expert in probability theory and mathematical statistics in the USSR. Khaim Borisovich also worked on scientific problems in statistics, medicine and technical diagnostics. He conducted joint research with the Department of Mathematical Statistics of the Faculty of Informatics and Cybernetics of Moscow State University, headed by Academician Yuri Vasilievich Prokhorov, and collaborated with Academician A. N. Kolmogorov.
Keywords: memories, probability theory, reliability theory, mathematics.
Cite: A. Andronov, V. Shestakov K.B. Kordonsky. Educator And Researcher (1917-1999). Reliability: Theory & Applications. 2023, March 1(72): 26-34. https://doi.org/10.24412/1932-2321-2023-172-26-34 |
26-34 |
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A MODIFIED INVERSE WEIBULL DISTRIBUTION USING KM TRANSFORMATION
Gauthami P., Mariyamma K. D., Kavya P. University of Calicut
In the subject of reliability engineering and statistics, a new reliability model is proposed, where survival analysis or life time data analysis is of major importance in the current scenario. The goal of this study is to introduce a new model that has applications to real data sets from the field of survival analysis. Deriving out the new model there are various methods to propose a new model, one of them is by using the method of transforming a variable to the variable of interest and there are numerous transformation methods which are in use right now. The newly proposed model is achieved by using the transformation method known as KM Transformation where it does not require any additional parameters to the baseline distribution which absolutely is an advantage. The model considered in this paper as baseline model is Inverse Weibull distribution with two parameters, one is a scale and other is a shape parameter. Inverse Weibull distribution is a continuous probability distribution which presently has great applications in real life phenomenon as well as so many modifications and advanced studies are introduced in this distribution from various fields. A proper study on the newly proposed model is done by deriving out its various functions and statistical properties such as Probability density function, Cumulative distribution function, Hazard rate function, Moments, Moment generating function, Characteristic function, Quantile function, Order statistics, etc. along with its Probability density function plot and Hazard rate function plot which have both upside-down and decreasing curves. Focusing on the inference procedures, the estimation of the parameters involved in this model is done by using the method of Maximum likelihood estimation. A simulation study for valuing the parameter consistency using two parameter combinations is carried out as well as a data analysis on an actual data set is also conducted. A comparison of the newly proposed model with other popular well-known models such as Inverse Weibull distribution (IW), KME distribution and KMW distribution using R programming language yielded that the new model is a better fit for the real data considered in this paper. The results and conclusions achieved throughout the paper are also mentioned at the last.
Keywords: KM Transformation, Inverse Weibull distribution, upside-down curve, decreasing curve
Cite: Gauthami P., Mariyamma K. D., Kavya P. A MODIFIED INVERSE WEIBULL DISTRIBUTION USING KM TRANSFORMATION. Reliability: Theory & Applications. 2023, March 1(72): 35-42. https://doi.org/10.24412/1932-2321-2023-172-35-42 |
35-42 |
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CLASSICAL AND BAYESIAN STOCHASTIC ANALYSIS OF A TWO UNIT PARALLEL SYSTEM WITH WORKING AND REST TIME OF REPAIRMAN
Vashali Saxena, Rakesh Gupta, Prof. Bhupendra Singh Department of Statistics, Ch. Charan Singh University, Meerut-250004(India)
The aim of the present paper is to deal with the analysis of the classical and Bayesian estimation of various measures of system effectiveness in a two non-identical unit parallel system. Each unit has two possible modes Normal (N) and total failure (F). A single repairman is always available with the system and after working for a random period he goes for rest for a random period. After taking complete rest he again starts the repair of the failed unit on a pre-emptive repeat basis. The system failure occurs when both the units are in (F-mode). The distributions of failure time as well as working and rest time of repairman are assumed to be exponential whereas repair time and rest time distribution of repairman are taken as general. A simulation study is also conducted for analysing the considered system model both in Classical and Bayesian setups. Bayesian estimates of various measure of system effectiveness are also obtained by taking different priors. The comparative study is made to judge the performance of Maximum likelihood estimation and Bayesian estimation methods. A simulation study at the end exhibits the behaviour of such a system. The Monte-Carlo technique is employed to draw observations for this simulation study. To obtain various interesting measure of system effectiveness technique have used the Regenerative point technique, MCMC technique and Gibbs sampler technique. From the graphs and tables we have drawn various important conclusions such that a smaller value of failure rate introduces a larger value of Maximum likelihood estimate and Bayes estimates for fixed value of the parameter of the repairman rest time distribution Moreso, when the value of the failure rate increases the mean time to system failure and net expected profit are also decreases. To compare the performance of asymptotic confidence interval and highest posterior density interval with the maximum likelihood estimates technique, it has been observed that width of the highest posterior density interval is less than the width of an asymptotic confidence interval.
Keywords: Transition probabilities, Mean sojourn time, mean time to system failure, Pre-emptive repeat repair, Regenerative point, Bayesian estimation, highest posterior density intervals, Maximum likelihood estimation, Gibbs sampler.
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43-55 |
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PROBABILISTIC ANALYSIS OF A TWO UNIT COLD STANDBY SYSTEM WITH REPAIR AND REPLACEMENT POLICIES
Alka Chaudhary, Suman Jaiswal, Nidhi Sharma Department of Statistics Meerut College, Meerut-250001 Ch. Charan Singh University, Meerut-250004 (India)
The present paper deals with two identical units, one is operative and the other of which other is kept on cold standby. If the operative unit fails, it goes under repair and after repair, it is not considered as good as new. If the unit fails after the first repair, it is replaced with a new unit. A single repairman is always available with the system to repair a failed unit. Failure time, repair time and replacement time distributions are taken as exponential to reduce the complexity of the system model. By using the regenerative point technique, the various important measures of system effectiveness have been obtained and are shown with the help of graph.
Keywords: Cold standby, replacement policy, MTSF, regenerative point, availability, transition probability and mean sojourn time.
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56-64 |
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DESIGN OF INERTIAL DELAY OBSERVER BASED MODEL FOLLOWING DYNAMIC SLIDING MODE CONTROL
S. S. Nerkar Department of Instrumentation Engineering, Government College of Engineering, Jalgaon, Maharashtra, India
B. M. Patre Department of Instrumentation Engineering, S.G.G.S. Institute of Engineering and Technology, Nanded, Maharashtra, India
This paper proposes the design and implementation of Inertial delay observer (IDO) based model following dynamic sliding mode control (DSMC). The Inertial delay observer estimates the states as well as the uncertainties and disturbances in an integrated manner. The DSMC is provides smooth control signal with the mechanism of chattering elimination while maintaining the accuracy of control. The efficacy of the proposed technique is demonstrated with numerical simulation of uncertain second order system. The observer-based model following DSMC technique is also validated through experimentation on Quanser DC servo motor. Results show the effectiveness of the combination of the controller-observer design for position control of DC motor against uncertainties and sensor noise. The technique is robust due to appropriate estimation and follows the model precisely which improves overall life of the system. The stability of the designed observer-based control scheme is provided by Lyapunov theory.
Keywords: Dynamic sliding mode control, Inertial delay observer, DC servo motor, Lyapunov theory
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65-77 |
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On Reliability: A Mathematical Fault Tree
M. S. Fahmy, A. I. Ahmed, M. Khalil Faculty of Engineering, October University for Modern Sciences and Arts (MSA), Egypt
Fault tree analysis (FTA) is a top down approach that was initially used and developed in Bell laboratories in the year 1962 by H Watson and A Mearns for the intercontinental ballistic missile (ICBM) system for the US air force called the Minuteman System. Since then, the technique has been adopted and adapted by many companies who are interested in reliability engineering and dangerous technology. Today FTA is widely used in system safety and reliability engineering, aerospace, nuclear power, chemical and process, pharmaceutical, petrochemical and other high-hazard industries; but is also used in fields as diverse as risk factor identification relating to social service system failure and in software engineering for debugging purposes and is closely related to cause-elimination technique used to detect bugs. Now FTA is considered as one of the most important system reliability and safety analysis techniques. Fault tree analysis has proved to be a useful analytical tool to analyze the potential for system or machine failure by graphically and mathematically representing the system itself. It is a top-down approach that reverse-engineers the root causes of a potential failure through the root cause analysis process. Our main contribution is to develop a mathematical theory of fault tree analysis using some statistical concepts relating to probability of series and parallel systems to set up a mathematical model that represent any hierarchical control system to calculate its reliability for both homogeneous and nonhomogeneous structures. A Fault Tree is a hierarchical model used to analyze the probability that an event will occur. Fault Tree provides all the tools needed to build graphic representations of large-scale problems gracefully so we can use it to set up a mathematical model that represent any hierarchical control system and evaluate its reliability using our general mathematical formula that represent the structure in its two cases. The graphical representation (fault tree diagram) for a hierarchical controlled system enabled us to set up a mathematical general formula that help us to evaluate the reliability of the system in general case (nonhomogeneous structure) and another derived formula for the special case (homogeneous structure). This analysis may help to understand how one or more small failure events lead to a catastrophic failure.
Keywords: Reliability, Mathematical Modeling, Analysis of Fault Tree, Serial and Parallel Systems
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78-85 |
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A TESTING-EFFORT BASED SRGM INCORPORATING IMPERFECT DEBUGGING AND CHANGE POINT
Umashankar Samal, ,Shivani Kushwaha, Ajay Kumar Department of Applied Sciences, ABV-IIITM Gwalior, Gwalior-474015, MP, India
In this paper, a scheme for constructing software reliability growth model based on Non-Homogeneous Poisson Process is proposed. Here, we consider the software reliability growth model that incorporates with imperfect debugging, change point and testing effort. However, most researchers assume a constant detection rate per fault in deriving their software reliability models. They suppose that all faults have equal probability of being detected during the software testing process, and the rate remains constant over the intervals between fault occurrences. In reality, the fault detection rate strongly depends on the skill of test teams, program size, and software testability. Also in most realistic situations, fault repair has associated with a fault re-introduction rate due to imperfect debugging phenomenon. In this case, the fault detection rate and fault introduction rate will be changed during the software development process. Therefore, here we incorporate both generalized logistic testing-effort function, change-point parameter into software reliability modelling. The Least Square Estimation approach is used to estimate the unknown parameters of the new model. So in our new proposed model we collect software testing data from real application and utilize it to illustrate the proposed model. Experimental results show that the proposed framework to incorporate both testing-effort and change-point for Imperfect-Debugging SRGM has a fairly accurate prediction capability.
Keywords: Stochastic software reliability model, Non-homogeneous Poisson process, Imperfect debugging, Testing effort, Change point.
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86-93 |
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A New Pi-Exponentiated Method for Constructing Distributions with an Application to Weibull Distribution
M. A. Lone Department of Statistics, University of Kashmir, Srinagar, India
T. R. Jan Department of Statistics, University of Kashmir, Srinagar, India
A novel method for generating families of continuous distributions is presented by introducing a new parameter referred as Pi-Exponentiated Transformation (PET). Various properties of the PET method have been obtained. The method has been specialized on two-parameter Weibull distribution, and a new distribution called Pi-Exponentiated Weibull (PEW) is attained. A comprehensive mathematical treatment of the new proposal is provided. Closed-form expressions for the density function, distribution function, reliability function, hazard rate function have been provided. The PEW distribution is quite flexible, and it can be used to model data with decreasing, increasing or bathtub shaped hazard rates. Simulation study has been carried out to assess the behavior of the model parameters. Finally, the effectiveness of the suggested method is demonstrated by examining two real-life data sets.
Keywords: Pi-Exponentiated Transformation; Quantile Function; Reliability Function; Mean Waiting Time; Maximum Likelihood Estimation.
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94-109 |
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A COMPREHENSIVE CASE STUDY ON INTEGRATED REDUNDANT RELIABILITY MODEL USING k-out-of-n CONFIGURATION
Srinivasa Rao Velampudi Department of Sciences and Humanities, Raghu Institute of Technology, Visakhapatnam, Andhra Pradesh, India
Sridhar Akiri Department of Mathematics, GITAM School of Science, GITAM (Deemed to be University), Visakhapatnam, Andhra Pradesh, India
Pavan Kumar Subbara Department of Mathematics, GITAM School of Science, GITAM (Deemed to be University), Bangalore Campus, Karnataka, India
Yadavalli V S S Department of Industrial & Systems Engineering, Pretoria University, 0002 Pretoria, South Africa
Designers may introduce a system with multiple technologies in series to improve system efficiency. The configuration can be applied to k out of n systems if each technology contains k out of n factors. The k out of n configuration method is successful until every component of the system is successful. The efficiency of the entire system is more in amount than that of a single system factor in a k out of n shape. An Integrated Reliability Model (IRM) for the k out of n, here, an additional system is suggested to account for both the efficiencies of the factors and the number of factors in every phase and the different constraints to optimize the efficiency of the system. To enhance system efficiency, the authors employed the numerous methods of Lagrangean approach to determine the numbers and efficiency of the factors as well as the reliabilities of the phase under different parameters namely load, size, and cost. The dynamic programming approach and simulation method have been adapted to attain an integer result as well as to see the values real.
Keywords: Reliability Theory, IRM, Lagrangean Approach, Stage Efficiency, D P Approach, System Efficiency
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110-119 |
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WEIBULL COMPARISON BASED ON RELIABILITY, AVAILABILITY, MAINTAINABILITY, AND DEPENDABILITY (RAMD) ANALYSIS
Anas Sani Maihulla Department of Mathematics, Sokoto State University, Sokoto-Nigeria
Ibrahim Yusuf Department of Mathematical sciences, Bayero University, Kano-Nigeria
Saminu I. Bala Department of Mathematical sciences, Bayero University, Kano-Nigeria
As a continuous probability distribution, the Weibull distribution is widely used in the study of reliability, availability and other life data. In this research, we propose the RAMD analysis to estimate the three-parameter Weibull distribution. The estimation of the distribution parameters is an important problem that has received a lot of attention from researchers because of their effects in several measurements. The real data results indicate that our proposed estimation method is significantly consistent in estimation compared to the RAMD analysis method. The numerical values of filtration system reliability and availability were calculated using Maple software. The system of first-order differential equations is formulated using a mnemonic approach and solved recursively. Several scenarios were examined to determine the impact of the models under consideration. The calculations were done with Maple 13 software. Other reliability measures such as mean time to failure (MTTF), mean time to repair (MTTR), and dependability ratio was estimated. The comparative analysis was conducted using a reverse osmosis (RO) filtration system.
Keywords: Availability, life data, Weibull-distribution, Maple, Reliability, Reverse Osmosis
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120-132 |
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New Cosine-Generator With an Example of Weibull Distribution: Simulation and Application Related to Banking Sector
Aijaz Ahmad Department of Mathematics, Bhagwant University, Ajmer, India
Muzamil jallal Department of Mathematics, Bhagwant University, Ajmer, India
Sh.A.M. Mubarak The Higher Institute of Engineering and Technology, Ministry of Higher Education, El-Minia, Egypt
In this work, we propose a novel trigonometric-based generator entitled the "New Cosine-Generator" to acquire elevated distribution adaptability. This generator is formed without the insertion of extra parameters. Adopting the Weibull distribution as the baseline distribution, and this distribution is referred to as the New Cosine-Weibull Distribution. Several statistical features of the investigated distribution were studied, including moments, moment generating functions, order statistics, and reliability measures. For different parameter values, a graphical representation of the probability density function (pdf) and the cumulative distribution function (cdf) is provided. The distribution̉s parameters are determined using the well-known maximum likelihood estimation approach. Finally, simulation analysis and an application is used to evaluate the effectiveness of the distribution.
Keywords: Cosine function, moments, maximum likelihood estimation, reliability indicators, simulation.
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133-145 |
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ON THE INFERENCES AND APPLICATIONS OF WEIBULL HALF LAPLACE {EXPONENTIAL} DISTRIBUTION
Adeyinka S. Ogunsanya Department of Statistics, University of Ilorin, Kwara State, Nigeria Correspondence
Obalowu Job Department of Statistics, University of Ilorin, Kwara State, Nigeria
The study of probability distribution has expanded the field of statistical modelling of real life data. It has also provided solution to the problems of skewed data which often violate the normality. This research work introduces a new T -Half-Lapalace{Exponential} family with a novel Half-Laplace distribution as baseline distribution with specific interest in three-parameter lifetime model called the Weibull-Half-Lapalace{Exponential} (W-HLa{E}) distribution. The W-HLa{E} model is capable of modeling various shapes of aging events. The W-HLa{E} distribution is derived by combining Half-Laplace and Weibull distribution using the quartile function of Exponential distribution. Some of its statistical properties such as the mean, mode, quantile function, median, variance, standard deviation, skewness, and kurtosis are derived. Other statistical properties such as survival function, hazard rate, moments, asymptotic limit, order statistics, and entropy which is the measure of uncertainty of a random variable are derived and studied. The parameter estimation method adopted in this study is the maximum likelihood method. The graphs of W-HLa{E} at different values of shape and scale parameters show that the distribution is unimodal hence the mode is given it is positively skewed with a steep peak. A simulation study is carried on the new proposed distribution using maximum likelihood estimation. The simulation also supported the theoretical expression of the statistical properties of the proposed distribution such as the location parameter does not affect the variance, skewness, and kurtosis of the new distribution. The importance and the flexibility of the proposed distribution in modeling some real-life data sets is demostrated inn the research. The results of the sudy shows that the proposed W-HLa{E} distribution perform better than other disribbutions in the literature.
Keywords: Laplace distribution; Half-Laplace distribution; Weibull Half-Laplace distribution; Censored data; Lifetime data; Maximum likelihood estimation
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146-160 |
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APPROXIMATE OPTIMUM STRATA BOUNDARIES FOR PROPORTIONAL ALLOCATION USING RANKED SET SAMPLING
Khalid Ul Islam Rather, S.E.H Rizvi, Manish Sharma Division of Statistics and Computer Science, SKUAST-Jammu, India
M. Iqbal Jeelani Division of Social and Basic Sciences Faculty of Forestry, SKUAST-Kashmir, India
Faizan Danish Department of Mathematics, School of Advanced Science(SAS) VIT-AP India
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. Optimum stratification is the method of choosing the best boundaries that make strata internally homogeneous, given some sample allocation. In order to make the strata internally homogenous, the strata should be constructed in such a way that the strata variances for the characteristic under study be as small as possible. This could be achieved effectively by having the distribution of the study variable known and create strata by cutting the range of the distribution at suitable points. If the frequency distribution of the study variable is unknown, it may be approximated from the past experience or some prior knowledge (auxiliary information) obtained at a recent study. The present investigation deals with paper the problem of optimum stratification on an auxiliary variable for proportional allocation under ranked set sampling (RSS), when the form of the regression of the estimation variable on the stratification variable given the variance function is known. A cum rule of finding approximately optimum strata boundaries has been developed. Further, empirical study has been made and presented along with relative efficiency which showed remarkable gain in efficiency as compared to unstratified RSS.
Keywords: Ranked set Sampling, approximately optimum strata boundaries, auxiliary variable optimum strata width
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161-171 |
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Study of reliability of the on-tether subsystem of a tethered high-altitude unmanned telecommunication platform
Dharmaraja Selvamuthua, Adwaith HSivama, Raina Raja Indian Institute of Technology Delhi, New Delhi, Indiaa
Vladimir Vishnevsky V.A. Trapeznikov Institute of Control Science, Moscow, Russiab
High-altitude platform (HAP) are stations on an object at an altitude of around 15-50 km at a specified nominal fixed point relative to Earth. Tethered high-altitude platform (tHAP) are unmanned aerial vehicle that are connected to the ground via a tether with a lift height of 100 . 150 meters, and a multi-copter as high altitude mode. The reliability of the tHAP can be assessed with a focus on the tether that connects it to the ground. This article proposes a Markov model which obtain the reliability of the tHAP. The tether is considered to be made up of multiple wires in such a way that the tether still operates for a given number of functioning wires. The failure rates of the wires are dependent on the number of failed wires. Through the reliability analysis of the proposed Markov model, the key performance measures such as reliability of the system, mean time between failures and the probability of the system being reliable are computed. The optimal number of wires is also obtained via the numerical computation of the performance measures.
Keywords: Markov chain, reliability, tethered high-altitude platform, unmanned aerial vehicle
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172-178 |
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TRUNCATED PRANAV DISTRIBUTION: PROPERTIES AND APPLICATIONS
Kamlesh Kumar Shukla Department of Community Medicine, Noida International Institute of Medical Sciences, Noida International University, Gautam Budh Nagar, India
In this paper, truncated Pranav distribution has been proposed. The behavior of truncated Pranav distribution has been presented graphically. Moment based measures including coefficient of variation, skewness, kurtosis, and Index of dispersion have been derived and presented graphically. Nature of survival and hazard rate functions are presented graphically. Maximum likelihood method has been used to estimate the parameter of proposed model. Simulation based study of proposed distribution has also been discussed. It has been applied on two data sets and its superiority has been compare and checked using goodness of fit (AIC and K. S. test) over other truncated distributions as well as one parameter distribution, such as exponential, Lindley, Pranav, Ishita, truncated Akash, truncated Lindley, and truncated Akash distribution. It was found good fit over above-mentioned distributions. It can be considered as good lifetime distribution especially for non-skewed data.
Keywords: Akash distribution, Lindley distribution, Moments, Right Truncated, Left Truncated
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179-192 |
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MARKOV APPROACH FOR RELIABILITY AND AVAILABILITY ANALYSIS OF A FOUR UNIT REPAIRABLE SYSTEM
A. D. Yadav, N. Nandal, S.C. Malik Department of Statistics, M.D. University, Rohtak
Efforts have been made to analyze reliability and availability of a repairable system using Markov approach. The system has four non-identical units which work simultaneously. The system is assumed as completely non-functional at the failure of all the units. The failure and repair times as usual follow negative exponential distribution. The reliability measures of the system have been obtained by solving the Chapman-Kolmogorov equations using Laplace transform technique. The values of availability, reliability and mean time to system failure have been evaluated for particular values of the parameters considering all the units identical in nature. The effect of failure rate, repair rate and operating time on reliability, MTSF and availability has been studied. The application of the work has also been discussed with a real life example.
Keywords: Repairable System, Non-Identical Units, Markov Approach, Reliability Measures, Chapman-Kolmogorov Equations, Laplace Transform Technique
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193-205 |
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A Novel Extended Version of the Ailamujia Inverted Weibull Distribution
Idzhar A. Lakibul Department of Mathematics and Statistics Mindanao State University -Iligan Institute of Technology Iligan City, Philippines idzhar.lakibul@g.msuiit.edu.ph
Statististical distributions with support on the set of non-negative real numbers are important in modelling and describing the behaviour of lifetime data. Ailamujia distribution is one of the non-negative continuous distribution that has an application in lifetime data. In this paper, a new three-parameter non-negative continuous distribution which is an extension of the Ailamujia Inverted Weibull distribution is introduced. This extended distribution is labeled as the Cubic Transmuted Ailamujia Inverted Weibull distribution. The proposed distribution is derived from the cubic transmuted family of distributions by specifying Ailamujia Inverted Weibull distribution as a baseline distribution. The probability density function of the proposed distribution is derived and some of its plots are presented. It can be observed that the proposed distribution can model the data which are exponentially and skewed unimodal right tailed data. In addition, survival and hazard functions of the proposed distribution are derived. It reveals that the hazard function of the proposed distribution can model both monotonic and non-monotonic decreasing failure rate behaviour of the data. Some properties of the proposed distribution such as its moments, moment generating function, mean, variance are derived. The Maximum Likelihood approach is used to estimate the proposed distribution parameters. Furthermore, parameter estimates as well as the performance of the proposed distribution is investigated by utilizing two sets of lifetime data. For point of comparison, this paper uses the following criteria: Akaike Information Criterion, Bayesian Information Criterion, Kolmogorov -Smirnov statistics, Anderson-Darling and Cramer-von Mises. Results show that for both sets of data, the proposed distribution produce better estimate as compared to the Quasi Suja and the Weibull-Lindley distributions. So, the proposed distribution consider as the best model for modelling the given two real datasets.
Keywords: Ailamujia distribution, Ailamujia Inverted Weibull distribution, Cubic transmuted family of distributions
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206-213 |
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Reliability Measures of a 2-out-of-3: G System with Priority and Failure of Service Facility during Repair
Anuradha Department of Statistics, Maharshi Dayanand University Rohtak, India
S.C. Malik Department of Statistics, Maharshi Dayanand University Rohtak, India
Aim. The objective of this paper is to describe a particular case of the k-out-of-n: G system for k=2 and n=3 with different repair policies and to discuss the application of the proposed in a toxic waste incinerator. Methods. The system has all the three units identical in nature. The system model is developed using semi-Markov process and regenerative point technique. The preventive maintenance and repair activities of the units are carried out immediately by a single service facility whenever desires. The service facility is subjected to failure during repair of the units while it does preventive maintenance of the units without any problem. The failed service facility undergoes for treatment to restore its efficiency to perform the remaining jobs with full capacity. The provision of priority to preventive maintenance of the units has been made over the repair in order to avoid the earlier failure of the system. Findings. The measures that can affect and enhance the performance of the system have been discussed for arbitrary values of the rates which follow some arbitrary distributions including the negative exponential. The system is analysed in steady state and the graphs have been drawn to see the effect of different transition rates such as failure rate, preventive maintenance rate, treatment rate, and repair rate of the units on reliability measures and the profit. The study reveals that there is a decline in these measures with the increase of the rate by which unit undergoes for preventive maintenance, failure rates of the units and service facility. However, the values of reliability measures MTSF, availability and profit function keep on increasing with the increase of treatment rate, repair rate of the unit and preventive maintenance completion rate. The profit increases if the rate with which a unit completes its preventive maintenance. Hence, implementing the preventive maintenance repair policy for a 2-out-of-3 system is beneficial as it increases the availability and hence the profit of the system.
Keywords: 2-out-of-3 System, Preventive Maintenance, Treatment Rate, Priority, Failure of Service Facility and Reliability Measures
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214-223 |
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E-Bayesian estimations for Chen distribution under Type II censoring with medical application
Athirakrishnan R. B., E. I. Abdul Sathar Department of Statistics,University of Kerala
The study focuses on the E-Bayesian estimation of a Type-II censored sample from the Chen distribution. Three distinct prior distributions for the hyper-parameters and three different loss functions are considered here for deriving the E-Bayes estimators of the scale parameter and hazard rate of above said distribution under Type-II censoring. Also derived analytical expressions for the E-MSE of the proposed estimators. Additionally, several features of the E-Bayesian estimators and E-MSEs are derived. This paper compares E-Bayesian estimation with traditional estimation methods like MLE and Bayesian. The applicability of the proposed estimators is demonstrated using a real data application. Furthermore, the credible intervals of the scale parameter estimators are also provided. The numerical analysis demonstrates that the proposed method is simpler and more feasible than traditional techniques.
Keywords: Chen distribution; Type II censoring; Bayesian estimation; E-Bayesian estimation; E-MSE. Introduction
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224-241 |
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NEW MEDIAN BASED ALMOST UNBIASED EXPONENTIAL TYPE RATIO ESTIMATORS IN THE ABSENCE OF AUXILIARY VARIABLE
Sajad Hussain University School of Business, Chandigrah University, Mohali, Gharuan - 140413, INDIA
Vilayat Ali Bhat Department of Statistics, Pondicherry University, Puducherry - 605014, INDIA
The problem of biasness and availability of auxiliary variable for the estimating population mean is a big concern, both can be handled by proposing unbiased estimators in the absence of auxiliary variable. So in this paper unbiased exponential type estimators of population mean have been proposed. The estimators are proposed in the absence of the instrumental variable called the auxiliary variable by taking the advantage of the population and the sample median of the study variable. To about the first order approximation, the theoretical formulations of the bias and mean square error (MSE) are obtained. The circumstances in which the suggested estimators have the lowest mean squared error values when compared to the existing estimators were also deduced. In comparison to the currently used estimators, it was discovered that the suggested estimators of population mean had the lowest MSE, hence highest efficiency. Also least influence from the data’s influential observations when it came to accurately calculating the population mean for skewed data. The theoretical findings of the paper are validated by the numerical study.
Keywords: Dual estimator, Median, Study variable, Unbiased Estimator, Mean square error
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242-249 |
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PERFORMABILITY OPTIMISATION OF MULTISTATE COAL HANDLING SYSTEM OF A THERMAL POWER PLANT HAVING SUBSYSTEMS DEPENDENCIES USING PSO AND COMPARATIVE STUDY BY PETRI NETS
Er. Sudhir Kumar, Dr. P.C. Tewari Department of Production & Industrial Engineering National Institute of Technology, Kurukshetra, India
This paper deals with an analysis methodology for evaluating the performance of a coal handling system utilized in a coal based thermal power plant. To simulate the interactions between the subsystems, a stochastic Petri nets technique is used. A licensed software package named Petri module of GRIF were used for computations. This work addresses the performability and cost multi-objective optimization problem for a series-parallel coal handling system of a thermal power plant having subsystem failure dependencies. Performability of subsystems has been examined in relation to variations in failure and repair rates. The Particle Swarm Optimization Technique, which is based on an algorithm discussed, has been used to optimize the results. Based upon the observation and criticality of failure, the subsystems of the coal handling system were given maintenance order priority. A decision support provided at last which will the maintenance personnelÙs to take better and informed decision while forming the maintenance policies. It has been observed that the Crusher and Tippler are crucial components that demand the full attention of plant manager.
Keywords: Petri Nets, Particle Swarm Optimization, Performability, Decision Support System
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250-263 |
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Bayesian and Non-Bayesian Inference of Exponentiated Moment Exponential Distribution with Progressive Censored Samples
Amal S. Hassan Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Egypt
Samah A. Atia Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Egypt
Hiba Z. Muhammed Department of Mathematical Statistics, Cairo University, Faculty of Graduate Studies for Statistical Research, Egypt
In this paper, a progressive type-II censoring strategy is used to estimate the parameters, reliability and hazard rate functions of the exponentiated moment exponential distribution. The maximum likelihood and Bayesian techniques have been used to estimate the proposed estimators. Gamma (informative) and uniform (non-informative) priors are taken into account under the squared error loss function to produce the Bayesian estimators. The highest posterior density interval estimations and the 95% approximate confidence intervals along with coverage probability are calculated. In order to evaluate the effectiveness of estimates produced by the Metropolis-Hastings sampling algorithms, we provide a numerical research. According to the study's findings, the Bayes estimates under informative priors are typically more accurate than other estimates.
Keywords: Exponentiated moment exponential, gamma prior, credible interval, Metropolis-Hastings, Progressive censorning
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264-281 |
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Ratio Transformation Lomax Distribution with Applications
Shamshad Ur Rasool Department of Statistics, University of Kashmir, Srinagar, India
S.P. Ahmad Department of Statistics, University of Kashmir, Srinagar, India
It has been noted in the literature on probability theory that the classical probability distributions do not adequately ft real-world data and do not exhibit non-monotonic hazard rate behavior. To overcome this limitation, researchers are focusing on the improvement of these distributions. In this manuscript, we have introduced a new probability model called Ratio Transformation Lomax Distribution (RTLD) as a new generalization of Lomax distribution. A thorough mathematical analysis of the new distribution is provided in closed form such as density function, distribution function, the r-th moment, survival function, hazard function, moment generating function, generalized entropy and also the order statistics. The new model̉s parameters are calculated using the method of maximum likelihood estimation. The proposed distribution̉s performance and adaptability is backed by three sets of real lifetime data as well as simulated data.
Keywords: Ratio Transformation Lomax distribution, hazard rate function, moments, maximum likelihood estimation
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282-300 |
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Applications and Some Characteristics of Inverse Power Cauchy Distribution
Laxmi Prasad Sapkota, Vijay Kumar Department of Mathematics & Statistics, DDU Gorakhpur University, Gorakhpur, India
Based on the power Cauchy distribution, we have purposed a new distribution called inverse power Cauchy distribution that offers greater modeling flexibility for lifetime data. Real-world data can be efficiently analyzed using the suggested model because it is analytically sound. Its density function can take on a number of different shapes, including reversed-J, symmetrical, and right-skewed. Depending on the different values of the parameters, it can adapt to different hazard forms, such as an upside-down bathtub, a monotonically increasing or decreasing curve, and others. Its moments, quantile, reliability, hazard, order statistics with density function, moment generating function, and entropy are all given with various explicit forms. The ob≠served information matrix is created when the new model̉s parameters are calculated through maximum likelihood technique. A simulation study is conducted to investigate the behaviour of maximum likelihood estimators. The proposed model gets a superior fit compared to certain well-known distributions, according to the test of goodness-of-fit we conducted. The significance of the purposed distribution is demonstrated empirically using two real-world data sets.
Keywords: Entropy, Maximum likelihood estimation, Moment, order statistics, Power Cauchy distribution
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301-315 |
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PERFORMANCE AND BEHAVIOR ANALYSIS OF WATER CIRCULATION SYSTEM OF A THERMAL POWER PLANT
Seema Sharma Professor, Department of Mathematics and Statistics, Gurukul Kangri (Deemed to be University) Haridwar, Uttarakhand, India-249404
Sushma Research Scholar, Department of Mathematics and Statistics, Gurukul Kangri (Deemed to be University) Haridwar, Uttarakhand, India-249404
This paper analyses the performance and behavior of water circulation system (WCS) of a thermal power plant in fuzzy environment. For this purpose, fuzzy technique coupled with petrinet modelling has been used. To address the vagueness in data, trapezoidal fuzzy numbers have been employed in fuzzy technique. Various reliability indicators of WCS viz. failure rate, repair time, expected number of failures, mean time between failures, reliability and availability have been computed at ±15%, ±25% and ±40% spreads using fuzzy technique. Further, fuzzy values of reliability indicators have been defuzzified employing COA method and the failure dynamics of WCS have been studied on account of decreasing / increasing trends of reliability indicators. The outcomes of this study are of great importance for plant personnel / management to enhance the availability of WCS.
Keywords: thermal power plant, water circulation system, fuzzy technique, trapezoidal fuzzy number
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316-328 |
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RELIABILITY ANALYSIS OF PARALLEL SYSTEM USING PRIORITY TO PM OVER INSPECTION
Neetu Dabas Department of Statistics, Amity University, Noida, Uttar Pradesh-201313
Reetu Rathee School of Business, Galgtias University, Greater Noida, Uttar Pradesh-203201
Abhishek Sheoran Department of Statistics, Ramanujan College, University of Delhi, Delhi-110019
Reliability optimization of a system is an extant problem. By solving these problems, new methodologies are obtained that have invent new engineering technology and changes the management perspective. Aim of the reliability analysis is to study the failure mechanisms of a system and and outcomes of the analysis serve to identify design solutions and maintenance actions for preventing the failures from occurring. So, it is used to evaluate and improve the quality of products, processes, and systems. Measurement, planning, and improvement in the reliability are the things which are well do in any business but only when efforts are focused on important problems which are highlighted by monetary values, improve reliability, reduce unreliability costs, generate more profit, and get more business. To serve this purpose, present study investigates a parallel system of two identical units which is based on several assumptions like, the system is served by one serviceman who is immediately available for service when it will call. System failure rate is fix and the failure type (repairable or replaceable) is known by inspection. The failure and repair activities are stochastically independent, and their rates are exponentially distributed. Priority to PM over inspection is given in the system. Several measures of reliability effectiveness like MTSF, availability and cost-benefit analysis of the system are obtained by semi-Markov and regenerative point approach. Reliability characteristics parameters are random variables, and results are obtained in the form of graphs and tables by changing the values of these variables one by one, while keeping other variables constant at that point. From the results we conclude how to make the given system more profitable. Findings of present system model shows that when the failure rate is low then the system obtained more profit by increasing preventive maintenance rate. On the other hand, when failure rate going high then we make the system more profitable by increasing inspection rate. These insights of modelling and analysis helps the system developers and managers to make good choices of action against specified criteria that managing engineered products and industrial plants safely and reliably. This leads to more profit and making a business more growing.
Keywords: Parallel system, priority, inspection, semi-Markov, regenerative points, repair activities, profit.
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329-339 |
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SOME USEFUL PATHWAY MODELS FOR RELIABILITY ANALYSIS
T. Princy Department of Statistics Cochin University of Science and Technology Cochin-682022, Kerala, India
In this paper, we first discuss pathway model in general. Then a special case for the real scalar variable is considered. This special case is relevant in reliability problems. In the pathway model, an arbitrary function is introduced so that the hazard function resulting from this model is of a given shape such as a bathtub type hazard function. The model is also derived by using an entropy optimization procedure by introducing a new entropy measure. It is shown that a large number of densities in current use are connected to the pathway model. Certain combinations of pathway densities resulting in hazard functions of desired shapes, multi-component failure situation etc are examined from a reliability point of view. For further use of the proposed model, the unknown parameters are estimated using the method of maximum likelihood estimation. The behaviour of the reliability measure has been observed graphically for arbitrary values of the parameters related to the number of components and operating time.
Keywords: Pathway model, reliability analysis, hazard function, entropy optimization
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340-359 |
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REPRESENTATION OF CERTAIN LIFETIME MODELS VIA SEQUENCES OF SPECIAL NUMBERS
Christian Genest, Nikolai Kolev McGill University and Universidade de Sao Paulo
Stimulated by the work of Rz .adkowski et al. (2015, J. Nonlinear Math. Phys., 22 (2015), 374Ö380), the authors derive representations for certain classes of univariate and bivariate lifetime distributions in terms of sequences of Bell, Bernoulli, and Stirling numbers of the second kind, their generalizations, and associated polynomials. Gould Hopper polynomials are used in the bivariate case, leading to representations for large classes of distributions satisfying a law of uniform seniority for dependent lives formulated by Genest and Kolev (Scan. Act. J., 2021-8 (2021), 726Ö743).
Keywords: Bell numbers, Bernoulli numbers, Gould Hopper polynomials, law of uniform seniority, lifetime distributions, Stirling numbers of the second kind, survival functions.
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360-367 |
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POWER GENERALIZED DUS TRANSFORMATION IN WEIBULL AND LOMAX DISTRIBUTIONS
Beenu Thomas, V. M. Chacko St.Thomas College (Autonomous), Thrissur
A strong need for an appropriate lifetime model arises in reliability analysis. A large number of lifetime distributions are available in the literature. To analyze reliability data, a more suitable lifetime distribution is plausible. Power Generalized DUS (PGDUS) transformation of the lifetime model gives a solution to fit the data with more precision. PGDUS transformation of the exponential distribution is the first attempt in this regard. This new class of distributions can be used for model series systems in which the components are distributed as DUS transformations of some lifetime model. This paper introduces two novel classes of distributions using PGDUS transformation, which is a generalization of DUS transformation, with Weibull and Lomax distributions as the baseline distributions. Some analytical properties like moments, moment generating function, characteristic function, cumulant generating function, quantile function, distribution of order statistics, and Renyi entropy are derived. The maximum likelihood estimation procedure is employed to estimate the unknown parameters. Moreover, a simulation study has been conducted, and data has been analyzed for each of the proposed distributions to demonstrate how well the distributions would perform in a real-life situation. In comparison with some other recent new models, the proposed distribution is found to be a better model.
Keywords: PGDUS transformation, Weibull Distribution, Moments, Lomax Distribution, Maximum likelihood estimator, Simulation
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368-384 |
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On an extension of the two-parameter Lindley distribution
Jiju Gillariose Department of Statistics, CHRIST (Deemed to be University), Bangalore, KarnatakaÖ 560029, India
Lishamol Tomy Department of Statistics, Deva Matha College, Kuravilangad, Kerala, 686633, India
AIM: Lindley distribution has been widely studied in statistical literature because it accommodates several interesting properties. In lifetime data analysis contexts, Lindley distribution gives a good description over exponential distribution. It has been used for analysing copious real data sets, specifically in applications of modeling stress-strength reliability. This paper proposes a new generalized two-parameter Lindley distribution and provides a comprehensive description of its statistical properties such as order statistics, limiting distributions of order statistics, Information theory measures, etc. METHODS: We study shapes of the probability density and hazard rate functions, quantiles, moments, moment generating function, order statistic, limiting distributions of order statistics, information theory measures, and autoregressive models are among the key characteristics and properties discussed. The two-parameter Lindley distribution is then subjected to statistical analysis. The paper uses methods of maximum likelihood to estimate the parameters of the proposed distribution. The usefulness of the proposed distribution for modeling data is illustrated using a real data set by comparison with other generalizations of the exponential and Lindley distributions and is depicted graphically. RESULTS/FINDINGS: This paper presents relevant characteristics of the proposed distribution and applications. Based on this study, we found that the proposed model can be used quite effectively to analyzing lifetime data. CONCLUSIONS: In this article, we proffered a new customized Lindley distribution. The proposed distribution enfolds exponential and Lindley distributions as sub-models. Some properties of this distribution such as quantile function, moments, moment generating function, distributions of order statistics, limiting distributions of order statistics, entropy, and autoregressive time series models are studied. This distribution is found to be the most appropriate model to fit the carbon fibers data compared to other models. Consequently, we propose the MOTL distribution for sketching inscrutable lifetime data sets.
Keywords: Exponential distribution, Generalized family, Lindley distribution, Marshall-Olkin extended distribution, Maximum likelihood estimation
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385-402 |
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Analysing Random Censored Data from Discrete Teissier Model
Abhishek Tyagi, Bhupendra Singh, Amit Singh Nayal Department of Statistics, Chaudhary Charan Singh University, Meerut, India
Varun Agiwal Indian Institute of Public Health, Hyderabad, Telangana, India
This paper deals with the classical and Bayesian estimation of the discrete Teissier distribution with randomly censored data. We have obtained the maximum likelihood point and interval estimator for the unknown parameter. Under the squared error loss function, a Bayes estimator is also computed utilising informative and non-informative priors. Furthermore, an algorithm to generate randomly right-censored data from the proposed model is presented. The performance of various estimation approaches is compared through comprehensive simulation studies. Finally, the applicability of the suggested discrete model has been demonstrated using two real datasets. The results show that the suggested discrete distribution fits censored data adequately and can be used to analyse randomly right-censored data generated from various domains.
Keywords: Bayesian estimation; Classical estimation; Discrete Teissier distribution; Random censoring.
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403-411 |
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ON GOMPERTZ EXPONENTIATED INVERSE RAYLEIGH DISRIBUTION
Sule Omeiza Bashiru Prince Abubakar Audu University, Anyigba, Kogi State, Nigeria
Halid Omobolaji Yusuf Ekiti State University, Ado-Ekiti, Ekiti State, Nigeria
In this paper, we proposed a four parameter Gompertz Exponentiated Inverse Rayleigh Distribution. The proposed distribution is an extention of the Exponentiated Inverse Rayleigh Distribution which was compounded with the Gompertz generated family of distribution. Several of its statistical and mathematical properties including quantiles, median, moments, skewness and kurtosis are derived. Also, the reliability and hazard rate functions are derived. To estimate the new model parameters, the maximum likelihood technique is used. To evaluate the effectiveness of the estimators in this model, a simulation study was carried out and the result of the simulation study indicated that the model is consistent since the value of the mean square error decrease as sample size increases. Finally, the usefulness of the proposed distribution is illustrated with two datasets and it is discovered that this model is more adaptable when compared to well-known models.
Keywords: Maximum likelihood estimation; Skewness; Kurtosis; Probability density function; Cummulative probability distribution.
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412-424 |
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MODELLING OF RELIABILITY INDICATORS BY MEANS OF THE INTERFERENCE METHOD
Alena Breznicka, Pavol Mikus Faculty of Special Technology, Alexander Dubcek University of Trencin, Ku kyselke 469, 911 06, Trencin, Slovakia
The article describes the application of the simulation modeling of tasks of the interference theory of reliability (SSI -stress -strength interference reliability model) in the MATLAB programming language. It points to the possibility of creating your own purpose-built models designed to predict the evolution of the reliability of the technical system during the user's interactive activity. Reliability simulation by changing load and resistance parameters makes it possible to find acceptable reliability parameters.
Keywords: reliability, MATLAB programming, failure
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425-431 |
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SELECTION PROCEDURE FOR SKIP LOT SAMPLING PLAN OF TYPE SKSP-R BASED ON PERCENTILES OF EXPONENTIATED RAYLEIGH DISTRIBUTION
P. Umamaheswari Assistant Professor, Sona College of Arts & Science
K. Pradeepa Veerakumari Assistant Professor, Department of Statistics, Bharathiar University, Coimbatore, Tamil Nadu, India
S.Suganya Assistant Professor, Department of Statistics, PSG College of Arts & Science, Coimbatore, Tamil Nadu, India
In this study, acceptance sampling techniques are effective for reducing the cost and time of the submitted lots. In this hectic environment, a high level of product reliability and quality assurance is expected. Use the abbreviated life tests in the acceptance sampling plan as a result. To make a choice on the product, sampling plans with time-truncated life tests are used. This study uses percentiles under the exponentiated Rayleigh distribution to build a skip lot sampling plan of the SkSP-R type for a life test. A truncated life test may be carried out to determine the minimum sample size to guarantee a specific percentage life time of products. In particular, this paper highlights the construction of the Skip lot Sampling Plan of the type SkSP-R by considering the Singe Sampling Plan (SSP) and Double Sampling plan(DSP) as reference plans for life tests based on percentiles of Exponentiated Rayleigh Distribution (ERD). Calculations are made for various quality levels to determine the minimum sample size, prescribed ratio, and operational characteristic values. The proposed sampling plan, which is appropriate for the manufacturing industries for the selection of samples, is also analyzed in terms of its parameters and metrics. Illustrations are provided to help you comprehend the plan. In addition, it addresses the feasibility of the new strategy.
Keywords: Exponentiated Rayleigh Distribution, Percentiles, Life tests, Single Sampling Plan, SkSP ÖR.
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432-439 |
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APPLICATION OF FUZZY LINEAR PROGRAMMING APPROACH FOR SOLVING MIX-PRODUCT SELECTION PROBLEM
Mahesh M. Janolkar Department of First Year Engineering Prof Ram Meghe College of Engineering and Management Badnera-Amravati (MS India)
Kirankumar L. Bondar P. G. Department of Mathematics, Govt Vidarbh Institute of Science and Humanities, Amravati.
Pandit U. Chopade Research Supervisor, Department of Mathematics, D.S.M̉s Arts Commerce and Science College ,Jintur.
In this paper, the modified SMF system is used in the real MPS problem. This problem occurs in the production planning process where the decision maker plays an important role in making decisions in an uncertain environment. As researchers, we are trying to find the best solution for the final decision maker. SMF analyzed FLP production equipment using data actually collected from chocolate production companies. The problem of MPS incompatibility has been described. The aim of this article is to find the best UOP with high satisfaction and nonsense as the main thing. Since there are so many decisions to make, the best UOP table is defined in terms of insensitivity and satisfaction to find a solution with a high UOP level and a high level of satisfaction. OF indicates that a high UOP will not lead to a high level of satisfaction. The results of this work suggest that the best decision is based on the negative impact on the FS of the MPS. In addition, a high level of UOP is achieved when the blur is low.
Keywords: Linear Programming, Uncertainty, Fuzzy constraint, Mix-Product Selection.
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440-453 |
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STOCHASTIC ANALYSIS OF DISCRETE PARAMETRIC MARKOV CHAIN SYSTEM MODEL
Manoj Kumar D.A.V. College, Muzaffarnagar, U.P., (India)
Shiv Kumar J.V. College Baraut (Baghpat), U.P., (India)
The present paper deals with the behavior of the parallel model system of two non-identical units, warm standby models have been developed by in view of all random variables are independent. Initially priority unit is working and the non-priority unit is warm standby. Two repairmen are always available with the system to carry out the system operation as soon as possible, skilled repairmen carry out phase-1 repair while ordinary repairmen carry out a phase-2 repair. The main unit is take two phases for his repair while the repair of the ordinary unit is completed in one phase. The statistical measures of the model are analyzed probabilistically by applying the regenerative point technique the distribution of failure and repair time of the system taken as a geometric distribution with different parameters.
Keywords: Geometric distribution, Steady state transition probability, MTSF, Availability, Busy period, and Cost-benefit analysis.
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454-463 |
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PHASE TYPE QUEUEING MODEL OF SERVER VACATION, REPAIR AND DEGRADING SERVICE WITH BREAKDOWN, STARTING FAILURE AND CLOSE-DOWN
G. Ayyappan, S. Meena Department of Mathematics, Puducherry Technological University, Puducherry, India
We consider a single server phase type queueing model with server vacation, repair, breakdown, degrading service, starting failure and closedown. When the arrival rate of the customer follows the Markovian Arrival Process (MAP) and the service rate of the server follows the phase-type distribution. If no one is in the system when the server is back from the vacation, then the server will wait until the customer arrives. If the customer arrives at the moment with no starting failure, then he provides service, otherwise the server immediately goes to the repair process. Here, the service rate declining until degradation fxed. After completion of K services the degradation is addressed. During the period of service, the server may get a breakdown at any moment, and then the server immediately goes for a repair process. After completing the service, he switches to the close-down process, and then he goes on vacation. Using the Matrix-Analytic method, The stationary probability vector representing the total number of customers in the system is examined. The analysis of the busy period, the mean waiting time, and cost analysis are discussed. A few signifcant performance measures are attained. Finally, some numerical examples are given.
Keywords: Phase type Distribution, Markovian Arrival Process, Degrading Service, Server Vacation, Breakdown, Repair, Starting failure, Close-down, Matrix-analytic method.
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464-483 |
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COMPARISON OF MAXIMUM LIKELIHOOD ESTIMATION AND BAYESIAN ESTIMATION ON EXPONENTIATED POWER LOMAX DISTRIBUTION
S. Amirtha Rani Jagulin, A. Venmani Department of Mathematics and Statistics, College of Science and Humanities, SRM Institute of Science and Technology, Kattankulathur, Tamil Nadu, India
The aim of the paper is to apply the Bayesian estimation under squared error loss function to the Exponentiated Power Lomax (EPOLO) distribution to estimate the parameters and then compare with maximum likelihood estimation. The reliability of the distribution is analyzed by computing survival and hazard function for the exponentiated power lomax distribution. The mean square error will help to compare the different estimates like Bayesian and maximum likelihood estimation to decide the best one. Bayesian estimation and the maximum likelihood estimation are discussed for the distribution. A simulation study is done using the R programming software to generate random values and estimate the parameters for different n = 15, 30, 50, 100 and parameter values taken as 0.5 and 1.5. At n=100 and c= 0.5 the mean square error of bayes and mle are same and survival and hazard function mean square error are decreases when the sample size increases, this indicates the distribution is fitted good in all areas.
Keywords: Exponentiated Power Lomax (EPOLO) distribution, Bayesian estimation, Reliability, Mean Square Error (MSE), Monte Carlo simulation.
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484-490 |
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HUNTSBERGER TYPE SHRINKAGE ENTROPY ESTIMATOR FOR VARIANCE OF NORMAL DISTRIBUTION UNDER LINEX LOSS FUNCTION
Priyanka Sahni Department of Mathematics, Maharshi Dayanand University, Rohtak
Rajeev Kumar Department of Mathematics, Maharshi Dayanand University, Rohtak
The aim of the paper is to develop a better estimator for the entropy function of variance of the normal distribution. The present paper proposes a Huntsberger type shrinkage estimator of the entropy function for the variance of normal distribution. This Huntsberger type shrinkage entropy estimator is based on test statistic, which eliminates arbitrariness of choice of shrinkage factor. For the proposed estimator risk expressions under LINEX loss function have been calculated. Numerical computations and graphical analysis is carried out for risk and relative risks for the proposed estimators. It is also compared with the existing best estimator for distinct degrees of asymmetry and different levels of significance. Based on the criteria of relative risk, it is found that the proposed Huntsberger type shrinkage estimator is better than the existing estimator for the entropy function of variance of normal distribution for smaller values of level of significance and degrees of freedom.
Keywords: Normal distribution, entropy function, shrinkage estimation, LINEX loss function, level of significance, relative risk.
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491-499 |
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THE INVERSE BURR LOG-LOGISTIC DISTRIBUTION: PROPERTIES, APPLICATIONS AND DIFFERENT METHODS OF ESTIMATION
Festus C. Opone Department of Statistics, Delta State University of Science and Technology, Ozoro, Nigeria festus.opone@physci.uniben.edu
Kadir Karakaya Department of Statistics, Selcuk University, Konya, Turkey
Francis E.U. Osagiede Department of Mathematics, University of Benin, Benin City, Nigeria.
Lifetime distributions have played a significant role in lifetime data analysis. Despite the numerous distributions in literature, there have been several motivations for developing new ones. In this paper, a new lifetime distribution is proposed. Some important functions of the new distribution, such as probability density, cumulative distribution, survival, hazard, and quantile are derived in closed form. Some distributional properties such as moments, moment generating function, linear representation, probability weighted moments, etc. are obtained. Some estimators such as the least square estimator (LSE), the weighted least square estimator (WLSE), the Anderson-Darling estimator (ADE) and the Cramer-von Mises estimator (CvME) are investigated for three unknown parameters. The efficiency of the estimators is checked via Monte Carlo simulation based on the bias and mean square error criteria. The usability of the new distribution is investigated with two real data sets and empirical results obtained reveal that the new distribution offers a promising fit for the data sets under study.
Keywords: Bur distribution, log-logistic distribution, parameter estimation, quantile
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500-515 |
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ON STRESS STRENGTH RELIABILITY ESTIMATION OF EXPONENTIAL INTERVENED POISSON DISTRIBUTION
K. Jayakumar, C. J. Rehana Department of Statistics, University of Calicut, Kerala-673 635, India
Aim. Inferences on stress strength reliability has many applications in reliability theory. In this paper, we made a comparative study of Simple random sampling, Ranked set sampling and Percentile ranked set sampling by considering the estimation of stress strength reliability when the stress and strength are independently following Exponential Intervened Poisson distribution. Methods. We used the method of Maximum likelihood estimation for finding the estimate of stress strength reliability. The efficiency of the proposed estimators of stress strength reliability using three sampling schemes are compared via a Monte Carlo simulation study. Also at the end of the study a real life data set is analyzed to understand the usefulness of the study. Results. The findings in this study are the stress strength reliability estimates under Percentile ranked set sampling performs better than the corresponding ones under Simple random sampling and Ranked set sampling. Conclusion. So we can conclude that making refinements in Ranked set sampling increases the efficiency of estimators by minimizing the chance of incorrect ranking.
Keywords: maximum likelihood estimation, percentile ranked set sampling, ranked set sampling, stress strength reliability.
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516-526 |
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A DISCRETE PARAMETRIC MARKOV-CHAIN SYSTEM MODEL OF A TWO-UNIT STANDBY SYSTEM WITH TWO TYPES OF REPAIR
Laxmi Raghuvanshi, Rakesh Gupta, Pradeep Chaudhary Department of Statistics Ch. Charan Singh University, Meerut-250004 (India)
The aim of the present paper is to deal with the cost-benefit analysis of a two identical unit cold standby system model. There are two modes of a unit say Normal(N) and Total failure(F). When a unit operates then any of the two types of failure minor or major may occur some fixed known probabilities. Two repairmen are always available with the system to repair a unit failed with minor or major fault respectively. Upon failure of an operative unit the cold standby unit starts operations instantaneously with a perfect switching device. After minor and major repair of a failed unit it becomes as good as new. The distributions of failure times of minor and major faults and each type of repair time are assumed to follow geometric distributions with different parameters. Using regenerative point technique with the basic tools of probabilistic argument and Laplace Transform various important measures of system effectiveness useful to system designers and operations managers have been obtained.
Keywords: Cold standby, transition probabilities, mean sojourn time, regenerative pint, MTSF, geometric distribution.
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527-538 |
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Transmuted Exponentiated Kumaraswamy Distribution
Jeena Joseph, Meera Ravindran Department of Statistics St. Thomas’ College (Autonomous), Thrissur, India
In this paper, a generalization of the Exponentiated Kumaraswamy distribution referred to as the Transmuted Exponentiated Kumaraswamy distribution is proposed. The new transmuted distribution is developed using the quadratic rank transmutation map. The mathematical properties of the new distribution is provided. Explicit expressions are derived for the moments, incomplete moments, moment generating function, quantile function, entropy, mean deviation and order statistics. Survival analysis is also performed. The distribution parameters are estimated using the method of maximum likelihood. Simulation of random variables is performed in order to investigate the performance of the estimates. An analysis using real life data is conducted to demonstrate the usefulness of the proposed distribution.
Keywords: Bonferroni and Lorenz curves; Hazard function; Maximum likelihood estimation; Moments; Transmuted Exponentiated Kumaraswamy Distribution; Transmuted family.
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539-552 |
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A NONPARAMETRIC CONTROL CHART FOR JOINT MONITORING OF LOCATION AND SCALE
Vijaykumar Ghadage Department of Statistics Vidnyan Mahavidyalaya Sangola (MS)-413307, India
Vikas Ghute Department of Statistics Punyashlok Ahilyadevi Holkar Solapur University Solapur (MS)-413255, India
Traditional control charts are based on the assumption that the process observations are normally distributed. However, in many applications, there is insufficient information to justify this assumption. Thus, nonparametric control charts have been designed in literature to monitor location parameter and scale parameter of a process. In this paper, a single nonparametric control chart based on modified Lepage test is proposed for simultaneously monitoring of location and scale parameters of any continuous process distribution. The charting statistic combines two nonparametric test statistics namely Baumgartner test for location and Ansari-Bradely test for scale. The performance of the proposed chart is examined through simulation studies in terms of the mean, the standard deviation, the median and some percentiles of the run length distribution. The average run length (ARL) performance of the proposed chart is compared with that of the existing nonparametric Shewhart-Cucconi (SC) and Shewhart-Lepage (SL) charts for joint monitoring of location and scale.
Keywords: Control chart; average run length; joint monitoring; nonparametric tests; location parameter; scale parameter.
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553-563 | |||
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Maintenance policy costs considering imperfect repairs
Allan Jonathan da Silva Production engineering, CEFET/RJ Federal Center for Technological Education, Itaguai, 23812-101, RJ, Brazil
Objective: This paper extends the analysis of imperfect preventive maintenance interspaced with minimal repairs. The aim is to find the intervals of future scheduled maintenance actions considering different recovery factors and costs. Methods: The optimal preventive maintenance scheduling are obtained by minimizing the overall maintenance costs. Minimal repairs interspersed with scheduled imperfect preventive maintenance actions are considered. The model parameters of the power law process are estimated using the maximum likelihood estimation method and a Differential Evolution algorithm is used to solve the maximization problem. Results: The optimal preventive maintenance periods for different levels of maintenance restoration with respect to corrective and preventive maintenance costs are found. Graphs are drawn to highlight the effect of future maintenance costs and the hazard function paths. It is shown that the preventive maintenance becomes more frequent as the equipment ages and the hazard function increases. Also, it is perceived that the scheduled maintenance intervals become shorter as the corrective maintenance becomes more expensive. Conclusion: A hazard rate model which considers minimal repairs interspersed with scheduled imperfect preventive maintenance provides a useful tool for defining the optimal maintenance policy. The results obtained in this paper show that maintenance cost varies widely according to the recovery factor of the maintenance action and that the optimal interval of two consecutive preventive maintenance actions strongly depends on the costs.
Keywords: Reliability, imperfect maintenance, proportional age reduction model, maintenance costs, power law model.
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564-574 | |||
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A Generalization of Lindley Distribution: Characterizations, Methods of Estimation and Applications
A. Mohammed Shabeer, K. Jayakumar Department of Statistics, University of Calicut, India
Bindu Krishnan Department of Data Science, CS & IT, Jain (Deemed-to-be-University), India
Lindley distribution is a lifetime model with application in survival analysis and reliability theory problems often centred around its increasing hazard rate function and flexibility over exponential distribution. In this paper, we introduce a new generalization of the Lindley distribution referred to as Lindley Truncated Negative binomial (LTNB) distribution. The LTNB model has increasing, decreasing and upside-down bathtub (UBT) shapes for the hazard rate function. Various properties of the LTNB distribution are studied including moments, quantiles, and stochastic ordering. Characterizations of the new distribution are obtained. Maximum likelihood, Cramer-von-Mises, ordinary and weighted least squares methods of estimation are utilized to obtain the estimators of the model parameters. A simulation study is carried out to assess and compare the performance of different estimates. An autoregressive time series model with the LTNB as marginal is developed. The model is fitted to bladder cancer data set to show how the proposed model works in practice.
Keywords: Autoregressive Models, Characterizations, Lindley distribution, Maximum Likelihood, Stochastic Ordering.
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575-588 | |||
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RECOVERY PERIOD OF AIR TRANSPORTATION: A FORECAST WITH VECTOR ERROR CORRECTION MODEL
Tuzun Tolga Inan Bahcesehir University tuzuntolga.inan@sad.bau.edu.tr
Air transport is the primary module of civil aviation and because of its nature, air transport has been simultaneously affected by Pandemics and crises. The influence of COVID-19 was more devastating than the other Pandemics and crises due to its global effect. This effect has continued a long period that still this effect exists now with a slight trend. The aim of this study is to analyse the selected variables that shows the past and future trend of air transportation related to operational and financial status. These variables are the primary ones that can define the countries' general status in air transport. The forecasting results are examined by 9-months forecasting with Vector Error Correction Model. It is forecasted that slightly decreasing trend will proceed in the following 9≠months for passenger transportation due to fall and winter seasons. It is forecasted that slightly upward trend will proceed in the following 3-months and slightly decreased in the other 6-months for cargo transportation due to potential economic crisis in 2023. The originality of this paper is the first research related to analyse passenger and freight transportation together with the operational and financial parameters that defined in the sample of data and methodology sections.
Keywords: passenger load factor, cargo load factor, vector error correction model, air transportation, recovery period.
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589-606 | |||
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RELIABILITY MODELING OF TWO-UNIT GAS TURBINE SYSTEM CONSIDERING THE EFFECT OF HUMIDITY
Pinki Department of Mathematics, Maharshi Dayanand University Rohtak, India
Dalip Singh Department of Mathematics, Maharshi Dayanand University Rohtak, India
Aim. The purpose of this paper is to find the reliability measures and profit of a two-unit gas turbine power generating system incorporated with one gas turbine and one steam turbine. Effects of different humidity condition (humidity > 50%) are taken into consideration by fixing the range of temperature (5.-25.) for developing the model. At initial stage, both units (gas turbine and steam turbine) are in operative mode. If steam turbine fails, gas turbine remains in operative mode but if gas turbine fails, system goes to down state and when both unit fails, system fails. In this system we assume that failure time distribution is exponentially distributed while repair time distribution is arbitrary. Methods. In this paper we use the Laplace transform for mathematical analysis, and semi-markov process and regenerative point technique to investigate reliability measures and profit of the system. Findings. The system is analysed in steady state and different reliability measures such as mean time to system failure, availability for different cycles and for different humidity conditions, busy period, down time of the system etc. are calculated and the graphs have been drawn to see the effect of different transition rates such as failure rate and repair rate of the units for different humidity conditions on reliability measures and the profit for particular case is evaluated using the information/data collected from gas turbine power generating system located at Bawana, Delhi, India. Conclusion. Our finding shows that mean time to system failure and availability when both turbines are working decreases with increase in any one of failure rate while availability when only gas turbine is working increases with increase in steam turbine failure rate and profit for plant decreases with increase in failure rates. From this we concluded that availability for the fixed range of temperature (5.-25.) is higher when humidity is >50% as compared to when humidity is .50%. Thus, a comprehensive study of gas turbine system may be helpful to those who are involved in power generating industry.
Keywords: Gas Turbine, Steam Turbine, Failure Rate, Reliability Measures
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607-617 | |||
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