Abstract In the area of stress-strength models, there has been a large amount of work regarding the estimation of the reliability R = Pr ( X < Y ) {R=Pr(X
摘要在应力-强度模型领域，关于可靠性R= Pr(X
{"title":"On the Reliability for Some Bivariate Dependent Beta and Kumaraswamy Distributions: A Brief Survey","authors":"I. Ghosh","doi":"10.1515/eqc-2018-0029","DOIUrl":"https://doi.org/10.1515/eqc-2018-0029","url":null,"abstract":"Abstract In the area of stress-strength models, there has been a large amount of work regarding the estimation of the reliability R = Pr ( X < Y ) {R=Pr(X<Y)} . The algebraic form for R = Pr ( X < Y ) {R=Pr(X<Y)} has been worked out for the vast majority of the well-known distributions when X and Y are independent random variables belonging to the same univariate family. In this paper, forms of R are considered when ( X , Y ) {(X,Y)} follow bivariate distributions with dependence between X and Y. In particular, explicit expressions for R are derived when the joint distribution are dependent bivariate beta and bivariate Kumaraswamy. The calculations involve the use of special functions.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"11 1","pages":"115 - 121"},"PeriodicalIF":0.0,"publicationDate":"2019-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75367308","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The traffic intensity (ρ) is a vital parameter of queueing systems because it is a measure of the average occupancy of a server. Consequently, it influences their operational performance, namely queue lengths and waiting times. Moreover, since many computer, production and transportation systems are frequently modelled as queueing systems, it is crucial to use control charts to detect changes in ρ. In this paper, we pay particular attention to control charts meant to detect increases in the traffic intensity, namely: a short-memory chart based on the waiting time of the n-th arriving customer; two long-memory charts with more sophisticated control statistics, and the two cumulative sum (CUSUM) charts proposed by Chen and Zhou (2015). We confront the performances of these charts in terms of some run length related performance metrics and under different out-of-control scenarios. Extensive results are provided to give the quality control practitioner a concrete idea about the performance of these charts.
{"title":"Comparing Short and Long-Memory Charts to Monitor the Traffic Intensity of Single Server Queues","authors":"Marta Santos, M. Morais, A. Pacheco","doi":"10.1515/eqc-2018-0026","DOIUrl":"https://doi.org/10.1515/eqc-2018-0026","url":null,"abstract":"Abstract The traffic intensity (ρ) is a vital parameter of queueing systems because it is a measure of the average occupancy of a server. Consequently, it influences their operational performance, namely queue lengths and waiting times. Moreover, since many computer, production and transportation systems are frequently modelled as queueing systems, it is crucial to use control charts to detect changes in ρ. In this paper, we pay particular attention to control charts meant to detect increases in the traffic intensity, namely: a short-memory chart based on the waiting time of the n-th arriving customer; two long-memory charts with more sophisticated control statistics, and the two cumulative sum (CUSUM) charts proposed by Chen and Zhou (2015). We confront the performances of these charts in terms of some run length related performance metrics and under different out-of-control scenarios. Extensive results are provided to give the quality control practitioner a concrete idea about the performance of these charts.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"7 1","pages":"18 - 9"},"PeriodicalIF":0.0,"publicationDate":"2019-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82367805","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract This paper deals with predicting censored data in a general form for the underlying distribution based on generalized progressive hybrid censoring scheme. A conjugate prior is used and the predictive reliability function is obtained in the one-sample case. The special case of linear exponential distributed observations is considered and completed with numerical results.
{"title":"Bayesian Prediction Bounds for the Exponential-type Distribution Based on Generalized Progressive Hybrid Censoring Scheme","authors":"M. S. Kotb","doi":"10.1515/eqc-2018-0012","DOIUrl":"https://doi.org/10.1515/eqc-2018-0012","url":null,"abstract":"Abstract This paper deals with predicting censored data in a general form for the underlying distribution based on generalized progressive hybrid censoring scheme. A conjugate prior is used and the predictive reliability function is obtained in the one-sample case. The special case of linear exponential distributed observations is considered and completed with numerical results.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"28 1","pages":"101 - 93"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88497979","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this article, a generalization of the Weibull distribution called Harris extended Weibull distribution is studied, and its properties are discussed. We fit the distribution to a real-life data set to show the applicability of this distribution in reliability modeling. Also, we derive a reliability test plan for acceptance or rejection of a lot of products submitted for inspection with lifetimes following this distribution. The operating characteristic functions of the sampling plans are obtained. The producer’s risk, minimum sample sizes and associated characteristics are computed and presented in tables. The results are illustrated using two data sets on ordered failure times of products as well as failure times of ball bearings.
{"title":"On a Generalization of the Weibull Distribution and Its Application in Quality Control","authors":"K. K. Jose, Lishamol Tomy, Sophia P. Thomas","doi":"10.1515/eqc-2018-0011","DOIUrl":"https://doi.org/10.1515/eqc-2018-0011","url":null,"abstract":"Abstract In this article, a generalization of the Weibull distribution called Harris extended Weibull distribution is studied, and its properties are discussed. We fit the distribution to a real-life data set to show the applicability of this distribution in reliability modeling. Also, we derive a reliability test plan for acceptance or rejection of a lot of products submitted for inspection with lifetimes following this distribution. The operating characteristic functions of the sampling plans are obtained. The producer’s risk, minimum sample sizes and associated characteristics are computed and presented in tables. The results are illustrated using two data sets on ordered failure times of products as well as failure times of ball bearings.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"62 1","pages":"113 - 124"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78880665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The reliability properties of beta-transformed random variables are discussed. A necessary and sufficient condition for a beta-transformed geometric random variable to follow a power series distribution is derived. It is shown that a beta-transformed member of the Katz family does not belong to the Katz family unless it is a geometric distribution, thereby getting a characterization.
{"title":"Some Reliability and Other Properties of Beta-Transformed Random Variables","authors":"M. Sreehari, E. Sandhya, V. K. Mohamed Akbar","doi":"10.1515/eqc-2018-0017","DOIUrl":"https://doi.org/10.1515/eqc-2018-0017","url":null,"abstract":"Abstract The reliability properties of beta-transformed random variables are discussed. A necessary and sufficient condition for a beta-transformed geometric random variable to follow a power series distribution is derived. It is shown that a beta-transformed member of the Katz family does not belong to the Katz family unless it is a geometric distribution, thereby getting a characterization.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"125 1","pages":"83 - 92"},"PeriodicalIF":0.0,"publicationDate":"2018-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85260048","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract Reliability sampling plans are used for determining the acceptability of any product. In this paper, reliability sampling plans for acceptance or rejection of a lot of products submitted for inspection are developed when the lifetimes follow the Gumbel-uniform distribution. The sampling plan proposed here can save the test time in practical situations. Some tables are also provided for the new sampling plans so that this method can be used conveniently by practitioners. Operating characteristic values and minimum ratios of the true value and the required value of the parameter with a given producers risk with respect to the newly developed sampling plans are also presented. The new test plan is applied to ordered failure times of software release to illustrate its use in industrial contexts.
{"title":"Reliability Test Plan for the Gumbel-Uniform Distribution","authors":"K. K. Jose, Jeena Joseph","doi":"10.1515/eqc-2017-0011","DOIUrl":"https://doi.org/10.1515/eqc-2017-0011","url":null,"abstract":"Abstract Reliability sampling plans are used for determining the acceptability of any product. In this paper, reliability sampling plans for acceptance or rejection of a lot of products submitted for inspection are developed when the lifetimes follow the Gumbel-uniform distribution. The sampling plan proposed here can save the test time in practical situations. Some tables are also provided for the new sampling plans so that this method can be used conveniently by practitioners. Operating characteristic values and minimum ratios of the true value and the required value of the parameter with a given producers risk with respect to the newly developed sampling plans are also presented. The new test plan is applied to ordered failure times of software release to illustrate its use in industrial contexts.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"46 1","pages":"71 - 81"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84949691","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract In this paper, we propose a flexible extended quadratic hazard rate (EQHR) distribution with increasing, decreasing, bathtub and upside-down bathtub hazard rate function. The EQHR density is arc, right-skewed and symmetrical shaped. This distribution is also obtained from compounding mixture distributions. Stochastic orderings, descriptive measures on the basis of quantiles, order statistics and reliability measures are theoretically established. Characterizations of the EQHR distribution are studied via different techniques. Parameters of the EQHR distribution are estimated using the maximum likelihood method. Goodness of fit of this distribution through different methods is studied.
{"title":"On Extended Quadratic Hazard Rate Distribution: Development, Properties, Characterizations and Applications","authors":"F. Bhatti, G. Hamedani, Wenhui Sheng, M. Ahmad","doi":"10.1515/eqc-2018-0002","DOIUrl":"https://doi.org/10.1515/eqc-2018-0002","url":null,"abstract":"Abstract In this paper, we propose a flexible extended quadratic hazard rate (EQHR) distribution with increasing, decreasing, bathtub and upside-down bathtub hazard rate function. The EQHR density is arc, right-skewed and symmetrical shaped. This distribution is also obtained from compounding mixture distributions. Stochastic orderings, descriptive measures on the basis of quantiles, order statistics and reliability measures are theoretically established. Characterizations of the EQHR distribution are studied via different techniques. Parameters of the EQHR distribution are estimated using the maximum likelihood method. Goodness of fit of this distribution through different methods is studied.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"10 1","pages":"45 - 60"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76479892","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The log-logistic distribution is a right skewed distribution of a random variable whose logarithm has the logistic distribution. In this paper, characterizations based on truncated moments, functions of order statistics and record values are obtained. Also, limiting distributions for the extreme order statistics are studied.
{"title":"Some Characterizations of the Log-Logistic Distribution","authors":"M. Ahsanullah, A. Alzaatreh","doi":"10.1515/eqc-2018-0003","DOIUrl":"https://doi.org/10.1515/eqc-2018-0003","url":null,"abstract":"Abstract The log-logistic distribution is a right skewed distribution of a random variable whose logarithm has the logistic distribution. In this paper, characterizations based on truncated moments, functions of order statistics and record values are obtained. Also, limiting distributions for the extreme order statistics are studied.","PeriodicalId":37499,"journal":{"name":"Stochastics and Quality Control","volume":"15 1","pages":"23 - 29"},"PeriodicalIF":0.0,"publicationDate":"2018-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81023244","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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