Pub Date : 2023-01-08DOI: 10.1080/16843703.2022.2146904
L. A. Rodríguez-Picón, L. C. Méndez-González, Víctor Hugo Flores-Ochoa, Iván JC Pérez Olguín, Vicente García
ABSTRACT The stochastic modeling of performance characteristics is an important approach for the quality assessment of products. As part of the stochastic modeling, it is possible to consider different variation sources such as temporal, unit-to-unit heterogeneity and measurement error. These sources have been incorporated into different stochastic processes in the literature. Considering the unit-to-unit heterogeneity, two sources of variation can be found for certain products, particularly when the initial level and the critical threshold vary from unit-to-unit. Although, these sources have been studied separately, they have not been studied simultaneously. In this paper, a modeling approach is proposed which considers the gamma process to take into account the temporal uncertainty and the initial degradation level and the critical threshold level as two additional sources of variation. The modeling consists in first obtaining the distribution of the subtraction of the critical threshold and the initial level via a deconvolution operation. Then, the cumulative distribution function of the first passage time distribution is obtained through numerical integration. A simulation study is conducted to evaluate the performance of the proposed method, where different scenarios are analyzed. Furthermore, this approach is applied to a fatigue-crack propagation case study, from which a reliability assessment is performed.
{"title":"Degradation modeling based on the gamma process with random initial degradation level and random threshold","authors":"L. A. Rodríguez-Picón, L. C. Méndez-González, Víctor Hugo Flores-Ochoa, Iván JC Pérez Olguín, Vicente García","doi":"10.1080/16843703.2022.2146904","DOIUrl":"https://doi.org/10.1080/16843703.2022.2146904","url":null,"abstract":"ABSTRACT The stochastic modeling of performance characteristics is an important approach for the quality assessment of products. As part of the stochastic modeling, it is possible to consider different variation sources such as temporal, unit-to-unit heterogeneity and measurement error. These sources have been incorporated into different stochastic processes in the literature. Considering the unit-to-unit heterogeneity, two sources of variation can be found for certain products, particularly when the initial level and the critical threshold vary from unit-to-unit. Although, these sources have been studied separately, they have not been studied simultaneously. In this paper, a modeling approach is proposed which considers the gamma process to take into account the temporal uncertainty and the initial degradation level and the critical threshold level as two additional sources of variation. The modeling consists in first obtaining the distribution of the subtraction of the critical threshold and the initial level via a deconvolution operation. Then, the cumulative distribution function of the first passage time distribution is obtained through numerical integration. A simulation study is conducted to evaluate the performance of the proposed method, where different scenarios are analyzed. Furthermore, this approach is applied to a fatigue-crack propagation case study, from which a reliability assessment is performed.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"20 1","pages":"730 - 750"},"PeriodicalIF":2.8,"publicationDate":"2023-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41950341","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-01-01DOI: 10.1080/16843703.2022.2132450
Kuo-Hsiung Wang, Chia-Huang Wu, T. Yen
ABSTRACT With the rapid development of the Internet and hardware, cloud computing has been widely applied in various industries. Supporting services using high-quality and reliable communications equipment with an effective repair system is essential. A potential application of a cloud computing system for online data analysis services with multiple virtual machines is presented herein. The primary and standby virtual machines are both assumed to be unreliable. In this study, we analyze a retrial machine repair system with warm standbys and switching failure. When the repair facility is inaccessible, the failed machine joins a retrial pool and tries to access the repair service after a random period. The Laplace transform technique and matrix-analytical method are employed to derive the system performance measures of the reliability and mean time to failure. Moreover, numerical results are provided to investigate the effects of system parameters on system performances.
{"title":"Reliability analysis of redundant retrial machining system subject to standby switching failure","authors":"Kuo-Hsiung Wang, Chia-Huang Wu, T. Yen","doi":"10.1080/16843703.2022.2132450","DOIUrl":"https://doi.org/10.1080/16843703.2022.2132450","url":null,"abstract":"ABSTRACT With the rapid development of the Internet and hardware, cloud computing has been widely applied in various industries. Supporting services using high-quality and reliable communications equipment with an effective repair system is essential. A potential application of a cloud computing system for online data analysis services with multiple virtual machines is presented herein. The primary and standby virtual machines are both assumed to be unreliable. In this study, we analyze a retrial machine repair system with warm standbys and switching failure. When the repair facility is inaccessible, the failed machine joins a retrial pool and tries to access the repair service after a random period. The Laplace transform technique and matrix-analytical method are employed to derive the system performance measures of the reliability and mean time to failure. Moreover, numerical results are provided to investigate the effects of system parameters on system performances.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"20 1","pages":"561 - 576"},"PeriodicalIF":2.8,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44344521","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-26DOI: 10.1080/16843703.2022.2147688
Wenhui Wu, B. Wang, Jiayan Chen, Jiuzhou Miao, Qingyuan Guan
ABSTRACT In this paper, interval estimation of the two-parameter exponential distribution based on constant-stress accelerated life test data under Type-II censoring is studied. The life-stress models of the scale and location parameters are assumed to be log-linear. The maximum likelihood estimators of the model parameters are obtained. The exact and approximate confidence intervals for the parameters in the life-stress model of the scale parameter are developed. The generalized confidence intervals for the parameters in the life-stress model of the location parameter, and mean and reliability function at the designed stress level are derived. The performance of the proposed generalized confidence intervals is assessed by the Monte Carlo simulation. Finally, a real example is used to illustrate our methods.
{"title":"Interval estimation of the two-parameter exponential constant stress accelerated life test model under Type-II censoring","authors":"Wenhui Wu, B. Wang, Jiayan Chen, Jiuzhou Miao, Qingyuan Guan","doi":"10.1080/16843703.2022.2147688","DOIUrl":"https://doi.org/10.1080/16843703.2022.2147688","url":null,"abstract":"ABSTRACT In this paper, interval estimation of the two-parameter exponential distribution based on constant-stress accelerated life test data under Type-II censoring is studied. The life-stress models of the scale and location parameters are assumed to be log-linear. The maximum likelihood estimators of the model parameters are obtained. The exact and approximate confidence intervals for the parameters in the life-stress model of the scale parameter are developed. The generalized confidence intervals for the parameters in the life-stress model of the location parameter, and mean and reliability function at the designed stress level are derived. The performance of the proposed generalized confidence intervals is assessed by the Monte Carlo simulation. Finally, a real example is used to illustrate our methods.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"20 1","pages":"751 - 762"},"PeriodicalIF":2.8,"publicationDate":"2022-12-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48048350","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-15DOI: 10.1080/16843703.2022.2148884
L. C. Méndez-González, L. A. Rodríguez-Picón, Ivan Juan Carlos Pérez Olguín, Vicente García, David Luviano-Cruz
ABSTRACT In this paper, the Additive Perks Distribution (ADP) is presented; this distribution describes the behavior of the bathtub curve, which is one of the most deeply rooted concepts in reliability analysis. The proposed distribution is based on the sum of the positive and negative hazard rate functions of the Perks distribution. ADP’s statistical properties include Measures of Central Tendency, moments, moment generating function, statistical order, residual lifetime, reversed residual lifetime, Rényi entropy, time-varying, and life-stress relationship modeling presented. For estimating the ADP parameters, the Maximum Likelihood Method is used. On the other hand, the APD is tested in three case studies and compared with other distributions that can describe the failure rates in a bathtub curve. The results from the case studies showed that the APD is a good choice for describing the failure times in the shape of a bathtub curve.
{"title":"The additive Perks distribution and its applications in reliability analysis","authors":"L. C. Méndez-González, L. A. Rodríguez-Picón, Ivan Juan Carlos Pérez Olguín, Vicente García, David Luviano-Cruz","doi":"10.1080/16843703.2022.2148884","DOIUrl":"https://doi.org/10.1080/16843703.2022.2148884","url":null,"abstract":"ABSTRACT In this paper, the Additive Perks Distribution (ADP) is presented; this distribution describes the behavior of the bathtub curve, which is one of the most deeply rooted concepts in reliability analysis. The proposed distribution is based on the sum of the positive and negative hazard rate functions of the Perks distribution. ADP’s statistical properties include Measures of Central Tendency, moments, moment generating function, statistical order, residual lifetime, reversed residual lifetime, Rényi entropy, time-varying, and life-stress relationship modeling presented. For estimating the ADP parameters, the Maximum Likelihood Method is used. On the other hand, the APD is tested in three case studies and compared with other distributions that can describe the failure rates in a bathtub curve. The results from the case studies showed that the APD is a good choice for describing the failure times in the shape of a bathtub curve.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"20 1","pages":"784 - 808"},"PeriodicalIF":2.8,"publicationDate":"2022-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44835449","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-05DOI: 10.1080/16843703.2022.2138113
Lou Ren, Pei-Pei Li, Yan-Gang Zhao
ABSTRACT The reliability assessment of the project duration is essential for successful project management; this has prompted the development of various methods to assess whether a project will be completed within the target duration. In this study, an efficient and effective method for assessing the reliability of project duration based on the method of moments is proposed, which utilizes bivariate-dimension reduction technology and the third-moment reliability index. The proposed method can avoid the extensive calculations of various factors in the commonly used methods: the correlation coefficients between each pair of paths and the joint failure probability of each pair of representative paths. From two numerical examples, it can be concluded that the proposed method can obtain almost the same results as Monte Carlo simulations with less calculation.
{"title":"An efficient and effective method for reliability assessment of project duration","authors":"Lou Ren, Pei-Pei Li, Yan-Gang Zhao","doi":"10.1080/16843703.2022.2138113","DOIUrl":"https://doi.org/10.1080/16843703.2022.2138113","url":null,"abstract":"ABSTRACT The reliability assessment of the project duration is essential for successful project management; this has prompted the development of various methods to assess whether a project will be completed within the target duration. In this study, an efficient and effective method for assessing the reliability of project duration based on the method of moments is proposed, which utilizes bivariate-dimension reduction technology and the third-moment reliability index. The proposed method can avoid the extensive calculations of various factors in the commonly used methods: the correlation coefficients between each pair of paths and the joint failure probability of each pair of representative paths. From two numerical examples, it can be concluded that the proposed method can obtain almost the same results as Monte Carlo simulations with less calculation.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"20 1","pages":"689 - 706"},"PeriodicalIF":2.8,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48229778","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-05DOI: 10.1080/16843703.2022.2136360
B. Krishna Kumar, R. Navaneetha Krishnan, R. Sankar, R. Rukmani
ABSTRACT This paper designs and analyzes a novel single-channel cognitive radio retrial queueing network wherein a waiting line buffer is deployed for secondary users (SUs). A finite source system generates the primary users (PUs). Apart from these, PUs having preemptive priority over SUs, the effect of retrial/repeated attempts of PUs is taken into consideration. In such a system, the stability condition and the joint steady-state probability distribution of PUs and SUs are studied by using the matrix-analytic method. Several performance metrics of interest, such as blocking probability, throughput, mean waiting time, etc., have been determined. The first-passage time to reach a congestion level in the SUs waiting line buffer and its related characteristics are investigated by employing the first-step principle. In addition, correlation coefficients for various events of SUs and PUs during this period have been assessed. Finally, extensive numerical results are presented graphically for the system insights.
{"title":"Performance analysis of cognitive wireless retrial queueing networks with admission control for secondary users","authors":"B. Krishna Kumar, R. Navaneetha Krishnan, R. Sankar, R. Rukmani","doi":"10.1080/16843703.2022.2136360","DOIUrl":"https://doi.org/10.1080/16843703.2022.2136360","url":null,"abstract":"ABSTRACT This paper designs and analyzes a novel single-channel cognitive radio retrial queueing network wherein a waiting line buffer is deployed for secondary users (SUs). A finite source system generates the primary users (PUs). Apart from these, PUs having preemptive priority over SUs, the effect of retrial/repeated attempts of PUs is taken into consideration. In such a system, the stability condition and the joint steady-state probability distribution of PUs and SUs are studied by using the matrix-analytic method. Several performance metrics of interest, such as blocking probability, throughput, mean waiting time, etc., have been determined. The first-passage time to reach a congestion level in the SUs waiting line buffer and its related characteristics are investigated by employing the first-step principle. In addition, correlation coefficients for various events of SUs and PUs during this period have been assessed. Finally, extensive numerical results are presented graphically for the system insights.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"20 1","pages":"633 - 670"},"PeriodicalIF":2.8,"publicationDate":"2022-12-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43079340","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-12-01DOI: 10.1080/16843703.2022.2147690
Liangliang Zhuang, Ancha Xu, Binbing Wang, Yuguo Xue, Songzi Zhang
ABSTRACT Progressive-stress accelerated life testing (PSALT) is a special type of experiment that tests the lifetime of a product with continuously varying stress levels. Due to the limitations of testing equipments and costs, the lifetime data collected by PSALT are usually censored and have group effects. In order to deal with the two characteristics in the data, this paper presents a novel PSALT model with group effects under progressive censoring. Two-stage and Gauss-Hermite quadrature methods are proposed to estimate the model parameters, while the interval estimates are constructed by bootstrap and the asymptotic theorem, respectively. Simulation studies are conducted to compare the proposed model with the traditional models without group effects in terms of the relative bias and root mean squared error under different scenarios. The results show that the proposed model can detect group-to-group variation, and that the models without group effects will result in large biases for estimating the characteristic lifetime of the product. Finally, the proposed model is validated by a real dataset.
{"title":"Data analysis of progressive‐stress accelerated life tests with group effects","authors":"Liangliang Zhuang, Ancha Xu, Binbing Wang, Yuguo Xue, Songzi Zhang","doi":"10.1080/16843703.2022.2147690","DOIUrl":"https://doi.org/10.1080/16843703.2022.2147690","url":null,"abstract":"ABSTRACT Progressive-stress accelerated life testing (PSALT) is a special type of experiment that tests the lifetime of a product with continuously varying stress levels. Due to the limitations of testing equipments and costs, the lifetime data collected by PSALT are usually censored and have group effects. In order to deal with the two characteristics in the data, this paper presents a novel PSALT model with group effects under progressive censoring. Two-stage and Gauss-Hermite quadrature methods are proposed to estimate the model parameters, while the interval estimates are constructed by bootstrap and the asymptotic theorem, respectively. Simulation studies are conducted to compare the proposed model with the traditional models without group effects in terms of the relative bias and root mean squared error under different scenarios. The results show that the proposed model can detect group-to-group variation, and that the models without group effects will result in large biases for estimating the characteristic lifetime of the product. Finally, the proposed model is validated by a real dataset.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"20 1","pages":"763 - 783"},"PeriodicalIF":2.8,"publicationDate":"2022-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42462627","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-14DOI: 10.1080/16843703.2022.2126263
Nan Zhang, Sen Tian, Bin Liu, Jun Zhang
ABSTRACT This paper addresses the integrated optimization of the economic manufacturing quantity and the condition-based maintenance policy of a deteriorating manufacturing system. The considered facility produces a single type of product and is inspected at the end of each production run. Upon inspection, two dependent indicators are revealed: one implies whether the production process is in control or not and the other one represents the deterioration level of the facility. The dependence between the two indicators is that whenever the facility deterioration exceeds a pre-determined level, the system becomes more vulnerable such that the production process may switch to the out-of-control state. In the out-of-control state, a proportion of defective items is fabricated. Considering the inter-dependencies between production process and machine degradation, this paper develops an integrated production and maintenance model to minimize the overall cost. The expected cost rate in the long run is taken as the objective function to assess the proposed model, where the joint optimization of the lot-sizing and the maintenance policy is developed. The problem is formulated in the context of a semi-Markov decision process and solved with the successive approximation method. A numerical example is given to illustrate the applicability of the proposed model.
{"title":"Joint optimization of production lot-sizing and condition-based maintenance in an imperfect production process with dependent indicators","authors":"Nan Zhang, Sen Tian, Bin Liu, Jun Zhang","doi":"10.1080/16843703.2022.2126263","DOIUrl":"https://doi.org/10.1080/16843703.2022.2126263","url":null,"abstract":"ABSTRACT This paper addresses the integrated optimization of the economic manufacturing quantity and the condition-based maintenance policy of a deteriorating manufacturing system. The considered facility produces a single type of product and is inspected at the end of each production run. Upon inspection, two dependent indicators are revealed: one implies whether the production process is in control or not and the other one represents the deterioration level of the facility. The dependence between the two indicators is that whenever the facility deterioration exceeds a pre-determined level, the system becomes more vulnerable such that the production process may switch to the out-of-control state. In the out-of-control state, a proportion of defective items is fabricated. Considering the inter-dependencies between production process and machine degradation, this paper develops an integrated production and maintenance model to minimize the overall cost. The expected cost rate in the long run is taken as the objective function to assess the proposed model, where the joint optimization of the lot-sizing and the maintenance policy is developed. The problem is formulated in the context of a semi-Markov decision process and solved with the successive approximation method. A numerical example is given to illustrate the applicability of the proposed model.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"20 1","pages":"511 - 527"},"PeriodicalIF":2.8,"publicationDate":"2022-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48592877","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-11DOI: 10.1080/16843703.2022.2071535
Chien-Tai Lin, Yen-Chou Chen, Tzu‐Chi Yeh, H. K. T. Ng
ABSTRACT This article discusses the estimation of model parameters and the determination of optimal life-testing plans for Weibull-distributed lifetimes under a joint progressive Type-II censoring scheme. We obtain the maximum likelihood estimates numerically and propose a modified variable-neighborhood-search-based approach for determining the optimum joint progressive Type-II censoring scheme. Different optimal criteria, including a cost minimization criterion, the A-optimality criterion, and the D-optimality criterion, are considered. A sensitivity analysis is used to study the effect of misspecification of parameter values on the optimal schemes.
{"title":"Statistical inference and optimum life-testing plans with joint progressively type-II censoring scheme","authors":"Chien-Tai Lin, Yen-Chou Chen, Tzu‐Chi Yeh, H. K. T. Ng","doi":"10.1080/16843703.2022.2071535","DOIUrl":"https://doi.org/10.1080/16843703.2022.2071535","url":null,"abstract":"ABSTRACT This article discusses the estimation of model parameters and the determination of optimal life-testing plans for Weibull-distributed lifetimes under a joint progressive Type-II censoring scheme. We obtain the maximum likelihood estimates numerically and propose a modified variable-neighborhood-search-based approach for determining the optimum joint progressive Type-II censoring scheme. Different optimal criteria, including a cost minimization criterion, the A-optimality criterion, and the D-optimality criterion, are considered. A sensitivity analysis is used to study the effect of misspecification of parameter values on the optimal schemes.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"20 1","pages":"279 - 306"},"PeriodicalIF":2.8,"publicationDate":"2022-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49341827","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-11-06DOI: 10.1080/16843703.2022.2138111
Minjae Park
ABSTRACT We develop a novel class of distributions after the exponentiated Weibull family and vtub-shaped failure rate for systems are considered and compounded together. This combined class of distributions can be applied to reliability applications using the data, and we investigate its properties. We study the mathematical properties of combined distributions including order statistics and estimation by maximum likelihood. In addition, we implement an EM algorithm to determine unknown parameters using maximum likelihood estimates, and maximum entropy characterizations are discussed under appropriate constraints. Using maximum likelihood estimation, we obtain point estimates and interval estimation for parameters. We develop a novel approach to measuring the reliability of multi-component systems as well as a single-component system and illustrate the usefulness of the proposed approach. We apply the approach to real data sets and discuss numeric examples to show the statistical properties of the new compounding class of distributions derived in the paper.
{"title":"Combined class of distributions with an exponentiated Weibull family for reliability application","authors":"Minjae Park","doi":"10.1080/16843703.2022.2138111","DOIUrl":"https://doi.org/10.1080/16843703.2022.2138111","url":null,"abstract":"ABSTRACT We develop a novel class of distributions after the exponentiated Weibull family and vtub-shaped failure rate for systems are considered and compounded together. This combined class of distributions can be applied to reliability applications using the data, and we investigate its properties. We study the mathematical properties of combined distributions including order statistics and estimation by maximum likelihood. In addition, we implement an EM algorithm to determine unknown parameters using maximum likelihood estimates, and maximum entropy characterizations are discussed under appropriate constraints. Using maximum likelihood estimation, we obtain point estimates and interval estimation for parameters. We develop a novel approach to measuring the reliability of multi-component systems as well as a single-component system and illustrate the usefulness of the proposed approach. We apply the approach to real data sets and discuss numeric examples to show the statistical properties of the new compounding class of distributions derived in the paper.","PeriodicalId":49133,"journal":{"name":"Quality Technology and Quantitative Management","volume":"20 1","pages":"671 - 687"},"PeriodicalIF":2.8,"publicationDate":"2022-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47968052","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"工程技术","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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