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Roy S, Pradhan B, Purakayastha A. On inference and design under progressive type-I interval censoring scheme for inverse Gaussian lifetime model. INTERNATIONAL JOURNAL OF QUALITY & RELIABILITY MANAGEMENT 2022. [DOI: 10.1108/ijqrm-07-2020-0222] [Citation(s) in RCA: 1] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Abstract] [Track Full Text] [Subscribe] [Scholar Register] [Indexed: 11/17/2022]
Abstract
PurposeThis article considers Inverse Gaussian distribution as the basic lifetime model for the test units. The unknown model parameters are estimated using the method of moments, the method of maximum likelihood and Bayesian methods. As part of maximum likelihood analysis, this article employs an expectation-maximization algorithm to simplify numerical computation. Subsequently, Bayesian estimates are obtained using the Metropolis–Hastings algorithm. This article then presents the design of optimal censoring schemes using a design criterion that deals with the precision of a particular system lifetime quantile. The optimal censoring schemes are obtained after taking into account budget constraints.Design/methodology/approachThis article first presents classical and Bayesian statistical inference for Progressive Type-I Interval censored data. Subsequently, this article considers the design of optimal Progressive Type-I Interval censoring schemes after incorporating budget constraints.FindingsA real dataset is analyzed to demonstrate the methods developed in this article. The adequacy of the lifetime model is ensured using a simulation-based goodness-of-fit test. Furthermore, the performance of various estimators is studied using a detailed simulation experiment. It is observed that the maximum likelihood estimator relatively outperforms the method of moment estimator. Furthermore, the posterior median fares better among Bayesian estimators even in the absence of any subjective information. Furthermore, it is observed that the budget constraints have real implications on the optimal design of censoring schemes.Originality/valueThe proposed methodology may be used for analyzing any Progressive Type-I Interval Censored data for any lifetime model. The methodology adopted to obtain the optimal censoring schemes may be particularly useful for reliability engineers in real-life applications.
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Bhattacharya R, Balakrishnan N. A MCMC-type simple probabilistic approach for determining optimal progressive censoring schemes. COMMUN STAT-SIMUL C 2022. [DOI: 10.1080/03610918.2022.2057537] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/03/2022]
Affiliation(s)
- Ritwik Bhattacharya
- Department of Industrial Engineering, School of Engineering and Sciences, Instituto Tecnologico y de Estudios Superiores de Monterrey, Monterrey, México
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Amiri L, Ganjali M, Hashemi R, Khazaei M. The competing risks analysis for parallel and series systems using Type-II progressive censoring. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2019.1620779] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Leila Amiri
- Department of Statistics, Shahid Beheshti University, Tehran, Iran
| | - Mojtaba Ganjali
- Department of Statistics, Shahid Beheshti University, Tehran, Iran
| | - Reza Hashemi
- Department of Statistics, Razi University, Kermanshah, Iran
| | - Mojtaba Khazaei
- Department of Statistics, Shahid Beheshti University, Tehran, Iran
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Laumen B, Cramer E. Stage life testing with random stage changing times. COMMUN STAT-THEOR M 2020. [DOI: 10.1080/03610926.2020.1805764] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/23/2022]
Affiliation(s)
- Benjamin Laumen
- Department of Mathematics, Institute of Statistics, RWTH Aachen University, Aachen, Germany
| | - Erhard Cramer
- Department of Mathematics, Institute of Statistics, RWTH Aachen University, Aachen, Germany
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Mishra N. Optimal one-step censoring schemes under entropy criterion. COMMUN STAT-SIMUL C 2020. [DOI: 10.1080/03610918.2018.1511804] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/27/2022]
Affiliation(s)
- Nutan Mishra
- Department of Mathematics and Statistics, University of South Alabama, Mobile, Alabama, USA
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Lodhi C, Mani Tripathi Y, Kumar Rastogi M. Estimating the parameters of a truncated normal distribution under progressive type II censoring. COMMUN STAT-SIMUL C 2019. [DOI: 10.1080/03610918.2019.1614619] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/26/2022]
Affiliation(s)
- Chandrakant Lodhi
- Department of Mathematics, Indian Institute of Technology Patna, Bihta, Bihar, India
| | - Yogesh Mani Tripathi
- Department of Mathematics, Indian Institute of Technology Patna, Bihta, Bihar, India
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Bhattacharya R, Saha BN, Farías GG, Balakrishnan N. Multi-criteria-based optimal life-testing plans under hybrid censoring scheme. TEST-SPAIN 2019. [DOI: 10.1007/s11749-019-00660-8] [Citation(s) in RCA: 5] [Impact Index Per Article: 1.0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Affiliation(s)
- Shuvashree Mondal
- Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India
| | - Debasis Kundu
- Department of Mathematics and Statistics, Indian Institute of Technology Kanpur, Kanpur, India
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Computation of optimum Type-II progressively hybrid censoring schemes using variable neighborhood search algorithm. TEST-SPAIN 2017. [DOI: 10.1007/s11749-017-0534-6] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/19/2022]
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Salemi UH, Rezaei S, Nadarajah S. A-optimal and D-optimal censoring plans in progressively Type-II right censored order statistics. Stat Pap (Berl) 2017. [DOI: 10.1007/s00362-017-0877-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Salehi M, Ahmadi J, Dey S. Comparison of two sampling schemes for generating record-breaking data from the proportional hazard rate models. COMMUN STAT-THEOR M 2016. [DOI: 10.1080/03610926.2014.909938] [Citation(s) in RCA: 5] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/22/2022]
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Bayat M, Torabi H. Type-II stepwise progressive censoring. COMMUNICATIONS FOR STATISTICAL APPLICATIONS AND METHODS 2016. [DOI: 10.5351/csam.2016.23.1.057] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/11/2022]
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On optimum life-testing plans under Type-II progressive censoring scheme using variable neighborhood search algorithm. TEST-SPAIN 2015. [DOI: 10.1007/s11749-015-0449-z] [Citation(s) in RCA: 22] [Impact Index Per Article: 2.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Beutner E, Cramer E. Using linear interpolation to reduce the order of the coverage error of nonparametric prediction intervals based on right-censored data. J MULTIVARIATE ANAL 2014. [DOI: 10.1016/j.jmva.2014.04.007] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/25/2022]
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Nonparametric prediction intervals for progressive Type-II censored order statistics based on $$k$$ k -records. Comput Stat 2013. [DOI: 10.1007/s00180-013-0430-9] [Citation(s) in RCA: 4] [Impact Index Per Article: 0.4] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/26/2022]
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Ding C, Tse SK. Design of accelerated life test plans under progressive Type II interval censoring with random removals. J STAT COMPUT SIM 2013. [DOI: 10.1080/00949655.2012.660155] [Citation(s) in RCA: 2] [Impact Index Per Article: 0.2] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/28/2022]
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Pradhan B, Kundu D. Inference and optimal censoring schemes for progressively censored Birnbaum–Saunders distribution. J Stat Plan Inference 2013. [DOI: 10.1016/j.jspi.2012.11.007] [Citation(s) in RCA: 43] [Impact Index Per Article: 3.9] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 12/01/2022]
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Progressively first-failure censored reliability sampling plans with cost constraint. Comput Stat Data Anal 2012. [DOI: 10.1016/j.csda.2011.12.008] [Citation(s) in RCA: 18] [Impact Index Per Article: 1.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 11/19/2022]
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Dahmen K, Burkschat M, Cramer E. A- and D-optimal progressive Type-II censoring designs based on Fisher information. J STAT COMPUT SIM 2012. [DOI: 10.1080/00949655.2011.560118] [Citation(s) in RCA: 9] [Impact Index Per Article: 0.8] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Park S, Ng HKT. Missing information and an optimal one-step plan in a Type II progressive censoring scheme. Stat Probab Lett 2012. [DOI: 10.1016/j.spl.2011.10.012] [Citation(s) in RCA: 7] [Impact Index Per Article: 0.6] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Submit a Manuscript] [Subscribe] [Scholar Register] [Indexed: 11/29/2022]
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Park S, Balakrishnan N, Kim SW. Fisher information in progressive hybrid censoring schemes. STATISTICS-ABINGDON 2011. [DOI: 10.1080/02331888.2010.504988] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Cramer E, Bagh C. Minimum and Maximum Information Censoring Plans in Progressive Censoring. COMMUN STAT-THEOR M 2011. [DOI: 10.1080/03610926.2010.489176] [Citation(s) in RCA: 6] [Impact Index Per Article: 0.5] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/18/2022]
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Parsi S, Bairamov I. Expected values of the number of failures for two populations under joint Type-II progressive censoring. Comput Stat Data Anal 2009. [DOI: 10.1016/j.csda.2009.03.023] [Citation(s) in RCA: 10] [Impact Index Per Article: 0.7] [Reference Citation Analysis] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Indexed: 10/20/2022]
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