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Bayesian accelerated life testing under competing log-location-scale family of causes of failure. (English) Zbl 1342.65052
Summary: This article provides Bayesian analyses of data arising from multi-stress accelerated life testing of series systems. The component log-lifetimes are assumed to independently belong to some log-concave location-scale family of distributions. The location parameters are assumed to depend on the stress variables through a linear stress translation function. Bayesian analyses and associated predictive inference of reliability characteristics at usage stresses are performed using Gibbs sampling from the joint posterior. The developed methodology is numerically illustrated by analyzing a real data set through Bayesian model averaging of the two popular cases of Weibull and log-normal, with the later getting a special focus in this article as a slightly easier example of the log-location-scale family. A detailed simulation study is also carried out to compare the performance of various Bayesian point estimators for the log-normal case.

MSC:
65C60 Computational problems in statistics (MSC2010)
62N05 Reliability and life testing
Software:
BayesDA; SPLIDA
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[1] Basu, S; Sen, A; Banerjee, M, Bayesian analysis of competing risks with partially masked cause of failure, J R Stat Soc Ser C (Appl Stat), 52, 77-93, (2003) · Zbl 1111.62326
[2] Berger, J, The case for objective Bayesian analysis, Bayesian Anal, 1, 385-402, (2006) · Zbl 1331.62042
[3] Berger JO (1985) Statistical decision theory and Bayesian analysis, 2nd edn. Springer, New York
[4] Berger, JO; Pericchi, LR, The intrinsic Bayes factor for model selection and prediction, J Am Stat Assoc, 91, 109-122, (1996) · Zbl 0870.62021
[5] Bunea, C; Mazzuchi, TA, Competing failure modes in accelerated life testing, J Stat Plan Inference, 136, 1608-1620, (2006) · Zbl 1090.62109
[6] Carlin, BP; Chib, S, Bayesian model choice via Markov chain Monte Carlo methods, J R Stat Soc Ser B (Methodol), 57, 473-484, (1995) · Zbl 0827.62027
[7] Cowles, MK; Carlin, BP, Markov chain Monte Carlo convergence diagnostics: a comparative review, J Am Stat Assoc, 91, 883-904, (1996) · Zbl 0869.62066
[8] Fan, Th; Hsu, Tm, Constant stress accelerated life test on a multiple-component series system under Weibull lifetime distributions, Commun Stat Theory Methods, 43, 2370-2383, (2014) · Zbl 1462.62617
[9] Fernández, C; Steel, MF, Reference priors for the general location-scale modelm, Stat Probab Lett, 43, 377-384, (1999) · Zbl 1054.62527
[10] Gelman A, Carlin JB, Stern HS, Dunson DB, Vehtari A, Rubin DB (2013) Bayesian data analysis, 3rd edn. Chapman and Hall/CRC, Boca Raton · Zbl 0736.62088
[11] Gilks, WR; Wild, P, Adaptive rejection sampling for Gibbs sampling, Appl Stat, 41, 337-348, (1992) · Zbl 0825.62407
[12] Godsill, SJ, On the relationship between Markov chain Monte Carlo methods for model uncertainty, J Comput Graph Stat, 10, 230-248, (2001)
[13] Green, PJ, Reversible jump Markov chain Monte Carlo computation and Bayesian model determination, Biometrika, 82, 711-732, (1995) · Zbl 0861.62023
[14] Hauschildt, M; Gall, M; Thrasher, S; Justison, P; Hernandez, R; Kawasaki, H; Ho, PS, Statistical analysis of electromigration lifetimes and void evolution, J Appl Phys, 101, 523, (2007)
[15] Hoeting, JA; Madigan, D; Raftery, AE; Volinsky, CT, Bayesian model averaging: a tutorial, Stat Sci, 14, 382-401, (1999) · Zbl 1059.62525
[16] Jiang, R, Analysis of accelerated life test data involving two failure modes, Adv Mater Res, 211-212, 1002-1006, (2011)
[17] Kadane, JB; Lazar, NA, Methods and criteria for model selection, J Am Stat Assoc, 99, 279-290, (2004) · Zbl 1089.62501
[18] Kass, RE; Raftery, AE, Bayes factors, J Am Stat Assoc, 90, 773-795, (1995) · Zbl 0846.62028
[19] Kim, CM; Bai, DS, Analyses of accelerated life test data under two failure modes, Int J Reliab Qual Saf Eng, 9, 111-125, (2002)
[20] Kim, JS; Yum, B, Selection between Weibull and lognormal distributions: a comparative simulation study, Comput Stat Data Anal, 53, 477-485, (2008) · Zbl 1231.62018
[21] Kim, SW; Ibrahim, JG, On Bayesian inference for proportional hazards models using noninformative priors, Lifetime Data Anal, 6, 331-341, (2000) · Zbl 0971.62011
[22] Klein, JP; Basu, AP, Weibull accelerated life tests when there are competing causes of failure, Commun Stat Theory Methods, 10, 2073-2100, (1981) · Zbl 0469.62080
[23] Klein, JP; Basu, AP, Accelerated life testing under competing exponential failure distributions, IAPQR Trans, 7, 1-20, (1982) · Zbl 0498.62085
[24] Klein, JP; Basu, AP, Accelerated life tests under competing Weibull causes of failure, Commun Stat Theory Methods, 11, 2271-2286, (1982) · Zbl 0498.62083
[25] Kundu, D; Manglick, A, Discriminating between the Weibull and log-normal distributions, Nav Res Logist, 51, 893-905, (2004) · Zbl 1052.62019
[26] Liu, JS; Wu, YN, Parameter expansion for data augmentation, J Am Stat Assoc, 94, 1264-1274, (1999) · Zbl 1069.62514
[27] Meeker WQ, Escobar LA (1998) Statistical methods for reliability data. Wiley, New York
[28] Mukhopadhyay, C; Basu, S, Bayesian analysis of masked series system lifetime data, Commun Stat Theory Methods, 36, 329-348, (2007) · Zbl 1109.62092
[29] Nelson, W, Accelerated life testing-step-stress models and data analyses, Reliab IEEE Trans, 29, 103-108, (1980) · Zbl 0462.62078
[30] Nelson WB (1990) Accelerated testing: statistical models, test plans and data analysis. Wiley, New York · Zbl 0717.62089
[31] Pascual, F, Accelerated life test planning with independent Weibull competing risks, Reliab IEEE Trans, 57, 435-444, (2008)
[32] Pascual, F, Accelerated life test planning with independent lognormal competing risks, J Stat Plan Inference, 140, 1089-1100, (2010) · Zbl 1179.62147
[33] Pathak, PK; Singh, AK; Zimmer, WJ, Bayes estimation of hazard & acceleration in accelerated testing, Reliab IEEE Trans, 40, 615-621, (1991) · Zbl 0736.62088
[34] Roy, S; Mukhopadhyay, C; John, B (ed.); Acharya, UH (ed.); Chakraborty, AK (ed.), Bayesian accelerated life testing under competing exponential causes of failure, 229-245, (2013), New Delhi
[35] Roy, S; Mukhopadhyay, C, Bayesian accelerated life testing under competing Weibull causes of failure, Commun Stat Theory Methods, 43, 2429-2451, (2014) · Zbl 1462.62630
[36] Roy, S; Mukhopadhyay, C, Maximum likelihood analysis of multi-stress ALT data of series systems with competing log-normal causes of failure, J Risk Reliab, 229, 119-130, (2015)
[37] Tan Y, Zhang C, Chen X (2009) Bayesian analysis of incomplete data from accelerated life testing with competing failure modes. In: 8th international conference on reliability, maintainability and safety, pp 1268 -1272 · Zbl 0870.62021
[38] Tanner, MA; Wong, WH, The calculation of posterior distributions by data augmentation, J Am Stat Assoc, 82, 528-540, (1987) · Zbl 0619.62029
[39] Tojeiro, CAV; Louzada-Neto, F; Bolfarine, H, A Bayesian analysis for accelerated lifetime tests under an exponential power law model with threshold stress, J Appl Stat, 31, 685-691, (2004) · Zbl 1053.62117
[40] Dorp, JR; Mazzuchi, TA, A general Bayes exponential inference model for accelerated life testing, J Stat Plan Inference, 119, 55-74, (2004) · Zbl 1031.62087
[41] Dorp, JR; Mazzuchi, TA, A general Bayes Weibull inference model for accelerated life testing, Reliab Eng Syst Saf, 90, 140-147, (2005)
[42] Xu, A; Tang, Y, Objective Bayesian analysis of accelerated competing failure models under type-I censoring, Comput Stat Data Anal, 55, 2830-2839, (2011) · Zbl 1218.62110
[43] Zellner, A, Bayesian estimation and prediction using asymmetric loss functions, J Am Stat Assoc, 81, 446-451, (1986) · Zbl 0603.62037
[44] Zhang, Y; Meeker, WQ, Bayesian methods for planning accelerated life tests, Technometrics, 48, 49-60, (2006)
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