A reference optimality criterion has been proposed by Xu and Tang based on the expected Kullback–Leibler divergence between the posterior and the prior distributions of the parameters of interest. In this paper, we use the reference optimality criterion to plan simple step-stress accelerated life tests for log-location-scale distributions. Monte Carlo algorithms are developed to find the optimal plans. Effects of the priors on the optimal plans are also investigated. Results indicate that the optimal Bayesian plans are robust to the choice of the priors.
Van DorpJRMazzuchiTAFornellGEPollockLR. A Bayes approach to step-stress accelerated life testing. IEEE Trans Reliab1996; 45: 491–498.
2.
BalakrishnanNZhangLXieQ. Inference for a simple stepstress model with Type-I censoring and lognormally distributed lifetimes. Commun Statist Theory Meth2009; 38: 1690–1709.
3.
LinCTChouCC. Statistical inference for a lognormal step-stress model with type-I censoring. IEEE Trans Reliab2012; 61: 361–377.
4.
MillerRNelsonW. Optimum simple step-stress plans for accelerated life testing. IEEE Trans Reliab1983; 32: 59–65.
5.
BaiDSKimMS. Optimum simple step-stress accelerated life tests for Weibull distribution and Type I censoring. Naval Res Logist1993; 40: 193–210.
6.
MaHMeekerWQ. Optimum step-stress accelerated life test plans for log-location-scale distributions. Naval Res Logist2008; 55: 551–562.
7.
GuanQTangYCFuJYXuAC. Optimal multiple constant-stress accelerated life tests for generalized exponential distribution. Commun Statist Sim Comput2014; 43: 1852–1865.
8.
ErkanliASoyerR. Simulation-based designs for accelerated life tests. J Statist Plan Inf2000; 90: 335–348.
9.
ZhangYMeekerWQ. Bayesian methods for planning accelerated life tests. Technometrics2006; 48: 49–60.
10.
XuACTangYC. A Bayesian method for planning accelerated life testing. IEEE Trans Reliab2014; in press.
11.
EscobarLAMeekerWQ. Planning accelerated life test plans with two or more experimental factors. Technometrics1995; 37: 411–427.
12.
NelsonW. Accelerated life testin-Step-stress models and data analysis. IEEE Trans Reliab1980; 29: 103–108.
13.
YuanTLiuXKuoW. Planning simple step-stress accelerated life tests using Bayesian methods. IEEE Trans Reliab2012; 61: 254–263.
14.
ClarkeBSBarronAR. Information theoretic asymptotics of Bayes methods. IEEE Trans Inform Theory1990; 36: 453–471.
15.
ChalonerKLarntzK. Optimal Bayesian design applied to logistic regression experiments. J Statist Plan Inf1989; 21: 191–208.
16.
GhoshJKMukerjeeR. Noninformative priors (with discussion). In BernardoJMBergerJODawidAPSmithAFM (eds), Bayesian Statistics, vol. 4. Oxford: Oxford University Press: 1992; 195–210.
17.
PascualF. Accelerated life test planning with independent lognormal competing risks. J Statist Plan Inf2010; 140: 1089–1100.
18.
WhittleP. Some general points in the theory of optimal experimental design. J R Statist Soc Ser B1973; 35: 123–130.
19.
TsengSTBalakrishnanNTsaiCC. Optimal step-stress accelerated degradation test plan for gamma degradation processes. IEEE Trans Reliab2009; 58: 611–618.
20.
GuanQTangYC. Optimal step-stress test under Type-I censoring for multivariate exponential distribution. J Statist Plan Inf2012; 142: 1908-1923.
