Effect of Progressive Type-I Right Censoring on Bayesian Statistical Inference of Simple Step–Stress Acceleration Life Testing Plan under Weibull Life Distribution

Authors: Saleem Z. Ramadan

Abstract:

This paper discusses the effects of using progressive Type-I right censoring on the design of the Simple Step Accelerated Life testing using Bayesian approach for Weibull life products under the assumption of cumulative exposure model. The optimization criterion used in this paper is to minimize the expected pre-posterior variance of the P^th percentile time of failures. The model variables are the stress changing time and the stress value for the first step. A comparison between the conventional and the progressive Type-I right censoring is provided. The results have shown that the progressive Type-I right censoring reduces the cost of testing on the expense of the test precision when the sample size is small. Moreover, the results have shown that using strong priors or large sample size reduces the sensitivity of the test precision to the censoring proportion. Hence, the progressive Type-I right censoring is recommended in these cases as progressive Type-I right censoring reduces the cost of the test and doesn't affect the precision of the test a lot. Moreover, the results have shown that using direct or indirect priors affects the precision of the test.

Keywords: Reliability, Accelerated life testing, Cumulative exposure model, Bayesian estimation, Progressive Type-I censoring, Weibull distribution.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1090813

References:

[1] E. Gouno, N. Balakrishnan, "Step-stress accelerated life test". In Handbook of Statistics-20: Advances in Reliability (Eds., N. Balakrishnan and C. R. Rao), 623-639, North-Holland, Amsterdam (2001).
[2] A. C. Cohen, "Progressively censored samples in life testing". Technometrics, 5, 327-329 (1963).
[3] R. Miller, W. Nelson. "Optimum simple step-stress plans for accelerated life testing". IEEE Trans. Reliability 32, 59–65(1983).
[4] D.S. Bai, M.S. Kim, S.H. Lee. "Optimum simple step-stress accelerated life tests with censoring". IEEE Trans. Reliability 38, 528–532 (1989).
[5] I.H. Khamis. "Optimum M-step, step-stress test with k stress variables". Commun. Statist. Simulation Computation 26, 1301–1313 (1997).
[6] H.K.T. Ng, P.S. Chan, N. Balakrishnan. "Optimal progressive censoring plans for the Weibull distribution". Technometrics 46, 470--481(2004).
[7] S.J. Wu, Y.P. Lin, and Y.J. Chen. "Planning step-stress life test with progressively type I group-censored exponential data". Statist. Neerlandica 60, 46--56 (2006).
[8] N. Balakrishnan. "Progressive censoring methodology: an appraisal (with discussion)". Test 16, 211--296 (., 2007).
[9] W. Nelson, and T. Kielpinski. "Theory for Optimum Censored Accelerated Life Tests for Normal and Lognormal Life Distributions”, Technometrics, Vol. 18, No. 1, pp. 105-113, (1976).
[10] D. Bai, and M. Kim."Optimum Simple Step-Stress Accelerated Life tests for Weibull Distribution and Type I Censoring". Naval Research Logistics, Vol. 40, pp.193-210 (1993). http://dx.doi.org/10.1002/1520-6750(199303)40:2<193::AID-NAV3220400205>3.0.CO;2-J
[11] L. Escobar, and W. Meeker. ” Planning Accelerated Life Tests with Two or More Experimental factors". Technometrics, 37(4), 411-427 (1995). http://dx.doi.org/10.2307/1269733
[12] V. Dorp. "Step-Stress Accelerated Life Testing. IEEE Transactions on Reliability", 45(3), 491-498. http://dx.doi.org/10.1109/24.537021 (1996).
[13] S. Ramadan, and K. Ramadan. "Bayesian Simple Step–stress Acceleration Life Testing Plan under Progressive Type-I Right Censoring for Exponential Life Distribution". Modern Applied Science, 6, (3) (2012).