Abstract
This paper presents the optimum stress changing times for 3-step, step stress accelerated life testing under the cumulative exposure model with type-I censoring. The lifetimes of test units are assumed to follow Weibull distribution. The scale parameter of the Weibull failure time at constant stress level is assumed to be a log-quadratic function of the stress level. We derive an optimum test plans to minimize the asymptotic variance of maximum likelihood estimator of given pth percentile of the distribution at a design stress. The optimum test plan based on simulated observations is illustrated through a numerical example. The maximum likelihood estimates and asymptotic interval estimates are obtained using R software.
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References
Alhadeed AA, Yang SS (2005) Optimal simple step-stress plan for cumulative exposure model using log-normal distribution. IEEE Trans Reliab 54:64–68
Bai DS, Kim MS, Lee SH (1989) Optimum simple step-stress accelerated life tests with censoring. IEEE Trans Reliab 38(5):528–532
Chandra N, Khan MA, Pandey M (2014) Optimum test plan for 3-step, step-stress accelerated life tests. Int J Perform Eng 10(1):03–14
Ebrahem MAH, Al-Masri AQ (2007) Optimum simple step-stress plan for log logistic cumulative exposure model. Metron, LXV, pp 23–34
Ebrahem MAH, Al-Masri AQ (2009) Optimum quadratic three-step stress plans for log–logistic distribution. Metron 67:243–255
Ebrahem MAH, Al-Masri AQ (2010) Optimum three-step step-stress plans for cumulative exposure model using log–logistic distribution. JPSS 8:35–44
Elsayed EA, Zhang H (2005) Design of optimum simple step-stress accelerated life testing plans. In: Proceedings of international workshop on recent advances in stochastic operations research. Canmore, Canada
Escobar LA, Meeker WQ (1995) Planning accelerated life tests with two or more experiemtnal factors. Technometrics 37:411–427
Fard N, Li C (2009) Optimal simple step stress accelerated life test design for reliability prediction. J Stat Plan Inference 139:1799–1808
Khamis IH, Higgins JJ (1996a) Optimum 3-step step-stress tests. IEEE Trans Reliab 45:341–345
Khamis IH, Higgins JJ (1996b) An alternative to the Weibull step-stress model. In: Proceedings of the American Statistical Association, Chicago, pp 123–127
Khamis IH, Higgins JJ (1998) A new model for step-stress testing. IEEE Trans Reliab 47:341–345
Miller R, Nelson WB (1983) Optimum simple step-stress plans for accelerated life testing. IEEE Trans Reliab R–32:59–65
Nelson WB (1990) Accelerated testing, statistical models, test plans and data analysis. Wiley, New York
Wang BX (2010) Interval estimation for exponential progressive type-II censored step-stress accelerated life-testing. J Stat Plan Inference 140:2706–2718
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The authors would like to thank the editor in chief and referees for the valuable comments in revising this paper.
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Chandra, N., Khan, M.A. & Gopal, G. Optimum quadratic step-stress accelerated life test plan for Weibull distribution under type-I censoring. Int J Syst Assur Eng Manag 8 (Suppl 2), 585–591 (2017). https://doi.org/10.1007/s13198-016-0473-8
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DOI: https://doi.org/10.1007/s13198-016-0473-8