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Bayesian accelerated life test plans for series systems with Weibull component lifetimes. (English) Zbl 1462.62609
Summary: This article presents optimal Bayesian accelerated life test plans for series systems under Type-I censoring scheme. First, the component lifetimes are assumed to follow independent Weibull distributions. The scale parameters of Weibull lifetime distributions are related to the external stress variable through a general stress translation function. For a fixed number of design points, optimal Bayesian ALT plans are first obtained by solving constrained optimization problems under two different Bayesian design criteria. The global optimality of the resulting fixed-point optimal designs is then verified via the General Equivalence Theorem. This article also provides the optimized compromise ALT plans which are extremely useful in real-life applications. A detailed sensitivity analysis is then performed to find out the effect of various planning inputs on the resulting optimal Bayesian ALT plans. A simulation study is then conducted to visualize the resulting sampling variations from the optimal Bayesian ALT plans. Finally, this article considers a series system with dependent component lifetimes. Optimal ALT plans are obtained assuming a Gamma frailty model.

MSC:
62N03 Testing in survival analysis and censored data
62N05 Reliability and life testing
62F15 Bayesian inference
62K05 Optimal statistical designs
Software:
SPLIDA
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References:
[1] Nelson, W. B., Accelerated Testing: Statistical Models, Test Plans and Data Analysis (2004), Wiley: Wiley New York
[2] Nelson, W. B., A bibliography of accelerated test plans, IEEE Trans. Reliab., 54, 194-197 (2005)
[3] Nelson, W. B., A bibliography of accelerated test plans part II - references, IEEE Trans. Reliab., 54, 370-373 (2005)
[4] Pascual, F., Accelerated life test planning with independent Weibull Competing risks with known shape parameter, IEEE Trans. Reliab., 56, 85-93 (2007)
[5] Pascual, F., Accelerated life test planning with independent Weibull competing risks, IEEE Trans. Reliab., 57, 435-444 (2008)
[6] Pascual, F., Accelerated life test planning with independent lognormal competing risks, J. Stat. Plann. Inference, 140, 1089-1100 (2010) · Zbl 1179.62147
[7] Liu, X., Planning of accelerated life tests with dependent failure modes based on a gamma frailty model, Technometrics, 54, 398-409 (2012)
[8] Chernoff, H., Locally optimum designs for estimating parameters, Ann. Stat., 24, 586-602 (1953) · Zbl 0053.10504
[9] Chaloner, K.; Verdinelli, I., Bayesian experimental design: a review, Stat. Sci., 10, 273-304 (1995) · Zbl 0955.62617
[10] Chaloner, K.; Larntz, K., Bayesian design for accelerated life testing, J. Stat. Plan. Inference, 33, 245-259 (1992) · Zbl 0781.62149
[11] Polson, N. G., A Bayesian perspective on the design of accelerated life tests, (Basu, A. P., Advances in Reliability (1993), Elsevier: Elsevier New York), 321-330
[12] Erkanli, A.; Soyer, R., Simulation-based designs for accelerated life tests, J. Stat. Plan. Inference, 90, 335-348 (2000) · Zbl 1080.62541
[13] Zhang, Y.; Meeker, W. Q., Bayesian methods for planning accelerated life tests, Technometrics, 48, 49-60 (2006)
[14] Xu, A.; Tang, Y., A Bayesian method for planning accelerated life testing, IEEE Trans. Reliab., 64, 1383-1392 (2015)
[15] Atkinson, A.; Donev, A.; Tobias, R., Optimum Experimental Designs, with SAS, Oxford Statistical Science Series (2007), Oxford University Press: Oxford University Press USA · Zbl 1183.62129
[16] Roy, S.; Mukhopadhyay, C., Bayesian \(D\)-optimal ALT plans for series systems with competing exponential causes of failure, J. Appl. Stat., 43, 1477-1493 (2016)
[17] Meeker, W. Q.; Escobar, L. A., Statistical Methods for Reliability Data (1998), Wiley: Wiley New York · Zbl 0949.62086
[18] Mukhopadhyay, C.; Roy, S., Bayesian accelerated life testing under competing log-location-scale family of causes of failure, Comput. Stat., 31, 89-119 (2016) · Zbl 1342.65052
[19] David, H. A.; Moeschberger, M. L., The Theory of Competing Risks (1978), Griffin: Griffin London · Zbl 0434.62076
[20] Fan, T.-H.; Hsu, T.-M., 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
[21] Chaloner, K.; Larntz, K., Optimal Bayesian design applied to logistic regression experiments, J. Stat. Plan. Inference, 21, 191-208 (1989) · Zbl 0666.62073
[22] Fedorov, V. V., Theory of Optimal Experiments (1972), Academic Press: Academic Press New York
[23] Firth, D.; Hinde, J. P., On Bayesian \(D\)-optimum design criteria and the equivalence theorem in non-linear models, J. R. Stat. Soc. Ser. B, 59, 793-797 (1997) · Zbl 0886.62074
[24] Varadhan, R., Numerical optimization in R: beyond optim, J. Stat. Softw., 60, 1-3 (2014)
[25] Clyde, M.; Chaloner, K., The equivalence of constrained and weighted designs in multiple objective design problems, J. Am. Stat. Assoc., 91, 1236-1244 (1996) · Zbl 0883.62079
[26] Liu, X.; Tang, L.-C., Accelerated life test plans for repairable systems with multiple independent risks, IEEE Trans. Reliab., 59, 115-127 (2010)
[27] 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
[28] Moeschberger, M. L., Life tests under dependent competing causes of failure, Technometrics, 16, 39-47 (1974) · Zbl 0277.62073
[29] Tsiatis, A., A nonidentifiability aspect of the problem of competing risks, Proceedings of the National Academy of Sciences of the United States of America, 72, 20-22 (1975) · Zbl 0299.62066
[30] Crowder, M., Classical Competing Risk (2001), Chapman & Hall/CRC: Chapman & Hall/CRC Boca Raton
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