We discuss the optimal allocation problem in a multi-level accelerated life testing experiment under Type-I censoring when an exponential regression model is used for statistical analysis. We derive the expected Fisher information, and the asymptotic variance-covariance matrix of the maximum likelihood estimators. D-optimality is used to determine the optimal allocations. An algorithm is given to find the optimal allocation. A numerical example is used for illustration. The optimal allocations depends on the model parameters and the sensitivity of the optimal allocations due to the mis-specification of the model parameters is studied.
Arnold, B.C., Balakrishnan, N. and Nagaraja, H.N. (1992). A first Course in Order Statistics, John Wiley, New York.
Bai, D. S. and Chung, S. W. (1991). An optimal design of accelerated life test for exponential distribution, Reliab. Eng'ing. Syst. Safety, 31, 57–64.Bai, D. S. and Chung, S. W. (1992). Optimal design of partially accelerated life tests for the exponential distribution under type-I censoring, IEEE Trans. Reliab., 41, 400–406.
Bai, D. S. and Kim, M. S. (1993). Optimum simple step-stress accelerated life tests for the Weibull distribution and type I censoring, Nav. Res. Log., 40, 193–210.
Cox, D. R. (1964). Some applications of exponential ordered scores, J. Roy. Stat. Soc. B, 26, 103-110.
Chernoff, H. (1962). Optimal Accelerated life designs for estimation. Technometrics, 4, 381–408.
Epstein, B. (1958). The exponential distribution and its role in life-testing, Ind. Qual. Control, 15, 2–7.
Feigl, P. and Zelen, M. (1965). Estimation of exponential survival probabilities with concomitant information, Biometrics, 21, 826–838.
Glasser, M. (1967). Exponential survival with covariance, J. Am. Stat. Assoc., 62, 561-568.
Johnson, N. L., Kotz S. and Balakrishnan N. (1995). Continuous Univariate Distributions, Vol. 2, 2nd edition, New York: Wiley.
Ka, C.Y., Chan, P.S., Ng, H.K.T. and Balakrishnan, N. (2010). Optimal sample size allocation for multi-level stress testing with Weibull regression under type II cesnoring, Statistics, to appear.
Lawless, J.F. (2003). Statistical Models & Methods For Lifetime Data 2nd Edition, John Wiley & Sons, New York.
Lee, E.T. (1992). Statistical Methods for Survival Data Analysis 2nd Edition, John Wiley, New York.
McCool, J. I. (1980). Confidence limits for Weibull regression with censored data, IEEE Transactions on Reliability, 29145-150.
Monroe, E.C., Pan, R., Anderson-Cook, Montgomery, D.G. and Borror, C.M. (2010). Sensitivity analysis of optimal designs for accelerated life testing, J. Qual. Tech., 42, No. 2, 121–135.
Nelson, W. and Meeker, W. Q. (1978). Theory for optimum accelerated censored life tests for Weibull and extreme value distributions, Technometrics, 20, 171-177.
Ng, H.K.T., Balakrishnan, N. and Chan, P.S. (2007). Optimal sample size allocation for tests with multiple levels of stress with extreme value regression, Nav. Res. Log., 54, 237–249.
Silvey, S. D. (1980). Optimal Design, Chapman and Hall, New York.
Keywords: accelerated life testing; exponential regression; optimal design; type I censoring
Biography: Prof. Chan is an associate Professor of Department of Statistics, The Chinese University of Hong Kong. He is an elected member of ISI.