This thesis is concerned with the problems of estimating and designing constant stress accelerated life tests (ALTs) when extrinsic failure mode as well as intrinsic one exists. It is assumed that each failure time follows a location-scale distribution and the location parameter is a linear function of stress. This thesis consists of the following three parts.
(i) An estimation of lifetime distribution at use condition for constant stress ALT is considered. Under the assumption that the lifetime follows a mixture of two distributions, an estimation procedure using the expectation and maximization (EM) algorithm is proposed and specific formulas for Weibull and lognormal distributions are obtained. Simulation studies are performed to investigate the properties of the estimates and the effects of stress level. The proposed method is compared with the existing method for single failure mode.
(ii) Optimum constant stress ALT plans for products with two failure modes are considered. It is assumed that the lifetime distribution for each failure mode is Weibull. Minimizing the generalized asymptotic variance of maximum likelihood estimators of model parameters is used as an optimality criterion. The optimum test plans are presented for selected values of design parameters and the effects of errors in pre-estimates of the design parameters are investigated.
(iii) A method of analyzing ALT data with general limited failure population model is considered. When no failure-cause information is available, methods of obtaining maximum likelihood estimators and confidence intervals of parameters are outlined and specific formulas for Weibull distribution are obtained. The properties of the estimates are investigated by numerical study and the estimators obtained by the proposed methods are compared with the ones obtained by assuming that the cause of failure before a threshold time is extrinsic and all other failures come from intrinsic failure mode.