Optimal experimental plan for multi-level stress testing with Weibull regression under progressive Type-II extremal censoring

Abstract

In the design of constant-stress life-testing experiments, the optimal allocation in a multi-level stress test with Type-I or Type-II censoring based on the Weibull regression model has been studied in the literature. Conventional Type-I and Type-II censoring schemes restrict our ability to observe extreme failures in the experiment and these extreme failures are important in the estimation of upper quantiles and understanding of the tail behaviors of the lifetime distribution. For this reason, we propose the use of progressive extremal censoring at each stress level, whereas the conventional Type-II censoring is a special case. The proposed experimental scheme allows some extreme failures to be observed. The maximum likelihood estimators of the model parameters, the Fisher information and asymptotic variance-covariance matrices of the maximum likelihood estimates are derived. We consider the optimal experimental planning problem by looking at four different optimality criteria. To avoid the computational burden in searching for the optimal allocation, a simple search procedure is suggested. Optimal allocation of units for 2-and 4-stress-level situations are determined numerically. The asymptotic Fisher information matrix and the asymptotic optimal allocation problem are also studied and the results are compared with optimal allocations with specified sample sizes. Finally, conclusions and some practical recommendations are provided.

Bayesian Sequential Design Based on Dual Objectives for Accelerated Life Tests

“…Several work such as Chernoff [3] and Meeker and Hahn [4,5] studied optimum designs and compromise plans and outlined practical guidelines for planning an efficient ALT. Some recent developments on ALT include Ye et al [6], Pan and Yang [7], Tsai et al [8], and Ng et al [9]. Escobar and Meeker [2] provided a review on the accelerated test models.…”