Optimal Model Discrimination Designs for Accelerated Life Tests with Type-I Censoring

Abstract

Existing experimental design methods for accelerated life tests (ALTs) primarily focus on parameter estimation under a single prespecified model. In practice, however, substantial uncertainty often remains in both the stress-life relationship and the lifetime distribution, especially under Type-I censoring; this uncertainty can lead to biased reliability predictions and costly design decisions. We propose an optimal modeldiscrimination framework based on a new censored Kullback-Leibler (cKL) divergence criterion that explicitly accounts for information loss in censored reliability data. We establish a general equivalence theorem for cKL-optimal designs and provide a practical directional-derivative diagnostic for optimality assessment. To solve the resulting nonsmooth nested optimization problem, we implement a hybrid particle swarm optimization and quasi-Newton (PSO-QN) algorithm. We evaluate the proposed approach in two benchmark reliability studies: a nickel-based superalloy fatigue-life experiment and a temperature-accelerated life test. The results show that cKL-optimal designs substantially improve discrimination among competing models, while practical compromise designs remain effective even when the optimal design is singular. 

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