Optimal reliability test design for the Chen lifetime distribution under generalized type-III hybrid censoring

This paper develops optimal test designs for the Chen lifetime distribution under generalized Type-III hybrid censoring, whose four parameters jointly determine the termination rule according to the observed early-failure process. Profile maximum likelihood estimation and the observed information matrix are derived for the censored sample. The asymptotic variance of mission-time reliability is adopted as the local c-optimality criterion, and two failure thresholds and two inspection times are jointly selected subject to constraints on expected cost, expected test duration, minimum failure information, and the upper-tail risk of test duration. To account for uncertainty in the pilot parameter estimates, Bayesian and standardized minimax-regret designs are further developed. Simulation results show that, under the prescribed resource constraints, the generalized Type-III scheme achieves reliability-estimation precision comparable to or better than that of existing schemes. The improvement is more pronounced in the scenario with a rapidly increasing hazard rate considered in this study. Under parameter setting B, the local, Bayesian, and standardized minimax-regret criteria select the same plan. A rolling-bearing lifetime dataset is used to illustrate how a follow-up test plan can be determined from pilot estimates.