Optimal Robust Design of Step Stress Accelerated Life Test Scheme under Weibull Distribution

The traditional accelerated life test scheme is necessary to give the rough values of some model parameters in advance, but the influence of fluctuation on the stability of test scheme is irregulared. Based on the prior life test information, this paper aims to minimize the mean and variance of asymptotic variance of $p$-quantile life estimate under normal test stress level, using maximum likelihood estimation theory and Nelson cumulative failure principle, the optimal robust design mathematical model of step stress accelerated life test scheme with uncertainty parameters under Weibull distribution is established. The results of optimal robust design of step stress accelerated life test scheme for electrical connectors show that: comparing with the optimal design of step stress test scheme in the literature, the optimal robust design scheme is not sensitive to the uncertainty of model parameters when the asymptotic variance of median life estimate is basically the same; Comparing with the optimal design of constant accelerated life test scheme, when the statistical accuracy of test data is basically the same, the number of samples required can be reduced by 1/5, and the test time can be reduced by about 1/4.