Reliability Modeling of Accelerated Life Tests with Both Random Effects and Nonconstant Shape Parameters

In accelerated life tests (ALTs), test units may come from different groups (subsampling, blocking, and clustering) and the group effect is random and significant. The ALTs, in this case, are not completely randomized designs (CRDs). Previous studies on ALTs assume that the failure mechanism of Weibull distribution remains constant over all accelerating stresses. However, in practical reliability experiments, the failure mechanism may depend on accelerating stresses. To correctly incorporate both group effects and different failure mechanisms into the analysis, one needs to run a regression model with both random effects and nonconstant shape parameters. As shown in this study, a Weibull regression model was used to make inferences from accelerated life tests. Both scale and shape parameters of the Weibull distribution are assumed to be a log-linear relationship with stresses. Random effects are assumed to be an exponential relationship with the scale parameter. One common reliability data set of glass capacitors with grouped data is used to illustrate this problem for models with and without considering random effects and nonconstant shape parameters. The scale parameter decreases as voltage and temperature stresses increase and it shows a similar varying tendency under different models. When both nonconstant shape parameter assumption and random effects are considered, the shape parameter decreases with the voltage stress and increases with the temperature stress. A simulation study reveals that the model with both random effects and nonconstant shape parameters performs better than other models in percentile estimation.