Abstract
The performance of reliability inference strongly depends on the modeling of a product’s lifetime distribution. Therefore, the effects of model mis-specification on the product’s lifetime prediction is an interesting research topic. For highly reliable products, this study addresses the effects of model mis-specification in an ALT experiment when the GG3 distribution is either mis-specified as Lognormal or Weibull distribution. We first derive the analytical expressions for the expected log likelihood function when GG3 distribution is either mis-specified as Lognormal or Weibull distribution. Then, the best parameters for the wrong model can be obtained directly via a numerical optimization. Furthermore, we also define the relative bias (RB) and relative variability (RV) to measure the accuracy and precision of the estimated p-th quantile of the product’s lifetime distribution. Both complete and censored ALT models are studied. The results demonstrate that the tail quantiles are significantly overestimated (underestimated) when data wrongly fitted by Lognormal (Weibull) distribution; while the variability of the tail quantiles significantly enlarged when data wrongly fitted by Lognormal (Weibull) distribution. Furthermore, when the sample size and censoring ratio are not large enough, a simulation study shows that the effect of model mis-specification on the tail quantiles is not negligible.