Inference and Optimal Plan in Stage Life Testing Using Maximum Product of Spacings and Maximum Likelihood Estimation Method

ABSTRACT This paper introduces a novel approach by implementing Type II censoring on both stages of the stage life testing (SLT) experiment. First, we have assumed that the lifetime of the experimental units follows a combination of Weibull distribution on initial stage and an exponential distribution on the accelerated stage. Furthermore, we have also considered a case where the lifetime of the experimental units on both stages follows Weibull distribution with same shape parameter and different scale parameters. The distributions under the two stress levels are connected through the cumulative exposure model. We derive maximum likelihood estimation (MLE) in the SLT model under different lifetime distributions. As an alternative to MLE, we also derive the maximum product of spacings (MPS) estimation method and compare the performance of the MPS and MLE methods through a simulation study. Additionally, we derive asymptotic confidence intervals (CIs) based on the asymptotic normality of MLE, and we also employ bootstrap methods to obtain the boot‐ and boot‐ CIs. Further, we proposed an optimal design for the SLT experiment based on two optimality criteria. Finally, an extensive simulation study and a real data analysis have been carried out to demonstrate the effectiveness of our approach.