Unbiased estimations for the exponential distribution based on step-stress accelerated life-testing data

This paper derives the unbiased estimations of the mean life and the failure rate at a design stress based on the failure censored step-stress accelerated life-testing data. An exponential life distribution with a mean that is a log-linear function of stress, and a cumulative exposure model are assumed. The simulation results show that the maximum likelihood estimations of the mean life and the failure rate at the design stress have positive bias, and the unbiased estimations of the mean life and the failure rate at the design stress have smaller mean squared errors than the maximum likelihood estimations of these parameters in small and moderate samples.