A Bayesian Approach for Step-Stress-Accelerated Life Tests for One-Shot Devices Under Exponential Distributions

Abstract

AbstractIn practice, accelerated life tests are commonly used to collect failure time data within a short period of time by elevating stress levels. In this chapter, step-stress-accelerated life tests with multiple stress levels are considered for one-shot devices that can be used only once. As the exact failure times of one-shot devices cannot be observed from accelerated life tests, a Bayesian approach incorporating with prior information provides some useful inference on the reliability. To extrapolate the reliability under normal operating conditions from elevated stress levels, cumulative exposure models with exponential distributions are adopted. The Markov Chain Monte Carlo method via Metropolis–Hastings algorithm is performed to estimate the model parameters, the reliability, and the mean lifetime. Finally, comprehensive simulation studies for normal (subjective) and Jeffreys (objective) priors are carried out to evaluate the performance of the Bayesian estimation in terms of bias and root mean square error. A real data on samples of grease-based magnetorheological fluids is analyzed for illustration of the Bayesian estimation.