Reliability Analysis for a Mixed Poisson‐Lindley Stress‐Strength Model

ABSTRACT Over the past few decades, stress‐strength models have garnered significant attention in reliability engineering and survival analysis. This study investigates a mixed stress‐strength model, where stress () follows a Poisson distribution and strength () follows a Lindley distribution. The primary objective is to estimate the reliability parameter , representing the likelihood that the system's strength exceeds the applied stress. The mean remaining strength is derived to assess the residual lifetime under stress. In the classical framework, we derive estimators for , including the maximum likelihood estimator, maximum product spacings estimator, and the uniformly minimum variance unbiased estimator. In the Bayesian framework, Bayes estimators are obtained using informative gamma priors with the squared error loss function, and posterior expectations are computed using Lindley's approximation and Markov Chain Monte Carlo methods. A Monte Carlo simulation study is conducted to evaluate the performance of these estimators in terms of bias and mean squared error. Finally, the model's practical utility is illustrated using a real‐world reliability dataset.