Reliability analysis of imperfect repair and switching failures: A Bayesian inference and Monte Carlo simulation approach

Abstract

Reliability analysis of complex systems is essential to ensuring their dependable operation. This study examines a dual-active, single-standby storage unit system, which is integral to various industrial and technological applications. The research delves into the reliability metrics of this system, particularly addressing the challenges posed by unreliable repairs and standby switching failures. Bayesian inference, utilizing Gamma and Beta prior distributions along with Monte Carlo simulations, offers a robust methodology for estimating unknown parameters and deriving posterior distributions. The analysis assumes exponential distributions for both time-to-failure and time-to-repair, while time-to-inspection for perfect and imperfect rejuvenations also follows exponential distributions. The probability of unsuccessful standby switching, denoted as $q$, is incorporated into the model. The results, presented through detailed tables and graphical representations, provide valuable insights into the system’s reliability and the effectiveness of the statistical methods employed.