Bayesian modeling of repairable systems with imperfect coverage and delayed detection dynamics

Abstract

In this research article, we thoroughly examine the dynamics of a repairable system, emphasizing a two-unit configuration through a Bayesian perspective. The study integrates diverse prior distributions to model the uncertainty of unknown parameters, incorporating the coverage factor as a probabilistic measure of successful recovery from operational unit failures. The temporal characteristics of unit failure and repair are modeled using exponential distributions, ensuring analytical tractability and robustness. The repair process is bifurcated into two distinct phases: fault detection and location, followed by actual repair, with each phase governed by exponential distributions. Additionally, recovery and reboot times for failed units are also characterized by exponential distributions to maintain consistency in the probabilistic model. To address parameter uncertainty, we adopt a Bayesian methodology, enabling a comprehensive evaluation of system performance metrics. Monte Carlo simulations are employed to derive posterior distributions for critical parameters, including the mean time to system failure and steady-state availability, offering deeper insights into the system's reliability profile. To validate the efficacy of the proposed methodology, extensive numerical experiments are conducted, providing a robust confirmation of the analytical models and computational techniques.