Bayesian multivariate imperfect repair model

Abstract

This paper generalizes a multivariate imperfect repair model by adapting a Bayesian approach. We concern with modeling a system whose components have specific multivariate distribution of dependent lifelengths. Upon failure, each components undergoes imperfect repair. Different sources of failure which affect the probabilities of perfect and minimal repair are distinguished. Each probability of perfect (minimal) repair is assumed unknown and assigned a prior distribution. Based on the proposed model, we derive the distribution of waiting time between two successive perfect repairs and its corresponding failure rates. We also study some preservation properties for certain nonparametric classes of life distributions and describe the singularity for the resulting distribution.

Extended Optimal Replacement Policy for a Two-Unit System With Shock Damage Interaction

“…Consider a system subject to shocks that weaken the system and make it more expensive to run (Sheu and Griffith [31], [32], Sheu [33], Sheu et al [34], [35], Chang et al [8], and Chien et al [9]). Cumulative damage models are developed for systems which fail when the total damage exceeds a specified level (Cox [11]).…”