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.

Keywords and phrases:

• Perfect repair
• minimal repair
• replacement
• reliability
• preservation property