Virtual Age Models: Monitoring Information Level and Quality of Parametric Estimation

Abstract

An industrial system is subject to failures during its lifetime. These failures are corrected by maintenances, and then the system works again until the next failure. However, the system is not necessarily in the same state as just before the failure. A typical assumption is the As Bad As Old hypothesis, where the system stays in the same state after the failure. Another hypothesis is the As Good As New case, in which the system is totally renewed after a failure. But between minimal and perfect repairs, there exists a wide range of imperfect maintenances. Virtual age models are a way to deal with an imperfect maintenance effect. They also take into account the intrinsic wear of the system. Numeric estimation is used to infer the values of the parameters for some data set.In some cases, we are able to observe several identical and independent systems. Then, we can record some differences between these systems. This information can be added in the virtual age model as covariates. However, we may lack the continuous observation of the covariates. For example, periodic inspections of the systems will only provide discrete covariates, that we can use in the estimation as step-wise constant covariates. The first purpose of this paper is to understand how the frequency of inspection of the covariates impacts the quality of the parametric estimation.Too frequent inspections of the systems could lead to unexpected and unwanted costs. The frequency of inspection should be balanced so that their cost is reasonable compared to the risk of a bad quality estimation. The finding of an optimal cost is the second aim of this paper.