An asymptotical method to estimate the parameters of a deteriorating system under condition-based maintenance

TL;DR

This paper introduces an asymptotic estimation method for parameters of deteriorating systems under perfect condition-based maintenance, leveraging renewal process theory and establishing a CLT, with comparisons to maximum likelihood methods.

Contribution

It presents a novel asymptotic approach for parameter estimation in deteriorating systems, providing theoretical CLT results and empirical comparisons with existing methods.

Findings

The method is accurate and fast in various examples.

It outperforms the maximum likelihood method in certain scenarios.

The CLT provides a theoretical foundation for the estimators.

Abstract

In this paper, we develop a new method to estimate the parameters of a deteriorating system under perfect condition-based maintenance. This method is based on the asymptotical behavior of the system, which is studied by using the renewal process theory. We obtain a Central Limit Theorem (CLT in the following) for the parameters. We compare the accuracy and the speed of the method with the maximum likelihood one (ML method in the following) on different examples.