Maximum entropy model applied to Reliability Centered Maintenance scheme for replaceable systems.

Abstract

Based on methodologies of variational calculus and differential entropy, we propose in this work a non-parametric model that provides a robust estimation of reliability to be used in a RCM scheme. A Weibull analysis is presented first in a case study within the usual RCM schemes. If the sample of data is severly reduced the weibull analysis lost preciscion, impacting in the RCM scheme. To solve this limitation, a maximum entropy aproach is propoused.Differential entropy has been shown as a solid tool to model the response of a random variable when reduced sample size information is available. We take advantage of the formalism of the variational calculus to express a functional that obeys the Euler-Lagrange equations and supported by the Kolmogorov axioms, we extract a generalized non-parametric probability density. By subjecting this density to appropriate boundary conditions in terms of the first moments of the generalized probability density.