Optimal condition-based maintenance policy for a partially observable system with two sampling intervals

Abstract

In this paper, we propose an optimal Bayesian control policy with two sampling intervals minimizing the long-run expected average maintenance cost per unit time for a partially observable deteriorating system. Unlike the previous optimal Bayesian approaches which used periodic sampling models with equidistant intervals, a novel sampling methodology is proposed which is characterized by two sampling intervals and two control thresholds. The deterioration process is modeled as a 3-state continuous time hidden-Markov process with two unobservable operatingstates and an observable failure state. At each sampling epoch, the multivariate observation data provides only partial information about the actual state of the system. We start observing the system with a longer sampling interval. If the posterior probability that the system is in the warning state exceeds a warning limit, observations are taken more frequently, i.e., the sampling interval changes to a shorter one, and if the posterior probability exceeds a maintenance limit, the full inspection is performed, followed possibly by preventive maintenance. We formulate the maintenance control problem in a partially observable Markov decision process (POMDP) framework to find the two optimal control limits and two sampling intervals. Also, the mean residual life (MRL) of the system is calculated as a function of the posterior probability. A numerical example is provided and comparison of the proposed scheme with several alternative sampling and maintenance control strategies is carried out.F. Naderkhani ZG · V. Makis ( ) Mechanical and Industrial Engineering

The effect of multi-sensor data on condition-based maintenance policies

“…As in our work, the authors translated their POMDP into an MDP by means of the λ-minimization technique (Aven & Bergman, 1986) and showed that the optimal policy over the infinite horizon consists of at most four and at most three regions, respectively. Our modeling approach is inspired by that of Kim & Makis (2013), Naderkhani & Makis (2015) and Maillart et al (2018).…”

Condition-Based Maintenance—An Extensive Literature Review

“…Alternatively, Monte Carlo simulation represents a valuable approach since it enables modeling a large set of realistic scenarios [107,108]. In large multi-component systems, analytical models are indeed less effective than simulation models, as proven by Markov models [109,110], continuous-time Markov, time hidden-Markov chains [111,112], gamma processes [113,114] or competition/cooperative heuristic hybrid games [115]. The genetic algorithm has been used as well in combination with Monte Carlo simulation [107] or for risk management associated with strategy selection [116].…”

“…Examples in this sense are represented by the application of support vector machine [175,176] or neural networks [62,65] and their derived self-organizing maps [64,171]. A large number of papers suggests the application of hidden semi-Markov model [159,189,196] or hidden Markov model [112,190,229] for diagnosis or prognosis.…”

Continuous-Observation Partially Observable Semi-Markov Decision Processes for Machine Maintenance

“…In many practical problems, it is common for observations to be continuous, because sensors often provide continuous readings. Recently, [19], [20] and [21] coupled the POSMDP model with the Bayesian control chart. They assumed that, conditioned on the state of the machine, the observation vector follows a multivariate normal distribution.…”