Optimal preventive maintenance policy under fuzzy Bayesian reliability assessment environments

Abstract

Reliability assessment is an important issue in reliability engineering. Classical reliability-estimating methods are based on precise (also called “crisp”) lifetime data. It is usually assumed that the observed lifetime data take precise real numbers. Due to the lack, inaccuracy, and fluctuation of data, some collected lifetime data may be in the form of fuzzy values. Therefore, it is necessary to characterize estimation methods along a continuum that ranges from crisp to fuzzy. Bayesian methods have proved to be very useful for small data samples. There is limited literature on Bayesian reliability estimation based on fuzzy reliability data. Most reported studies in this area deal with single-parameter lifetime distributions. This article, however, proposes a new method for determining the membership functions of parameter estimates and the reliability functions of multi-parameter lifetime distributions. Also, a preventive maintenance policy is formulated using a fuzzy reliability framework. An artificial neural network is used for parameter estimation, reliability prediction, and evaluation of the expected maintenance cost. A genetic algorithm is used to find the boundary values for the membership function of the estimate of interest at any cut level. The long-run fuzzy expected replacement cost per unit time is calculated under different preventive maintenance policies, and the optimal preventive replacement interval is determined using the fuzzy decision making (ordering) methods. The effectiveness of the proposed method is illustrated using the two-parameter Weibull distribution. Finally, a preventive maintenance strategy for a power generator is presented to illustrate the proposed models and algorithms.

Keywords:

• Preventive maintenance
• T-age replacement
• Bayesian estimation
• fuzzy lifetime data
• fuzzy reliability
• fuzzy parameter estimation
• reliability assessment
• fuzzy value ranking
• neural network
• genetic algorithm

Acknowledgements

This research was partially supported by the National Natural Science Foundation of China under contract number 50775026 and the Natural Sciences and Engineering Research Council of Canada. The authors also wish to acknowledge the constructive comments from reviewers and the editor.