Reliability analysis and spares provisioning for repairable systems with dependent failure processes and a time-varying installed base

ABSTRACT

Line Replaceable Units (LRUs), which can be quickly replaced at a first-level maintenance facility, are widely deployed on capital-intensive systems in order to maintain high system availability. Failed LRU are repaired after replacement and reused as fully serviceable spare units. Demand for spare LRUs depends on factors such as the time-varying installed base, reliability deterioration or growth over maintenance cycles, procurement leadtime of new LRUs, turn-around leadtime of repaired LRUs, etc. In this article, we propose an integrated framework for both reliability analysis and spares provisioning for LRUs with a time-varying installed base. We assume that each system consists of multiple types of LRUs and associated with each type of LRU is a non-stationary sub-failure process. The failure of a system is triggered by sub-failure processes that are statistically dependent. A hierarchical probability model is developed for the demand forecasting of LRUs. Based on the forecasted demand, the optimum inventory level is found through dynamic programming. An application example is presented. A computer program, called the Integrated Platform for Reliability Analysis and Spare Provision, is available that makes the proposed methods readily applicable.

Keywords:

• Line replaceable units
• repairable systems
• spares provisioning
• reliability analysis
• bayesian statistics

Acknowledgements

The authors would like to thank the reviewers and the Department Editor for their constructive suggestions and comments during the revision of this article.

Appendix

A. Approximation to the full conditionals

The primary model parameters are sampled from the full conditionals using the Metropolis–Hasting algorithm described by Tierney (1994). In particular, we approximate the full conditionals by normal densities and use the approximate distributions as the proposed distributions for sampling.

The full conditionals π(α_j| · ), π(β_j| · ), and π(z| · ) have normal limiting distributions, , , and N(μ_z, σ_z); see Berger (1985).

In particular, is the mode, or the generalized MLE, of π(α_j| · ) given by (A1) and (A2) where (A3)

Note that the closed-form solution of does not exist. Let Xi = ∑ni, jq = 1log xi, q, can be found by solving the equation (A4)

In the program MAT-IPRS,this equation is efficiently solved using Newton's secant method. Finally, μ_z is the mode; i.e., the generalized MLE of π(z| · ): (A5) and (A6) where (A7)

B. The Code: MAT-IPRS

To facilitate the use of the proposed approach in industry, a purpose-built software was written under the GUIDE of MATLAB. The Graphical User Interface (GUI) of this program is shown in Fig. A1. It is seen that this program is capable of (i) calculating summary statistics of field data, (ii) conducting reliability analysis using the MCMC method based on the field data and prior engineering knowledge, and (iii) generating the optimum BCOS level and the order size for current time period. The program is available from the authors.

Figure A1. The GUI of MAT-IPRS.

Additional information

Notes on contributors

Xiao Liu

Xiao Liu joined IBM T. J. Watson Research Center as a research staff member in 2015 after spending three years with the IBM Research Collabotoray Singapore. He is also an Adjunct Assistant Professor with the Department of Industrial and Systems Engineering, National University of Singapore (NUS). He received his Ph.D. degree in Industrial Engineering from NUS and his B.Eng. degree in Mechanical Engineering from the Harbin Institute of Technology, China. He also studied at the Hong Kong University of Science and Technology as an exchange student. He has published in peer-reviewed journals including Technometrics, IEEE Transactions on Reliability, Journal of Quality Technology, IIE Transactions, etc. He received the prestigious 2011 Ralph A. Evans/P.K. McElroy Award for the best paper at the 2011 Reliability and Maintainability Symposium and 2015 IBM Outstanding Technical Achievement Award.

Loon Ching Tang

Loon Ching Tang is a Professor and Director of the Temasek Defence Systems Institute in the National University of Singapore. He obtained his Ph.D. in 1992 from Cornell University in the field of Operations Research. He was presented with the IIE Transactions 2010 Best Application Paper Award and the 2012 Ralph A. Evans/P.K. McElroy Awards. He has been on the editorial review board of the Journal of Quality Technology since 2006. He is the main author of the book Six Sigma: Advanced Tools for Black Belts and Master Black Belts (which was presented the inaugural Masing Book Prize by International Academy of Quality) and a co-author of Markov-Modulated Processes and Semiregenerative Phenomena.