A One-Stage Two-Machine Replacement Strategy Based on the Bayesian Inference Method

Document Type : Research Paper

Authors

Department of Industrial Engineering, Sharif University of Technology P.O. Box 11365-9414, Azadi Ave., Tehran, Iran

Abstract

In this research, we consider an application of the Bayesian Inferences in machine replacement problem. The application is concerned with the time to replace two machines producing a specific product; each machine doing a special operation on the product when there are manufacturing defects because of failures. A common practice for this kind of problem is to fit a single distribution to the combined defect data, usually a distribution with an increasing hazard rate. While this may be convenient, it does not adequately capture the fact that there are two different underlying causes of failures. A better approach is to view the defect as arising from a mixture population: one due to the first machine failures and the other due to the second one. This allows one to estimate the various parameters of interest including the mixture proportion and the distribution of time between productions of defective products for each machine, separately. To do this, first we briefly introduce the data augmentation method for Bayesian inferences in the context of the finite mixture models. Then, we discuss the analysis of time-to-failure data and propose an optimal decision-making procedure for machine replacement strategy. In order to demonstrate the application of the proposed method we provide a numerical example.

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[1] Box G.E.P., Tiao G.C. (1992), Bayesian inferences in statistical analysis; Wiley Classic Library
Edition; New York.
[2] Chen T.M., Popova E. (2000), Bayesian maintenance policies during a warranty period;
Communications in Statistics –Stochastic Models 16; 121-142.
[3] Childress S., Durango-Cohen P. (2005), On parallel machine replacement problems with general
replacement cost functions and stochastic deterioration; Naval Research Logistics 52; 409-419.
[4] Damien P., Galenko A., Popova E., Hanson T. (2007), Bayesian semi-parametric analysis for a single
item maintenance optimization; European Journal of Operational Research 182; 794-805.
[5] Gupta A., Lawsirirat C. (2006), Strategically optimum maintenance of monitoring-enabled multicomponent
systems using continuous-time jump deterioration model; Journal of Quality in
Maintenance Engineering 12; 306-329.
[6] Hamada M., Martz H.F., Reese C.S., Graves T., Johnson V., Wilson A.G. (2004), A fully Bayesian
approach for combining multilevel failure information in fault tree quantification and optimal followon
resource allocation; Reliability Engineering and System Safety 86; 297-305.
[7] Hritonenko N., Yatsenko Y. (2007), Optimal equipment replacement without paradoxes: A continuous
analysis; Operations Research Letters 35; 245-250.
[8] Jardine A.K.S., Banjevic D., Makis V. (1997), Optimal replacement policy and the structure of
software for condition-based maintenance; Journal of Quality in Maintenance Engineering 3; 109-119.
[9] Mann L., Saxena A., Knapp G. (1995), Statistical-based or condition-based preventive maintenance;
Journal of Quality in Maintenance Engineering 1; 46-59.
[10] Mazzuchi T.A., Soyer R. (1996), A Bayesian perspective on some replacement strategies; Reliability
Engineering and System Safety 51; 295-303.
[11] Merrick J.R.W., Soyer R., Mazzuchi T.A. (2003), A Bayesian semi-parametric analysis of the
reliability and maintenance of machine tools; Technometrics 45; 58-69.
[12] Mobley K.R (1989), An introduction to predictive maintenance; Butterworth-Heinemann, New York.
[13] Moubray J. (1990), Reliability centered maintenance; Butterworth-Heinemann, Oxford.
[14] Nair V.N., Tang B., Xu L. (2001), Bayesian inference for some mixture problems in quality and
reliability; Journal of Quality Technology 33; 16-28.
[15] Saranga H. (2002), A dynamic opportunistic maintenance policy for continuously monitored systems;
Journal of Quality in Maintenance Engineering 8; 92-105.
[16] Sethi S.P., Sorger G., Zhou X.Y. (2000), Stability of real-time lot-scheduling and machine replacement
policies with quality levels; IEEE Transactions on Automatic Control 45; 2193-2196.
[17] Sherwin J.D. (1999), Age-based opportunity maintenance; Journal of Quality in Maintenance
Engineering 5; 221-235.
[18] Sherwin J.D., Al-Najjar B. (1999), Practical models for condition-based monitoring inspection
intervals; Journal of Quality in Maintenance Engineering 5; 203-209.
[19] Sinuany-Stern Z.S. (1993), Replacement policy under partially observed Markov process;
International Journal of Production Economics 29; 159-166.
[20] Sinuany-Stern Z.S., David I., Biran S. (1997), An efficient heuristic for a partially observable Markov
decision process of machine replacement; Journal of Computers in Operations Research 24; 117-126.
[21] Tanner M.A., Wong W.H. (1987), The calculation of posterior distributions by data augmentation;
Journal of the American Statistical Association 82; 528-540.
[22] Tsang A. (1995), Condition-based maintenance: tools and decision making; Journal of Quality in
Maintenance Engineering 1; 3-17.
[23] Valdez-Florez C., Feldman R. (1989), A survey of preventive maintenance models for stochastically
deteriorating single unit systems; Naval Research Logistics 36; 419-446.
[24] Wang C.H., Hwang S.L. (2004), A stochastic maintenance management model with recovery factor;
Journal of Quality in Maintenance Engineering 10; 154-164.
[25] Wilson J.G., Popova E. (1998), Bayesian approaches to maintenance intervention; In Proceedings of
the section on Bayesian Science of the American Statistical Association, 278-284.
[26] Zhou X., Xi L., Lee J. (2006), A dynamic opportunistic maintenance policy for continuously
monitored systems; Journal of Quality in Maintenance Engineering 12; 294-305