Optimal Maintenance Policy Using Non-Informative Prior Distribution and Marcov Chain Monte Carlo Method

사전확률분포와 Marcov Chain Monte Carlo법을 이용한 최적보전정책 연구

  • Received : 2017.06.09
  • Accepted : 2017.09.12
  • Published : 2017.09.25

Abstract

Purpose: The purpose of this research is to determine optimal replacement age using non-informative prior information and Bayesian method. Methods: We propose a novel approach using Bayesian method to determine the optimal replacement age in block replacement policy by defining the prior probability with data on failure time and repair time. The Marcov Chain Monte Carlo simulation is used to investigate the asymptotic distribution of posterior parameters. Results: An optimal replacement age of block replacement policy is determined which minimizes cost and nonoperating time when no information on prior distribution of parameters is given. Conclusion: We find the posterior distribution of parameters when lack of information on prior distribution, so that the optimal replacement age which minimizes the total cost and maximizes the total values is determined.

Keywords

References

  1. Barlow, R. and Hunter, L. (1960). "Optimum Preventive Maintenance Policies." Operations Research, Vol. 8, No. 1, pp. 90-100. https://doi.org/10.1287/opre.8.1.90
  2. Beichelt, F. (1993). "A Unifying Treatment of Replacement Policies with Minimal Repair." Naval Research Logistics, Vol. 40, No. 1, pp. 51-67. https://doi.org/10.1002/1520-6750(199302)40:1<51::AID-NAV3220400104>3.0.CO;2-V
  3. Gibbons, D. I. and Vance, L. C. (1981). "A Simulation Study of Estimators for the 2-parameter Weibull Distribution." IEEE Transactions on Reliability, Vol. 30, No. 1, pp. 61-66.
  4. Sinha, S. K. and Sloan, J. A. (1988). "Bayes Estimation of the Parameters and Reliability Function for the 3 parameter Weibull Distribution." IEEE Transactions on Reliability, Vol. 37, No. 4, pp. 364-369. https://doi.org/10.1109/24.9840
  5. Wilson, J. G. and Benmerzouga, A. (1995). "Bayesian Group Replacement Policies." Operations Research, Vol. 43, No. 3, pp. 471-476. https://doi.org/10.1287/opre.43.3.471
  6. Bassin, W. (1973). "A Bayesian Optimal Overhaul Interval Model for the Weibull Restoration process." Journal of the American Statistical Association, Vol. 68, No. 343, pp. 575-578. https://doi.org/10.1080/01621459.1973.10481384
  7. Boland, P. J. (1982). "Periodic Replacement When Minimal Repair Costs Vary with Time." Naval Research Logistics, Vol. 29, No. 4, pp. 541-546. https://doi.org/10.1002/nav.3800290402
  8. Mazzuchi, T. A. and Soyer, R. (1996). "A Bayesian Perspective on Some Replacement Strategies." Reliability Engineering and System Safety, Vol. 51, No. 3, pp. 295-303. https://doi.org/10.1016/0951-8320(95)00077-1
  9. Sheu et al. (1999). "A Bayesian Perspective on Age Replacement with Minimal Repair." Reliability Engineering and System Safety, Vol. 65, No. 1, pp. 55-64. https://doi.org/10.1016/S0951-8320(98)00087-8
  10. Jung, K. M. and Han, S. S. (2006). "A Bayesian Approach to Replacement Policy Based on Cost and Downtime." Journal of Korean Data & Information Science Society, Vol. 17, No. 3, pp. 743-752.
  11. Soland, R. M. (1969). "Bayesian Analysis of the Weibull Process with Unknown Scale and Shape Parameters." IEEE Transactions on Reliability, Vol. 18, No. 4, pp. 181-184.
  12. Sathe, P. T. and Hancock, W. M. (1973). "A Bayesian Approach to the Scheduling of Preventive Maintenance." IIE Transactions, Vol. 5, No. 2, pp. 172-179.
  13. Jiang, R. and Ji, P. (2002). "Age Replacement Policy: a Multi-attribute Value Model." Reliability Engineering and System Safety, Vol. 76, No. 3, pp. 311-318. https://doi.org/10.1016/S0951-8320(02)00021-2
  14. Soliman et al. (2012). "Modified Weibull model: A Bayes Study Using MCMC Approach Based on Progressive Censoring Data." Reliability Engineering and System Safety, Vol. 100, pp. 48-57. https://doi.org/10.1016/j.ress.2011.12.013