Journal of the Korean Data and Information Science Society

The Korean Data and Information Science Society (한국데이터정보과학회)
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A Bayesian approach to replacement policy following the expiration of non-renewing combination warranty based on cost and downtime

비재생혼합보증이 종료된 이후의 비용과 비가동시간에 근거한 교체정책에 대한 베이지안 접근

  • Jung, Ki-Mun (Department of Informational Statistics, Kyungsung University)
  • 정기문 (경성대학교 정보통계학과)
  • Received : 2010.07.09
  • Accepted : 2010.09.08
  • Published : 2010.09.30
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Abstract

This paper considers a Bayesian approach to replacement policy following the expiration of non-renewing combination warranty. The non-renewing combination warranty is the combination of the non-renewing free replacement warranty and the non-renewing pro-rata replacement warranty. We use the criterion based on the expected cost and the expected downtime to determine the optimal replacement period. To do so, we obtain the expected cost rate per unit time and the expected downtime per unit time, respectively. When the failure times are assumed to follow a Weibull distribution with uncertain parameters, we propose the optimal replacement policy based on the Bayesian approach. The overall value function suggested by Jiang and Ji (2002) is utilized to determine the optimal replacement period. Also, the numerical examples are presented for illustrative purpose.

본 논문에서는 비재생혼합보증이 종료된 이후의 교체정책에 대한 베이지안 접근을 고려한다. 이때, 비재생혼합보증은 비재생무료교체보증과 비재생비례교체보증의 혼합된 형태가 된다. 최적의 교체주기를 결정하기 위하여 기대비용과 기대비가동시간에 근거한 기준이 사용되는데, 이를 위해서 단위시간당 기대비용과 단위시간당 기대비가동시간이 각각 구해진다. 시스템의 고장시간이 불확실한 모수를 갖는 와이블분포를 할 때, 베이지안 접근에 근거하여 최적의 교체정책이 제안된다. 이때, 최적의 교체주기를 결정하기 위해서 Jiang과 Ji (2002)에 의해서 제안된 총밸류함수가 사용된다. 끝으로, 본 논문에서 제안된 베이지안 교체정책을 설명하기 위해서 수치적 예를 살펴본다.

Keywords

References

  1. Canfield, R. V. (1986). Cost optimization of periodic preventive maintenance. IEEE Transactions on Reliability, 35, 78-81. https://doi.org/10.1109/TR.1986.4335355
  2. Chien, Y. H. (2008). A general age replacement model with minimal repair under renewing free-replacement warranty. European Journal of Operational Research, 186, 1046-1058. https://doi.org/10.1016/j.ejor.2007.02.030
  3. Han, S. S. and Jung, G. M. (2002). Bayesian maintenance policy for a repairable system with non-renewing warranty. Journal of Korean Data & Information Science Society, 13, 55-65.
  4. Jiang, R. and Ji, P. (2002). Age replacement policy: A multi-attribute value model. Reliability Engineering and System Safety, 76, 311-318. https://doi.org/10.1016/S0951-8320(02)00021-2
  5. Jung, G. M. and Park, D. H.(2003). Optimal maintenance policies during the post-warranty period. Reliability Engineering and System Safety, 82, 173-185. https://doi.org/10.1016/S0951-8320(03)00144-3
  6. Jung, K. M. (2006). Optimal preventive maintenance policy for a repairable system. Journal of Korean Data & Information Science Society, 17, 367-377.
  7. Jung, K. M. (2007). A Bayesian approach to PM model with random maintenance quality. Journal of Korean Data & Information Science Society, 18, 689-696.
  8. Jung, K. M. (2009). Two PM policies following the expiration of free-re[air warranty. Journal of Korean Data & Information Science Society, 20, 999-1007.
  9. Jung, K. M., Han, S. S. and Park, D. H. (2008). Optimization of cost and downtime for replacement model following the expiration of warranty. Reliability Engineering and System Safety, 93, 995-1003. https://doi.org/10.1016/j.ress.2007.05.005
  10. Jung, K. M., Han, S. S. and Park, D. H. (2010). A Bayesian approach to maintenance policy based on cost and downtime after non-renewing warranty. Communication in Statistics-Theory and Method, 39, 2321-2332. https://doi.org/10.1080/03610921003778167
  11. Lin, D., Zuo, M. J. and Yam, R. C. M. (2000). General sequential imperfect preventive maintenance models. International Journal of Reliability Quality and Safety Engineering, 7, 253-266. https://doi.org/10.1142/S0218539300000213
  12. Malik, M. A. K. (1979). Reliable preventive maintenance scheduling. AIIE Transactions, 11, 221-228 https://doi.org/10.1080/05695557908974463
  13. Mazzuchi, T. A. and Soyer, R. (1996). A Bayesian perspective on some replacement strategies. Reliability Engineering and System Safety, 51, 295-303. https://doi.org/10.1016/0951-8320(95)00077-1
  14. Nakagawa, T. (1986). Periodic and sequential preventive maintenance policies. Journal of Applied Probability, 23, 536-542. https://doi.org/10.2307/3214197
  15. Nakagawa, T. (1988). Sequential imperfect preventive maintenance policies. IEEE Transactions on Reliability, 37, 295-298. https://doi.org/10.1109/24.3758
  16. Park, K. S. and Jun, C. H. (1997). An optimum maintenance policy: A Bayesian approach to periodic incomplete preventive maintenance with minimal repair at failure. Proceedings of '97 Conference of the Korean Operations Research and Management Science Society, 193-196.
  17. Sahin, I. and Polatoglu, H. (1996). Maintenance strategies following the expiration of warranty. IEEE Transactions on Reliability, 45, 220-228. https://doi.org/10.1109/24.510805
  18. Sheu, S. H., Yeh, R. H., Lin, Y. B. and Juang, M. G. (1999). A Bayesian perspective on age replacement with minimal repair. Reliability Engineering and System Safety, 65, 55-64. https://doi.org/10.1016/S0951-8320(98)00087-8
  19. Yeh, R. H., Chen, M. Y. and Lin, C. Y. (2007). Optimal periodic replacement policy for repairable products under free-repair warranty. European Journal of Operational Research, 176, 1678-1686. https://doi.org/10.1016/j.ejor.2005.10.047