Journal of Korean Society for Quality Management (품질경영학회지)

Korean Society for Quality Management (한국품질경영학회)
권호 표지
DOI QR코드

DOI QR Code

Determining an Optimal Production Time for EPQ Model with Preventive Maintenance and Defective Rate

생산설비의 유지보수서비스와 제품의 불량률을 고려한 최적 생산주기 연구

  • Kim, Migyoung (Department of Applied Statistics, Yonsei University) ;
  • Park, Minjae (College of Business Administration, Hongik University)
  • Received : 2019.02.07
  • Accepted : 2019.02.20
  • Published : 2019.03.31
Download PDF
⟨ Previous Next ⟩

Abstract

Purpose: The purpose of this paper is to determine an optimal production time for economic production quantity model with preventive maintenance and random defective rate as the function of a machinery deteriorates. Methods: If a machinery shifts from "in-control" state to "out-of-control" state, a proportion of defective items being produced increases. It is assumed that time to state shift is a random variable and follows an arbitrary distribution. The elapsed time until process shift decreases stochastically as a production cycle repeats and quasi-renewal process is used to implement for production facilities to deteriorate. Results: When the exponential parameter for exponential distribution increases, the optimal production time increases. When Weibull distribution is considered, the optimal production time is closely affected by the shape parameter of Weibull distribution. Conclusion: A mathematical model is suggested to find optimal production time and optimal number of production cycles and numerical examples are implemented to validate the patterns for changes of optimal times under different parameters assumptions. The real application is implemented using the proposed approach.

Keywords

PJGOB9_2019_v47n1_87_f0001.png 이미지

Figure 1. Relationship between optimal production time and shape parameter κ for Weibull distribution

PJGOB9_2019_v47n1_87_f0002.png 이미지

Figure 2. Relationship between optimal production time and scale parameter λ for Weibull distribution

PJGOB9_2019_v47n1_87_f0003.png 이미지

Figure 3. Relationship between optimal production time and parameter μ for exponential distribution

Table 1. Optimal production time and optimal number of production cycle when a Weibull distribution is considered

PJGOB9_2019_v47n1_87_t0001.png 이미지

Table 2. Optimal production time and optimal number of production cycle when an exponential distribution is considered

PJGOB9_2019_v47n1_87_t0002.png 이미지

References

  1. Bai, Jun, and Hoang Pham. 2005. "Repair-limit risk-free warranty policies with imperfect repair." IEEE Transactions on Systems, Man, and Cybernetics-Part A: Systems and Humans 35(6):765-772. https://doi.org/10.1109/TSMCA.2005.851343
  2. Ben-Daya, Mohamed. 2002. "The economic production lot-sizing problem with imperfect production processes and imperfect maintenance." International Journal of Production Economics 76(3):257-264. https://doi.org/10.1016/S0925-5273(01)00168-2
  3. Groenevelt, Harry, Liliane Pintelon, and Abraham Seidmann. 1992. "Production lot sizing with machine breakdowns." Management Science 38(1):104-123. https://doi.org/10.1287/mnsc.38.1.104
  4. Ha, Jung Lang, and Minjae Park. 2017. "Optimal Maintenance Policy Using Non-Informative Prior Distribution and Marcov Chain Monte Carlo Method." Journal of the Applied Reliability 17(3):188-196.
  5. Hariga, M, and M. Ben-Daya. 1998. "Note: the economic manufacturing lot-sizing problem with imperfect production processes: bounds and optimal solutions." Naval Research Logistics 45(4):423-433. https://doi.org/10.1002/(SICI)1520-6750(199806)45:4<423::AID-NAV8>3.0.CO;2-7
  6. Kim, Chang Hyun, and Yushin Hong. 1999. "An optimal production run length in deteriorating production processes." International Journal of Production Economics 58(2):183-189. https://doi.org/10.1016/S0925-5273(98)00119-4
  7. Liao, Gwo-Liang, Yen Hung Chen, and Shey-Huei Sheu. 2009. "Optimal economic production quantity policy for imperfect process with imperfect repair and maintenance." European Journal of Operational Research 195(2):348-357. https://doi.org/10.1016/j.ejor.2008.01.004
  8. Lim, Jae Hak. 2017. "The Current Issues on Warranty & Maintenance Policy of the Second-Hand Products." Journal of the Applied Reliability 17(2):159-167.
  9. Lim, Jun Hyoung, Dong-Yeon Won, Hyun Su Sim, Cheol Hong Park, Kwan-Ju Koh, Jun-Gyu Kang, and Yong Soo Kim. 2018. "A Study on Condition-based Maintenance Policy using Minimum-Repair Block Replacement." Journal of the Applied Reliability 18(2):114-121. https://doi.org/10.33162/JAR.2018.06.18.2.114
  10. Lin, Gary C., and Dennis E Kroll. 2006. "Economic lot sizing for an imperfect production system subject to random breakdowns." Engineering Optimization 38(1):73-92. https://doi.org/10.1080/03052150500270578
  11. Lin, TM, ST Tseng, and MJ Liou. 1991. "Optimal inspection schedule in the imperfect production system under general shift distribution." Journal of the Chinese Institute of Industrial Engineers 8(2):73-81.
  12. Liu, Yu, and Hong-Zhong Huang. 2010. "Optimal replacement policy for multi-state system under imperfect maintenance." Reliability, IEEE Transactions on 59(3):483-495. https://doi.org/10.1109/TR.2010.2051242
  13. Park, Minjae, and Dong Ho Park. 2018. "Two-dimensional Warranty Policy for Items with Refund Based on Korean Lemon Law." Journal of the Applied Reliability 18(4):349-355. https://doi.org/10.33162/JAR.2018.12.18.4.349
  14. Park, Minjae, and Hoang Pham. 2008. "Warranty system-cost analysis using quasi-renewal processes." Opsearch 45(3):263-274. https://doi.org/10.1007/BF03398818
  15. Park, Minjae, and Hoang Pham. 2010. "Altered quasi-renewal concepts for modeling renewable warranty costs with imperfect repairs." Mathematical and Computer Modelling 52(9-10):1435-1450. https://doi.org/10.1016/j.mcm.2010.05.028
  16. Peterson, Rein, and Edward Allen Silver. 1979. Decision systems for inventory management and production planning: Wiley New York.
  17. Pham, Hoang, and Hongzhou Wang. 1996. "Imperfect maintenance." European Journal of Operational Research 94(3):425-438. https://doi.org/10.1016/S0377-2217(96)00099-9
  18. Pham, Hoang, and Hongzhou Wang. 2001. "A quasi-renewal process for software reliability and testing costs." Systems, Man and Cybernetics, Part A: Systems and Humans, IEEE Transactions on 31(6):623-631. https://doi.org/10.1109/3468.983418
  19. Porteus, Evan L. 1986. "Optimal lot sizing, process quality improvement and setup cost reduction." Operations research 34(1):137-144. https://doi.org/10.1287/opre.34.1.137
  20. Rosenblatt, Meir J., and Hau L. Lee. 1986. "Economic production cycles with imperfect production processes." IIE transactions 18(1):48-55. https://doi.org/10.1080/07408178608975329
  21. Shah, Nita H, Dushyantkumar G. Patel, and Digeshkumar B. Shah. 2018. "EPQ model for returned/reworked inventories during imperfect production process under price-sensitive stock-dependent demand." Operational Research 18(2):343-359. https://doi.org/10.1007/s12351-016-0267-4
  22. Sheu, Shey-Huei, and Jih-An Chen. 2004. "Optimal lot-sizing problem with imperfect maintenance and imperfect production." International journal of systems science 35(1):69-77. https://doi.org/10.1080/00207720310001657090
  23. Wang, Hongzhou, and Hoang Pham. 1996. "A quasi renewal process and its applications in imperfect maintenance." International journal of systems science 27(10):1055-1062. https://doi.org/10.1080/00207729608929311
  24. Whitin, Thomson M. 1957. Theory of inventory management: Princeton University Press.