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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)
  • 김미경 (연세대학교 응용통계학과) ;
  • 박민재 (홍익대학교 경영학과)
  • Received : 2019.02.07
  • Accepted : 2019.02.20
  • Published : 2019.03.31

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.

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

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

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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

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

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Acknowledgement

Supported by : National research Foundation of Korea

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