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Economic and economic-statistical designs of an X¯ control chart for two-unit series systems with condition-based maintenance

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  • Liu, Liping
  • Yu, Miaomiao
  • Ma, Yizhong
  • Tu, Yiliu

Abstract

The economic and economic-statistical designs of an X¯ control chart for two-identical unit series systems with condition-based maintenance is studied in this paper. This system is described using a five-state continuous time Markov chain. We assume that the system is monitored by an X¯ control chart to avoid costly failures. When the control chart gives an out-of-control signal, a full inspection will be conducted to confirm the actual system condition. Moreover, we assume that the system unit can be preventively replaced at a sampling epoch and must be replaced upon failure; the cost of preventive replacement is less than that of failure replacement. In addition, a random shift size is considered for two types of design. Based on these assumptions and by using renewal theory, optimization models have been developed to find the optimal control chart parameters for minimizing the average maintenance costs. A numerical example is presented to compare the two control chart designs. We also consider the effect of each statistical constraint on the decision variables and on the expected cost.

Suggested Citation

  • Liu, Liping & Yu, Miaomiao & Ma, Yizhong & Tu, Yiliu, 2013. "Economic and economic-statistical designs of an X¯ control chart for two-unit series systems with condition-based maintenance," European Journal of Operational Research, Elsevier, vol. 226(3), pages 491-499.
    • Handle: RePEc:eee:ejores:v:226:y:2013:i:3:p:491-499
    DOI: 10.1016/j.ejor.2012.11.031
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    2. Yeong, Wai Chung & Khoo, Michael B.C. & Lee, Ming Ha & Rahim, M.A., 2013. "Economic and economic statistical designs of the synthetic X¯ chart using loss functions," European Journal of Operational Research, Elsevier, vol. 228(3), pages 571-581.
    3. Do, Phuc & Assaf, Roy & Scarf, Phil & Iung, Benoit, 2019. "Modelling and application of condition-based maintenance for a two-component system with stochastic and economic dependencies," Reliability Engineering and System Safety, Elsevier, vol. 182(C), pages 86-97.
    4. Yin, Hui & Zhang, Guojun & Zhu, Haiping & Deng, Yuhao & He, Fei, 2015. "An integrated model of statistical process control and maintenance based on the delayed monitoring," Reliability Engineering and System Safety, Elsevier, vol. 133(C), pages 323-333.
    5. Liping Liu & Lining Jiang & Ding Zhang, 2017. "An integrated model of statistical process control and condition-based maintenance for deteriorating systems," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 68(11), pages 1452-1460, November.
    6. Moura Neto, F. & Souza, P. & de Magalhães, M.S., 2019. "Determining baseline profile by diffusion maps," European Journal of Operational Research, Elsevier, vol. 279(1), pages 107-123.
    7. Amir Ahmadi-Javid & Mohsen Ebadi, 2017. "Economic Design of Memory-Type Control Charts: The Fallacy of the Formula Proposed by Lorenzen and Vance (1986)," Papers 1708.06160, arXiv.org.
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