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A generalized model for the economic design of x̄control charts for production systems with increasing failure rate and early replacement

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  • M. A. Rahim
  • P. K. Banerjee

Abstract

This article generalizes the model for the economic design of x̄‐control charts of Duncan [4], starting from the more recent papers of Lorenzen and Vance [8] and Banerjee and Rahim [3]. The classical model of Duncan [4] and its several extensions including the unified model of Lorenzen and Vance [8] assumed exponentially distributed in‐control periods and provided uniform sampling schemes. Banerjee and Rahim [3], however, assumed a Weibull‐distributed in‐control period having an increasing failure rate and used variable sampling intervals. The present article is an extension of the work of Banerjee and Rahim [3], where a general distribution of in‐control periods having an increasing failure rate is assumed and the possibility of age‐dependent repair before failure is considered. Several different truncated and nontruncated probability models are chosen. It is proposed that economic benefits can be achieved by adopting a nonuniform inspection scheme and by truncating a production cycle when it attains a certain age. Numerical examples are presented to support this proposition. Finally, the effect of model specification in the choice of failure mechanism is investigated. © 1993 John Wiley & Sons, Inc.

Suggested Citation

  • M. A. Rahim & P. K. Banerjee, 1993. "A generalized model for the economic design of x̄control charts for production systems with increasing failure rate and early replacement," Naval Research Logistics (NRL), John Wiley & Sons, vol. 40(6), pages 787-809, October.
    • Handle: RePEc:wly:navres:v:40:y:1993:i:6:p:787-809
    DOI: 10.1002/1520-6750(199310)40:63.0.CO;2-4
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    Cited by:

    1. Ching-Hsin Wang & Feng-Chia Li, 2020. "Economic design under gamma shock model of the control chart for sustainable operations," Annals of Operations Research, Springer, vol. 290(1), pages 169-190, July.
    2. F L Chen & C H Yeh, 2011. "Economic statistical design for x-bar control charts under non-normal distributed data with Weibull in-control time," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 62(4), pages 750-759, April.
    3. Shoshana Anily & Abraham Grosfeld-Nir, 2006. "An Optimal Lot-Sizing and Offline Inspection Policy in the Case of Nonrigid Demand," Operations Research, INFORMS, vol. 54(2), pages 311-323, April.
    4. Viliam Makis, 1998. "Optimal lot sizing and inspection policy for an EMQ model with imperfect inspections," Naval Research Logistics (NRL), John Wiley & Sons, vol. 45(2), pages 165-186, March.
    5. M. A. Pasha & M. Bameni Moghadam & M. A. Rahim, 2020. "Effects of non-normal quality data on the integrated model of imperfect maintenance, early replacement, and economic design of $${\bar{X}}$$ X ¯ -control charts," Operational Research, Springer, vol. 20(4), pages 2519-2536, December.

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