Abstract
This paper presents the expected long-run cost per unit time for a system monitored by an adaptive control chart with variable sample sizes: if the control chart signals that the system is out of control, the sampling which follows will be conducted with a larger sample size. The system is supposed to have three states: in-control, out-of-control, and failed. Two levels of repair are applied to maintain the system. A minor repair will be conducted if an assignable cause is confirmed by an inspection, and a major repair will be performed if the system fails. Both the minor and major repairs are assumed to be perfect. We derive the expected long-run cost per unit time, which can be used to obtain the optimal inspection policy. Numerical examples are conducted to validate the derived cost.
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References
Tagaras G, Lee H (1988) Economic design of control charts with different control limits for different assignable causes. Manage Sci 34(11):1347–1366
Tagaras G, Lee H (1989) Approximate semi-economic design of control charts with multiple control limits. Nav Res Logist 36:337–353
Cheng A, Liu R, Luxhj J (1997) Thresholds for safety inspection measurements based on control charts. Int J Reliab Qual Saf Eng 42:205–225
Chan L, Wu S (2009) Optimal design for inspection and maintenance policy based on the ccc chart. Comput Ind Eng 57(3):667–676
Cassady R, Bowden R, Liew L, Pohl E (2000) Combining preventive maintenance and statistical process control: a preliminary investigation. IIE Trans (Institute of Industrial Engineers) 32(6):471–478
Goh T (1994) Some practical issues in the assessment of nonconforming rates in a manufacturing process. Int J Prod Econ 33(1–3):81–88
Xie M, Goh T, Ranjan P (2002) Some effective control chart procedures for reliability monitoring. Reliab Eng Syst Saf 77(2):143–150
Montgomery D (2001) Introduction to statistical quality control. Wiley, New York
Ohta H, Rahim M (1997) A dynamic economic model for an \(\bar{X}\)-control chart design. IIE Trans (Institute of Industrial Engineers) 29(6):481–486
Parkhideh B, Case K (1989) Economic design of a dynamic X-control chart. IIE Trans (Institute of Industrial Engineers) 21(4):313–323
De Magalhes M, Epprecht E, Costa A (2001) Economic design of a vp \(\bar{X}\) chart. Int J Prod Econ 74(1–3):191–200
Chen Y, Hsieh K, Chang C (2007) Economic design of the VSSI \(\bar{X}\) control charts for correlated data. Int J Prod Econ 107(2):528–539
Zhang S, Wu Z (2007) A CUSUM scheme with variable sample sizes for monitoring process shifts. Int J Adv Manuf Technol 33(9–10):977–987
Liu JY, Xie M, Goh TN, Liu QH, Yang ZH (2006) Cumulative count of conforming chart with variable sampling intervals. Int J Prod Econ 101(2):286–297
Natvig B (1982) Two suggestions of how to define a multistate coherent system. Adv Appl Probab 14(2):434–455
Wu S, Chan L (2003) Performance utility-analysis of multi-state systems. IEEE Trans Reliab 52(1):14–21
Wu S (2005) Joint importance of multistate systems. Comput Ind Eng 49(1):63–75
Tagaras G (1998) A survey of recent developments in the design of adaptive control charts. J Qual Technol 30(3):212–231
Ross S (2007) The exponential distribution and the Poisson process. Introduction to probability models, 9th edn. Academic, London, pp 302–364
Wu S, Zuo MJ (2010) Linear and nonlinear preventive maintenance models. IEEE Trans Reliab 59(1):242–249
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Wu, S. Optimal inspection policy for three-state systems monitored by variable sample size control charts. Int J Adv Manuf Technol 55, 689–697 (2011). https://doi.org/10.1007/s00170-010-3091-7
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DOI: https://doi.org/10.1007/s00170-010-3091-7