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Economic optimization of off-line inspection in a process that also produces non-conforming units when in control and conforming units when out of control

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  • Bendavid, Illana
  • Herer, Yale T.

Abstract

A finite batch of units is produced by a process subject to random failures. The process starts from the in-control state and may shift, while producing a unit, to the out of control state. We consider the case that inspection is conducted after all the units of the batch have been produced, when the production order of the units is preserved. Most research has assumed that while in the in-control state, the process produces only conforming units and in the out of control state, it produces only non-conforming ones. In our research we relax this assumption, i.e. we consider that in the in-control state the process may also produce non-conforming units and in the out of control state, it may also produce conforming ones. Using dynamic programming, we develop an optimal inspection/disposition policy that finds which units to inspect and how to dispose of uninspected units in order to minimize the expected cost, which includes inspection and penalty costs due to classification errors. In addition to the optimal policy, we develop several heuristic policies since the computational complexity of the dynamic programming calculations is O(3N). We then perform computational studies to check the behavior of the optimal and heuristic policies and also to compare the latter policies.

Suggested Citation

  • Bendavid, Illana & Herer, Yale T., 2009. "Economic optimization of off-line inspection in a process that also produces non-conforming units when in control and conforming units when out of control," European Journal of Operational Research, Elsevier, vol. 195(1), pages 139-155, May.
  • Handle: RePEc:eee:ejores:v:195:y:2009:i:1:p:139-155
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    References listed on IDEAS

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    1. Charles H. Fine, 1988. "A Quality Control Model with Learning Effects," Operations Research, INFORMS, vol. 36(3), pages 437-444, June.
    2. June S. Park & Michael H. Peters & Kwei Tang, 1991. "Note---Optimal Inspection Policy in Sequential Screening," Management Science, INFORMS, vol. 37(8), pages 1058-1061, August.
    3. Richard L. Marcellus & Maqbool Dada, 1991. "Interactive Process Quality Improvement," Management Science, INFORMS, vol. 37(11), pages 1365-1376, November.
    4. Sung, C. S. & Ock, Young Seok, 1992. "Optimal production policy for a single-product single-machine problem with intermediate machine inspection allowed," International Journal of Production Economics, Elsevier, vol. 28(1), pages 85-94, November.
    5. Evan L. Porteus, 1990. "Note---The Impact of Inspection Delay on Process and Inspection Lot Sizing," Management Science, INFORMS, vol. 36(8), pages 999-1007, August.
    6. Evan L. Porteus, 1986. "Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction," Operations Research, INFORMS, vol. 34(1), pages 137-144, February.
    7. Refael Hassin, 1984. "A Dichotomous Search for a Geometric Random Variable," Operations Research, INFORMS, vol. 32(2), pages 423-439, April.
    8. Yale T. Herer & Tzvi Raz, 2000. "Optimal Parallel Inspection for Finding the First Nonconforming Unit in a Batch---An Information Theoretic Approach," Management Science, INFORMS, vol. 46(6), pages 845-857, June.
    9. Jewkes, Elizabeth M., 1995. "Optimal inspection effort and scheduling for a manufacturing process with repair," European Journal of Operational Research, Elsevier, vol. 85(2), pages 340-351, September.
    10. Hsu, Lie-Fern & Kuo, Shyanjaw, 1995. "Design of optimal maintenance policies based on on-line sampling plans," European Journal of Operational Research, Elsevier, vol. 86(2), pages 345-357, October.
    11. 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.
    12. Hau L. Lee & Meir J. Rosenblatt, 1987. "Simultaneous Determination of Production Cycle and Inspection Schedules in a Production System," Management Science, INFORMS, vol. 33(9), pages 1125-1136, September.
    13. Hong, Sung Hoon & Kim, Sang Boo & Kwon, Hyuck Moo & Lee, Min Koo, 1998. "Economic design of screening procedures when the rejected items are reprocessed," European Journal of Operational Research, Elsevier, vol. 108(1), pages 65-73, July.
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    4. Costa Quinino, Roberto da & Colin, Emerson C. & Ho, Linda Lee, 2010. "Diagnostic errors and repetitive sequential classifications in on-line process control by attributes," European Journal of Operational Research, Elsevier, vol. 201(1), pages 231-238, February.

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