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Quality Control for Products Supplied with Warranty

Author

Listed:
  • Jinfa Chen

    (Columbia University, New York, New York)

  • David D. Yao

    (Columbia University, New York, New York)

  • Shaohui Zheng

    (Columbia University, New York, New York)

Abstract

A batch of products is to be supplied to customers with warranty. The units in the batch are either defective or nondefective, with different lifetime distributions. The defect rate—the proportion of defects in the batch—is itself a random variable, known only in terms of its distribution. We develop a sequential quality control procedure that exploits the knowledge of the defect distribution gained through inspection, and strikes an optimal balance between the inspection repair cost and the warranty cost. We identify a simple threshold policy, and we prove its optimality for a very general class of warranty cost functions without imposing any restrictions on the type of distributions involved. The key to optimality is that the warranty cost, as a function of the number of inspected units and the conditional defect index, satisfies a so-called K -submodularity property, which is a strengthening of the usual notion of submodularity.

Suggested Citation

  • Jinfa Chen & David D. Yao & Shaohui Zheng, 1998. "Quality Control for Products Supplied with Warranty," Operations Research, INFORMS, vol. 46(1), pages 107-115, February.
  • Handle: RePEc:inm:oropre:v:46:y:1998:i:1:p:107-115
    DOI: 10.1287/opre.46.1.107
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    References listed on IDEAS

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    1. Donald M. Topkis, 1978. "Minimizing a Submodular Function on a Lattice," Operations Research, INFORMS, vol. 26(2), pages 305-321, April.
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    Cited by:

    1. Yeh, Ruey Huei & Chen, Tzu-Hui, 2006. "Optimal lot size and inspection policy for products sold with warranty," European Journal of Operational Research, Elsevier, vol. 174(2), pages 766-776, October.
    2. David D. Yao & Shaohui Zheng, 1999. "Sequential Inspection Under Capacity Constraints," Operations Research, INFORMS, vol. 47(3), pages 410-421, June.
    3. Murthy, D. N. P. & Djamaludin, I., 2002. "New product warranty: A literature review," International Journal of Production Economics, Elsevier, vol. 79(3), pages 231-260, October.
    4. Jinfa Chen & David D. Yao & Shaohui Zheng, 2001. "Optimal Replenishment and Rework with Multiple Unreliable Supply Sources," Operations Research, INFORMS, vol. 49(3), pages 430-443, June.

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