On a conjecture of optimal repair-replacement strategies for warranted products

  • Authors:

  • X. Jiang;A. K. S. Jardine;D. Lugitigheid

  • Affiliations:

  • Department of Industrial Engineering, Louisiana State University, CEBA 3128, 70803 Baton Rouge, LA, United States;Department of Machnical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8;Department of Machnical and Industrial Engineering, University of Toronto, 5 King's College Road, Toronto, Ontario, Canada M5S 3G8

  • Venue:
  • Mathematical and Computer Modelling: An International Journal
  • Year:
  • 2006

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Abstract

Under a free replacement warranty policy, the manufacturer has the option of rectifying a failure by either repairing the failed item or replacing it with a new one. In [N. Jack, F. Van der Duyn Schouten, Optimal repair-replacement strategies for a warranted product, Int. J. Prod. Econ. 67 (2000) 95-100] a conjecture is made on the optimality of an age-limit policy: there exists a control limit AL(t), such that a minimal repair is performed on failure with t time units remaining in the warranty period if the age of the failing unit is less than or equal to AL(t). In this paper, we prove that this conjecture is indeed correct. Moreover, we show that for a more general model where the repair cost is random, a generalized repair-cost-limit policy is optimal, and the age-limit policy becomes its degenerated form. Numerical examples are provided to illustrate the computational algorithm and to compare the performance of these policies.