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FUNDING A WARRANTY RESERVE WITH CONTRIBUTIONS AFTER EACH SALE

Published online by Cambridge University Press:  01 June 2006

Peter S. Buczkowski  and
Vidyadhar G. Kulkarni
Peter S. Buczkowski
Affiliation:
Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, E-mail: pbuczkowski@cfl.rr.com; vkulkarn@email.unc.edu
Vidyadhar G. Kulkarni
Affiliation:
Department of Statistics and Operations Research, University of North Carolina at Chapel Hill, E-mail: pbuczkowski@cfl.rr.com; vkulkarn@email.unc.edu
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Abstract

We consider funding an interest-bearing warranty reserve with contributions after each sale. The problem for the manufacturer is to determine the initial level of the reserve fund and the amount to be put in after each sale, so as to ensure that the reserve fund covers all of the warranty liabilities with a prespecified probability over a fixed period of time. We assume a nonhomogeneous Poisson sales process, random warranty periods, and a constant failure rate for items under warranty. We derive the mean and variance of the reserve level as a function of time and provide a robust heuristic to aid the manufacturer in its decision.

Type
Research Article
Information
Probability in the Engineering and Informational Sciences , Volume 20 , Issue 3 , July 2006 , pp. 497 - 515
Copyright
© 2006 Cambridge University Press

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References

REFERENCES

Amato, H.N. & Anderson, E.E. (1976). Determination of warranty reserves: An extension. Management Science 22(12): 1391–1394.Google Scholar
Balcer, Y. & Sahin, I. (1986). Replacement costs under warranty: Cost moments and time variability. Operations Research 34(4): 554–559.Google Scholar
Blischke, W.R. & Murthy, D.N.P. (1994). Warranty cost analysis. New York: Marcel Dekker.
Cramér, H. (1955). Collective risk theory. Stockholm: Esselte Reklam.
Eick, S.G., Massey, W.A., & Whitt, W. (1993). The physics of the Mt /G/∞ queue. Operations Research 41(4): 731–742.Google Scholar
Eliashberg, J., Singpurwalla, N.D., & Wilson, S.P. (1997). Calculating the warranty reserve for a time and usage indexed warranty. Management Science 43(7): 966–975.Google Scholar
Glickman, T.S. & Berger, P.D. (1976). Optimal price and protection period decisions for a product under warranty. Management Science 22: 1381–1390.Google Scholar
Ja., S.S. (1998). Computation of warranty reserves for non-stationary sales processes. Ph.D. thesis, University of North Carolina at Chapel Hill.
Ja, S.S., Kulkarni, V.G., Mitra, A., & Patankar, J.F. (2002). Warranty reserves for non-stationary sales processes. Naval Research Logistics 49(5): 499–513.Google Scholar
Khintchine, A.Y. (1955). Mathematical models in the theory of queueing. Trudy Mat Inst. Steklov 49 (in Russian). (English translation by Charles Griffin and Co., London, 1960.)
Klugman, S.A., Panjer, H.H., & Willmot, G.E. (1998). Loss models: From data to decisions. New York: Wiley.
Mamer, J.W. (1982). Cost analysis of pro rate and free-replacement warranties. Naval Research Logistics Quarterly 29: 345–356.Google Scholar
Mamer, J.W. (1987). Discounted and per unit costs of product warranty. Management Science 33(7): 916–930.Google Scholar
Menke, W.W. (1969). Determination of warranty reserves. Management Science 15(10): 542–549.Google Scholar
Palm, C. (1988). Intensity variations in telephone traffic. Ericcson Technics 44: 1–189 (in German). (English translation by North-Holland, Amsterdam, 1988.)Google Scholar
Rolski, T., Schmidli, H., Schmidt, V., & Teugels, J. (1999). Stochastic processes for insurance and finance. Chichester: Wiley.
Takács, L. (1962). Introduction to the theory of queues. New York: Oxford University Press.
Tapiero, C.S. & Posner, M.J. (1988). Warranty reserving. Naval Research Logistics 35: 473–479.Google Scholar
U.S. Federal Trade Commission Improvement Act. (1975). 88 Stat 2183, Washington, DC, pp. 101–112.