A Study of Replacement Policies for Warranty Products with Different Failure Rate

This paper provides a replacement policy for warranty products with different failure rate from the consumer-s viewpoint. Assume that the product is replaced once within a finite planning horizon, and the failure rate of the second product is lower than the failure rate of the first product. Within warranty period (WP), the failed product is corrected by minimal repair without any cost to the consumers. After WP, the failed product is repaired with a fixed repair cost to the consumers. However, each failure incurs a fixed downtime cost to the consumers over a finite planning horizon. In this paper, we derive the model of the expected total disbursement cost within a finite planning horizon and some properties of the optimal replacement policy under some reasonable conditions are obtained. Finally, numerical examples are given to illustrate the features of the optimal replacement policy under various maintenance costs.

• Wen Liang Chang

• Planning horizon
• Free-repair warranty
• Minimal repair
• Replacement.

[1] R.E. Barlow and F. Proschan, Mathematical Theory of Reliability, Wiley,
New York, 1965.
[2] P.J. Boland and F. Proschan, "Periodic replacement with increasing
minimal repair costs at failure," Operations Research, vol. 30, pp.
1183-1189, 1982.
[3] T. Nakagawa and M. Kowada, "Analysis of a system with minimal repair
and its application to replacement policy," European Journal of
Operational Research, vol. 12, pp. 176-182, 1983.
[4] J.K. Chan and L. Shaw, "Modeling repairable systems with failure rates
dependent on age and maintenance," IEEE Transactions on Reliability,
vol. 42, pp. 566-570, 1993.
[5] Y.H. Chien, "Optimal age for preventive replacement under a combined
fully renewable free replacement with a pro-rata warranty," International
Journal of Production Economics, vol. 124, pp. 198-205, 2010.
[6] Y.H. Chien and J.A. Chen, "Optimal age-replacement policy for
repairable products under renewing free-replacement warranty,"
International Journal of Systems Science, vol. 38, pp. 759-769, 2007.
[7] K.J. Chung, "Optimal repair-cost limit for a consumer following expiry of
a warranty," Microelectronics and Reliability, vol. 34, pp. 1689-1692,
1994.
[8] A.N. Das and S.P. Sarmah, "Preventive replacement models: an overview
and their application in process industries," European Journal of
Industrial Engineering, vol. 4, pp. 280-307, 2010.
[9] W.R. Blischke and D.N.P. Murthy, Warranty Cost Analysis, Dekker, New
York, 1994.
[10] T. Aven, "Optimal replacement under a minimal repair strategy-a general
failure model," Advances in Applied Probability, vol. 15, pp.198-211,
1983.
[11] J. Jaturonnateea, D.N.P. Murthy and R. Boondiskulchoka, "Optimal
preventive maintenance of leased equipment with corrective minimal
repairs," European Journal of Operational Research, vol. 174, pp.
201-215, 2006.
[12] J.P. Jhang, "A study of the optimal use period and number of minimal
repairs of a repairable product after the warranty expires," International
Journal of Systems Science, vol. 36, pp. 697-704, 2005.
[13] C.H. Wang and S.H. Sheu, "Optimal lot sizing products sold under a
free-repair warranty," European Journal of Operational Research, vol. pp.
141, 2003.
[14] T. Nakagawa and S. Mizutani, "A summary of maintenance policies for a
finite interval," Reliability Engineering and System Safety, vol. 94, pp.
89-96, 2009.