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Applications of renewal theory in analysis of the free‐replacement warranty

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  • Wallace R. Blischke
  • Ernest M. Scheuer

Abstract

Under a free‐replacement warranty of duration W, the customer is provided, for an initial cost of C, as many replacement items as needed to provide service for a period W. Payments of C are not made at fixed intervals of length W, but in random cycles of length Y = W + γ(W), where γ(W) is the (random) remaining life‐time of the item in service W time units after the beginning of a cycle. The expected number of payments over the life cycle, L, of the item is given by MY(L), the renewal function for the random variable Y. We investigate this renewal function analytically and numerically and compare the latter with known asymptotic results. The distribution of Y, and hence the renewal function, depends on the underlying failure distribution of the items. Several choices for this distribution, including the exponential, uniform, gamma and Weibull, are considered.

Suggested Citation

  • Wallace R. Blischke & Ernest M. Scheuer, 1981. "Applications of renewal theory in analysis of the free‐replacement warranty," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 28(2), pages 193-205, June.
    • Handle: RePEc:wly:navlog:v:28:y:1981:i:2:p:193-205
    DOI: 10.1002/nav.3800280202
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    Cited by:

    1. Altındağ, Ömer & Aydoğdu, Halil, 2021. "Estimation of renewal function under progressively censored data and its applications," Reliability Engineering and System Safety, Elsevier, vol. 216(C).
    2. Hui Chen & Jie Chen & Yangyang Lai & Xiaoqi Yu & Lijun Shang & Rui Peng & Baoliang Liu, 2024. "Discrete Random Renewable Replacements after the Expiration of Collaborative Preventive Maintenance Warranty," Mathematics, MDPI, vol. 12(18), pages 1-21, September.
    3. Izzet Sahin & Hakan Polatoglu, 1995. "Distributions of manufacturer's and user's replacement costs under warranty," Naval Research Logistics (NRL), John Wiley & Sons, vol. 42(8), pages 1233-1250, December.

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