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Warranty analysis and renewal function estimation

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  • Edward W. Frees

Abstract

Estimation of the expected cost of a warranty for a stochastically failing unit is closely tied to estimation of the renewal function. The renewal function is a basic tool also used in probabilistic models arising in other areas such as reliability theory, inventory theory, and continuous sampling plans. In these other areas, estimation of a straight line approximation of the renewal function instead of direct estimation of the renewal function has proved successful. This approximation is based on a limit expression for large values of the argument, say t, of the renewal function. However, in warranty analusis, typically t is small compared to the mean failure time of the unit. Hence, alternative methods for renewal function estimation, both parametric and nonparametric, are presented and discussed. An important aspect of this paper is to discuss the performance of the renewal function estimators when only a small number of failed units is available. A Monte Carlo study is given which suggests guidelines for choosing an estimator under various circumstances.

Suggested Citation

  • Edward W. Frees, 1986. "Warranty analysis and renewal function estimation," Naval Research Logistics Quarterly, John Wiley & Sons, vol. 33(3), pages 361-372, August.
    • Handle: RePEc:wly:navlog:v:33:y:1986:i:3:p:361-372
    DOI: 10.1002/nav.3800330302
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    Cited by:

    1. Herbert Moskowitz & Young Hak Chun, 1994. "A poisson regression model for two‐attribute warranty policies," Naval Research Logistics (NRL), John Wiley & Sons, vol. 41(3), pages 355-376, April.
    2. 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).
    3. Michel Harel & Joseph Ngatchou-Wandji & Livasoa Andriamampionona & Victor Harison, 2022. "Weak convergence of nonparametric estimators of the multidimensional and multidimensional-multivariate renewal functions on Skorohod topology spaces," Statistical Inference for Stochastic Processes, Springer, vol. 25(3), pages 485-504, October.

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