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A simple approximation for the renewal function with an increasing failure rate

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  • Jiang, R.

Abstract

This paper proposes a simple approximation for the renewal function of a failure distribution with an (equivalently) increasing failure rate. The approximation is a linear combination of the cumulative distribution and hazard functions, and the coefficients are functions of the shape parameter of the distribution. The approximation is applied to the Weibull, gamma and lognormal distributions, and it is shown that the approximation is accurate for t up to a certain value of larger than the characteristic life. The approximation is useful for maintenance policy analysis and optimization where the renewal function needs to be evaluated.

Suggested Citation

  • Jiang, R., 2010. "A simple approximation for the renewal function with an increasing failure rate," Reliability Engineering and System Safety, Elsevier, vol. 95(9), pages 963-969.
    • Handle: RePEc:eee:reensy:v:95:y:2010:i:9:p:963-969
    DOI: 10.1016/j.ress.2010.04.007
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    References listed on IDEAS

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    1. Constantine, A. G. & Robinson, N. I., 1997. "The Weibull renewal function for moderate to large arguments," Computational Statistics & Data Analysis, Elsevier, vol. 24(1), pages 9-27, March.
    2. Jiang, R., 2008. "A Gamma–normal series truncation approximation for computing the Weibull renewal function," Reliability Engineering and System Safety, Elsevier, vol. 93(4), pages 616-626.
    3. Mark P. Kaminskiy, 2004. "Simple Bounds on Cumulative Intensity Functions of Renewal and G‐Renewal Processes with Increasing Failure Rate Underlying Distributions," Risk Analysis, John Wiley & Sons, vol. 24(4), pages 1035-1039, August.
    4. Jiang, R., 2009. "An accurate approximate solution of optimal sequential age replacement policy for a finite-time horizon," Reliability Engineering and System Safety, Elsevier, vol. 94(8), pages 1245-1250.
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    Citations

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    Cited by:

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    2. Asadi, Majid, 2023. "On a parametric model for the mean number of system repairs with applications," Reliability Engineering and System Safety, Elsevier, vol. 234(C).
    3. Brezavšček Alenka, 2013. "A Simple Discrete Approximation for the Renewal Function," Business Systems Research, Sciendo, vol. 4(1), pages 65-75, March.
    4. Gómez Fernández, Juan F. & Márquez, Adolfo Crespo & López-Campos, Mónica A., 2016. "Customer-oriented risk assessment in network utilities," Reliability Engineering and System Safety, Elsevier, vol. 147(C), pages 72-83.
    5. Wu, Shaomin, 2014. "Warranty return policies for products with unknown claim causes and their optimisation," International Journal of Production Economics, Elsevier, vol. 156(C), pages 52-61.
    6. R. Jiang, 2022. "Two approximations of renewal function for any arbitrary lifetime distribution," Annals of Operations Research, Springer, vol. 311(1), pages 151-165, April.
    7. Parsa, Hossein & Jin, Mingzhou, 2013. "An improved approximation for the renewal function and its integral with an application in two-echelon inventory management," International Journal of Production Economics, Elsevier, vol. 146(1), pages 142-152.
    8. Jiang, R., 2020. "A novel two-fold sectional approximation of renewal function and its applications," Reliability Engineering and System Safety, Elsevier, vol. 193(C).

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