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On continuous lifetime distributions with polynomial failure rate with an application in reliability

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  • Csenki, Attila

Abstract

It is shown that the Laplace transform of a continuous lifetime random variable with a polynomial failure rate function satisfies a certain differential equation. This generates a set of differential equations which can be used to express the polynomial coefficients in terms of the derivatives of the Laplace transform at the origin. The technique described here establishes a procedure for estimating the polynomial coefficients from the sample moments of the distribution. Some special cases are worked through symbolically using computer algebra. Real data from the literature recording bus motor failures is used to compare the proposed approach with results based on the least squares procedure.

Suggested Citation

  • Csenki, Attila, 2011. "On continuous lifetime distributions with polynomial failure rate with an application in reliability," Reliability Engineering and System Safety, Elsevier, vol. 96(11), pages 1587-1590.
    • Handle: RePEc:eee:reensy:v:96:y:2011:i:11:p:1587-1590
    DOI: 10.1016/j.ress.2011.06.008
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    References listed on IDEAS

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    1. Csenki, Attila, 2007. "Joint interval reliability for Markov systems with an application in transmission line reliability," Reliability Engineering and System Safety, Elsevier, vol. 92(6), pages 685-696.
    2. A Csenki, 2007. "On the three-state weather model of transmission line failures," Journal of Risk and Reliability, , vol. 221(3), pages 217-228, September.
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    Cited by:

    1. Csenki, Attila, 2012. "Asymptotics for continuous lifetime distributions with polynomial failure rate with an application in reliability," Reliability Engineering and System Safety, Elsevier, vol. 102(C), pages 1-4.
    2. Attila Csenki, 2015. "A Differential Equation for a Class of Discrete Lifetime Distributions with an Application in Reliability," Methodology and Computing in Applied Probability, Springer, vol. 17(3), pages 647-660, September.

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