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Asymptotics for continuous lifetime distributions with polynomial failure rate with an application in reliability

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  • Csenki, Attila

Abstract

This paper is a continuation of work reported by Csenki (2011 [1]), where the coefficients of a polynomial failure rate function of a continuous lifetime distribution were expressed in terms of derivatives of the Laplace transform of the distribution at the origin. Here it is shown that these expressions are asymptotically normal. The main tool employed is the Delta Method in conjunction with the Central Limit Theorem. The finding is used to derive asymptotic confidence intervals and tests for the coefficients. The suggested calculations are carried out for a set of bus failure data from the literature.

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  • 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.
    • Handle: RePEc:eee:reensy:v:102:y:2012:i:c:p:1-4
    DOI: 10.1016/j.ress.2012.02.004
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    References listed on IDEAS

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    1. 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.
    2. Jack, N. & Iskandar, B.P. & Murthy, D.N.P., 2009. "A repair–replace strategy based on usage rate for items sold with a two-dimensional warranty," Reliability Engineering and System Safety, Elsevier, vol. 94(2), pages 611-617.
    3. Yanyuan Ma & Marc Genton & Emanuel Parzen, 2011. "Asymptotic properties of sample quantiles of discrete distributions," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 63(2), pages 227-243, April.
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    1. 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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