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Sharp reliability bounds for the ℒ-like distributions, a class in which ageing is based on Laplace transform inequalities

Part of: Integral transforms, operational calculus Operations research and management science Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Chin-Yuan Hu  and
Gwo Dong Lin
Chin-Yuan Hu*
Affiliation:
National Changhua University of Education
Gwo Dong Lin*
Affiliation:
Academia Sinica, Taiwan
*
∗Postal address: Department of Business Education, National Changhua University of Education, Changhua, 50058, Taiwan, Republic of China. Email address: [email protected]
∗∗Postal address: Institute of Statistical Science, Academia Sinica, Taipei, 11529, Taiwan, Republic of China. Email address: [email protected]
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Abstract

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We establish Klar's (2002) conjecture about sharp reliability bounds for life distributions in the ℒα-class in reliability theory. The key idea is to construct a set of two-point distributions whose support points satisfy a certain system of equalities and inequalities.

Keywords

ℒ-classℒα-classreliability bound

MSC classification

Primary: 90B25: Reliability, availability, maintenance, inspection
Secondary: 44A10: Laplace transform 60E15: Inequalities; stochastic orderings
Type
Short Communications
Information
Journal of Applied Probability , Volume 42 , Issue 4 , December 2005 , pp. 1204 - 1208
Copyright
© Applied Probability Trust 2005 

References

Klar, B. (2002). A note on the { ℒ-class of life distributions. J. Appl. Prob. 39, 11–19.Google Scholar
Klefsjö, B. (1983). A useful ageing property based on the Laplace transform. J. Appl. Prob. 20, 615–626.Google Scholar
Lin, G. D. (1998). On weak convergence within the { ℒ-like classes of life distributions. Sankhyā A 60, 176–183.Google Scholar
Lin, G. D. and Hu, C.-Y. (2000). A note on the { ℒ-class of life distributions. Sankhyā A 62, 267–272.Google Scholar
Mohan, N. R. and Ravi, S. (2002). Some properties of two families of classes of life distributions. J. Appl. Prob. 39, 581–589.Google Scholar
Sengupta, D. (1995). Reliability bounds for the { ℒ-class and Laplace order. J. Appl. Prob. 32, 832–835.CrossRefGoogle Scholar