Hostname: page-component-84b7d79bbc-l82ql Total loading time: 0 Render date: 2024-07-30T07:47:50.675Z Has data issue: false hasContentIssue false
  • English
  • Français

Preservation of certain classes of life distributions under Poisson shock models

Part of: Special processes Distribution theory - Probability

Published online by Cambridge University Press:  14 July 2016

Enrico Fagiuoli  and
Franco Pellerey
Enrico Fagiuoli*
Affiliation:
University of Milano
Franco Pellerey*
Affiliation:
University of Milano
*
∗ Postal address of both authors: Department of Mathematics, Via Cicognara 7, 20129 Milano, Italy.
∗ Postal address of both authors: Department of Mathematics, Via Cicognara 7, 20129 Milano, Italy.
Get access Rights & Permissions [Opens in a new window]

Abstract

Recently defined classes of life distributions are considered, and some relationships among them are proposed. The life distribution H of a device subject to shocks occurring randomly according to a Poisson process is also considered, and sufficient conditions for H to belong to these classes are discussed.

Keywords

EQUILIBRIUM DISTRIBUTIONSPOISSON SHOCK MODELS-IFRS-IFRAS-NBUS-NBUFRS-NBAFRNBU(2)NBUC

MSC classification

Primary: 60K10: Applications (reliability, demand theory, etc.)
Secondary: 60E05: Distributions
Type
Research Papers
Information
Journal of Applied Probability , Volume 31 , Issue 2 , June 1994 , pp. 458 - 465
Copyright
Copyright © Applied Probability Trust 1994 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abouammoh, A. H. and Ahmed, A. N. (1988) The new better than used failure rate class of life distribution. Adv. Appl. Prob. 20, 237–240.Google Scholar
Averous, J. and Meste, M. (1989) Tailweight and life distributions. Statist. Prob. Lett. 8, 381–387.Google Scholar
Cao, J. and Wang, Y. (1991) The NBUC and NWUC classes of life distributions. J. Appl. Prob. 28, 473–479.Google Scholar
Deshpande, J. V., Kochar, S. C. and Singh, H. (1986) Aspects of positive ageing. J. Appl. Prob. 23, 748–758.Google Scholar
Esary, J. D., Marshall, A. W. and Proschan, F. (1973) Shock models and wear processes. Ann. Prob. 1, 627–649.Google Scholar
Karlin, S. (1968) Total Positivity, Vol. 1. Stanford University Press.Google Scholar
Klefsjö, B. (1981) HNBUE survival under some shock models. Scand. J. Statist. 8, 39–47.Google Scholar
Klefsjö, B. (1983) A useful ageing property based on the Laplace transform. J. Appl. Prob. 20, 615–625.CrossRefGoogle Scholar
Launer, R. L. (1984) Inequalities for NBUE and NWUE life distributions. Operat. Res. 32, 660–667.Google Scholar
Loh, W. (1984) A new generalization of the class of NBU distributions. IEEE Trans. Reliability 33, 419–422.Google Scholar
Singh, H. (1989) On partial ordering of life distribution. Naval Res. Log. 36, 103–110.Google Scholar
Singh, H. and Deshpande, J. V. (1985) On some new ageing properties. Scand. J. Statist. 12, 213–220.Google Scholar