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Preservation results for life distributions based on comparisons with asymptotic remaining life under replacements

Part of: Special processes Survival analysis and censored data

Published online by Cambridge University Press:  14 July 2016

M. C. Bhattacharjee ,
A. M. Abouammoh ,
A. N. Ahmed  and
A. M. Barry
M. C. Bhattacharjee*
Affiliation:
New Jersey Institute of Technology
A. M. Abouammoh*
Affiliation:
King Saud University
A. N. Ahmed*
Affiliation:
King Saud University
A. M. Barry*
Affiliation:
King Saud University
*
∗ Postal address: Center for Applied Mathematics and Statistics, Department of Mathematical Sciences, New Jersey Institute of Technology, Newark, NJ 07102, USA. Email address: mabhat@m.njit.edu
∗∗ Postal address: Department of Statistics and O.R., King Saud University, Riyadh 11451, Saudi Arabia.
∗∗ Postal address: Department of Statistics and O.R., King Saud University, Riyadh 11451, Saudi Arabia.
∗∗ Postal address: Department of Statistics and O.R., King Saud University, Riyadh 11451, Saudi Arabia.
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Abstract

We investigate some preservation properties of two nonparametric classes of survival distributions and their duals, under appropriate reliability operations. The aging properties defining these nonparametric classes are based on comparing the mean life of a new unit to the mean residual life function of the asymptotic remaining survival time of the unit under repeated perfect repairs. They are motivated from a point of view that realistic notions of degradation, applicable to repairable systems, should be based on contrasting some aspect of the remaining life of a repairable unit (under a given repair strategy, such as renewals) to the life of a new unit.

Keywords

Survival distributionsagingrenewalsasymptotic remaining life

MSC classification

Primary: 60K05: Renewal theory 60K10: Applications (reliability, demand theory, etc.)
Secondary: 62N05: Reliability and life testing
Type
Research Papers
Information
Journal of Applied Probability , Volume 37 , Issue 4 , December 2000 , pp. 999 - 1009
Copyright
Copyright © by the Applied Probability Trust 2000 

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