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New nonparametric classes of distributions in terms of mean time to failure in age replacement

Part of: Operations research and management science Survival analysis and censored data

Published online by Cambridge University Press:  16 January 2019

Muhyiddin Izadi ,
Maryam Sharafi  and
Baha-Eldin Khaledi
Muhyiddin Izadi*
Affiliation:
Razi University
Maryam Sharafi*
Affiliation:
Razi University
Baha-Eldin Khaledi*
Affiliation:
Razi University Portland Sate University
*
* Postal address: Department of Statistics, Razi University, Kermanshah, Iran.
* Postal address: Department of Statistics, Razi University, Kermanshah, Iran.
*** Current address: Fariborz Maseeh Department of Mathematics and Statistics, Portland Sate University, Portland, OR 97201, USA.
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Abstract

The mean time to failure (MTTF) function in age replacement is used to evaluate the performance and effectiveness of the age replacement policy. In this paper, based on the MTTF function, we introduce two new nonparametric classes of lifetime distributions with nonmonotonic mean time to failure in age replacement; increasing then decreasing MTTF (IDMTTF) and decreasing then increasing MTTF (DIMTTF). The implications between these classes of distributions and some existing classes of nonmonotonic ageing classes are studied. The characterizations of IDMTTF and DIMTTF in terms of the scaled total time on test transform are also obtained.

Keywords

BFR distributionconvex and concave functionsnonmonotonic ageing classNWBUE distributiontotal time on test transform

MSC classification

Primary: 62N05: Reliability and life testing
Secondary: 90B25: Reliability, availability, maintenance, inspection
Type
Research Papers
Information
Journal of Applied Probability , Volume 55 , Issue 4 , December 2018 , pp. 1238 - 1248
Copyright
Copyright © Applied Probability Trust 2018 

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