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Failure rate properties of parallel systems

Part of: Survival analysis and censored data Distribution theory - Probability

Published online by Cambridge University Press:  15 July 2020

Idir Arab ,
Milto Hadjikyriakou  and
Paulo Eduardo Oliveira
Idir Arab*
Affiliation:
University of Coimbra, CMUC, Department of Mathematics, Portugal
Milto Hadjikyriakou*
Affiliation:
University of Central Lancashire, Cyprus
Paulo Eduardo Oliveira*
Affiliation:
University of Coimbra, CMUC, Department of Mathematics, Portugal
*
*Postal address: Department of Mathematics, PO Box 3008, EC Santa Cruz, Coimbra, Portugal.
**Postal address: School of Sciences, 12-14 University Avenue, Pyla, 7080Larnaka, Cyprus.
***Postal address: Department of Mathematics, PO Box 3008, EC Santa Cruz, Coimbra, Portugal. Email: [email protected]
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Abstract

We study failure rate monotonicity and generalised convex transform stochastic ordering properties of random variables, with an emphasis on applications. We are especially interested in the effect of a tail-weight iteration procedure to define distributions, which is equivalent to the characterisation of moments of the residual lifetime at a given instant. For the monotonicity properties, we are mainly concerned with hereditary properties with respect to the iteration procedure providing counterexamples showing either that the hereditary property does not hold or that inverse implications are not true. For the stochastic ordering, we introduce a new criterion, based on the analysis of the sign variation of a suitable function. This criterion is then applied to prove ageing properties of parallel systems formed with components that have exponentially distributed lifetimes.

Keywords

Convex stochastic orderiterated failure ratesign variation

MSC classification

Primary: 60E15: Inequalities; stochastic orderings
Secondary: 60E05: Distributions 62N05: Reliability and life testing
Type
Original Article
Information
Advances in Applied Probability , Volume 52 , Issue 2 , June 2020 , pp. 563 - 587
Copyright
© Applied Probability Trust 2020

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