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Order statistics with memory: a model with reliability applications

Part of: Nonparametric inference Distribution theory - Probability

Published online by Cambridge University Press:  09 December 2016

Alexander Katzur  and
Udo Kamps
Alexander Katzur*
Affiliation:
RWTH Aachen University
Udo Kamps*
Affiliation:
RWTH Aachen University
*
* Postal address: Institute of Statistics, RWTH Aachen University, 52056 Aachen, Germany.
* Postal address: Institute of Statistics, RWTH Aachen University, 52056 Aachen, Germany.
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Abstract

An extended model of order statistics based on possibly different distributions is introduced and analyzed. In the interpretation of successive failure times in a 𝑘-out-of-𝑛 system, say, until each failure, the time periods under previous (increasing) loads exerted on the remaining components are recorded. Then the lifetime distribution of the system depends on the complete failure scheme. Thus, order statistics with memory provide an alternative to the use of sequential order statistics, which form a Markov chain. The quantities as well as their spacings, the interoccurrence times, can be compared by means of stochastic ordering.

Keywords

Order statistics𝑘-out-of-𝑛 systemsequential order statisticsordered data

MSC classification

Primary: 60E05: Distributions
Secondary: 60E15: Inequalities; stochastic orderings 62G30: Order statistics; empirical distribution functions
Type
Research Papers
Information
Journal of Applied Probability , Volume 53 , Issue 4 , December 2016 , pp. 974 - 988
Copyright
Copyright © Applied Probability Trust 2016 

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