Journal of Applied Probability

Order statistics with memory: a model with reliability applications

Alexander Katzur and Udo Kamps

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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.

Article information

J. Appl. Probab., Volume 53, Number 4 (2016), 974-988.

First available in Project Euclid: 7 December 2016

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 60E05: Distributions: general theory
Secondary: 60E15: Inequalities; stochastic orderings 62G30: Order statistics; empirical distribution functions

Order statistics 𝑘-out-of-𝑛 system sequential order statistics ordered data


Katzur, Alexander; Kamps, Udo. Order statistics with memory: a model with reliability applications. J. Appl. Probab. 53 (2016), no. 4, 974--988.

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