## Journal of Applied Probability

### Order statistics with memory: a model with reliability applications

#### 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.

#### Article information

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

Dates
First available in Project Euclid: 7 December 2016

https://projecteuclid.org/euclid.jap/1481132830

Mathematical Reviews number (MathSciNet)
MR3581235

Zentralblatt MATH identifier
1358.60037

#### Citation

Katzur, Alexander; Kamps, Udo. Order statistics with memory: a model with reliability applications. J. Appl. Probab. 53 (2016), no. 4, 974--988. https://projecteuclid.org/euclid.jap/1481132830

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