## Journal of Applied Probability

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

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

Alexander Katzur and Udo Kamps

#### 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

**Permanent link to this document**

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

**Mathematical Reviews number (MathSciNet)**

MR3581235

**Zentralblatt MATH identifier**

1358.60037

**Subjects**

Primary: 60E05: Distributions: general theory

Secondary: 60E15: Inequalities; stochastic orderings 62G30: Order statistics; empirical distribution functions

**Keywords**

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

#### 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