## Journal of Applied Probability

- J. Appl. Probab.
- Volume 40, Number 3 (2003), 721-740.

### Initial and final behaviour of failure rate functions for mixtures and systems

Henry W. Block, Yulin Li, and Thomas H. Savits

#### Abstract

In this paper we consider the initial and asymptotic behaviour of the failure rate function resulting from mixtures of subpopulations and formation of coherent systems. In particular, it is shown that the failure rate of a mixture has the same limiting behaviour as the failure rate of the strongest subpopulation. A similar result holds for systems except the role of strongest subpopulation is replaced by strongest min path set.

#### Article information

**Source**

J. Appl. Probab. Volume 40, Number 3 (2003), 721-740.

**Dates**

First available in Project Euclid: 24 July 2003

**Permanent link to this document**

http://projecteuclid.org/euclid.jap/1059060898

**Digital Object Identifier**

doi:10.1239/jap/1059060898

**Mathematical Reviews number (MathSciNet)**

MR1993263

**Zentralblatt MATH identifier**

1046.62111

**Subjects**

Primary: 62E10: Characterization and structure theory

Secondary: 62N05: Reliability and life testing [See also 90B25]

**Keywords**

Mixture IFR DFR bathtub shape failure rate asymptotic behaviour initial behaviour coherent system

#### Citation

Block, Henry W.; Li, Yulin; Savits, Thomas H. Initial and final behaviour of failure rate functions for mixtures and systems. J. Appl. Probab. 40 (2003), no. 3, 721--740. doi:10.1239/jap/1059060898. http://projecteuclid.org/euclid.jap/1059060898.