Extensions of the Freund Distribution with Applications in Reliability Theory

Moshe Shaked
Additional contact information
Moshe Shaked: University of Arizona, Tucson, Arizona

Operations Research, 1984, vol. 32, issue 4, 917-925

Abstract: The Freund distribution models situations in which the exponential residual lifetime of one component depends on the working status of another component. The literature has discussed generalizations and analogs of the Freund distribution. Such generalizations can be obtained by replacing exponential random variables by Weibull or gamma random variables, or by compounding (mixing) Freund distributions. This paper shows how to unify various well-known generalizations of the Freund distribution by using one simple functional representation. This functional representation has a physical meaning that sheds new light on the meaning of some of these generalizations. Furthermore, using this functional representation, we derive various properties of the Freund distribution and its extensions. In particular, we show that some random variables, which have the Freund distribution or one of its extensions, are positively associated and also belong to some classes of multivariate “increasing failure rate average” and “new better than used” distributions. These properties provide bounds for various probabilistic quantities of interest in reliability theory.

Keywords: 723 components with dependent life lengths; 725 extensions of exponential and other bivariate distributions (search for similar items in EconPapers)
Date: 1984
References: Add references at CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://dx.doi.org/10.1287/opre.32.4.917 (application/pdf)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:inm:oropre:v:32:y:1984:i:4:p:917-925

Access Statistics for this article

More articles in Operations Research from INFORMS Contact information at EDIRC.
Bibliographic data for series maintained by Chris Asher ().