Cart (Loading....) | Create Account
Close category search window

Statistical Analysis of a Compound Power-Law Model for Repairable Systems

Sign In

Cookies must be enabled to login.After enabling cookies , please use refresh or reload or ctrl+f5 on the browser for the login options.

Formats Non-Member Member
$31 $13
Learn how you can qualify for the best price for this item!
Become an IEEE Member or Subscribe to
IEEE Xplore for exclusive pricing!
close button

puzzle piece

IEEE membership options for an individual and IEEE Xplore subscriptions for an organization offer the most affordable access to essential journal articles, conference papers, standards, eBooks, and eLearning courses.

Learn more about:

IEEE membership

IEEE Xplore subscriptions

2 Author(s)
Engelhardt, Max ; Department of Mathematics and Statistics; University of Missouri; Rolla, Missouri 65401 USA. ; Bain, L.J.

A compound (mixed) Poisson distribution is sometimes used as an alternative to the Poisson distribution for count data. Such a compound distribution, which has a negative binomial form, occurs when the population consists of Poisson distributed individuals, but with intensities which have a gamma distribution. A similar situation can occur with a repairable system when failure intensities of each system are different. A more general situation is considered where the system failures are distributed according to nonhomogeneous Poisson processes having Power Law intensity functions with gamma distributed intensity parameter. If the failures of each system in a population of repairable systems are distributed according to a Power Law process, but with different intensities, then a compound Power Law process provides a suitable model. A test, based on the ratio of the sample variance to the sample mean of count data from s-independent systems, provides a convenient way to determine if a compound model is appropriate. When a compound Power Law model is indicated, the maximum likelihood estimates of the shape parameters of the individual systems can be computed and homogeneity can be tested. If equality of the shape parameters is indicated, then it is possible to test whether the systems are homogeneous Poisson processes versus a nonhomogeneous alternative. If deterioration within systems is suspected, then the alternative in which the shape parameter exceeds unity would be appropriate, while if systems are undergoing reliability growth the alternative would be that the shape parameter is less than unity.

Published in:

Reliability, IEEE Transactions on  (Volume:R-36 ,  Issue: 4 )

Date of Publication:

Oct. 1987

Need Help?

IEEE Advancing Technology for Humanity About IEEE Xplore | Contact | Help | Terms of Use | Nondiscrimination Policy | Site Map | Privacy & Opting Out of Cookies

A not-for-profit organization, IEEE is the world's largest professional association for the advancement of technology.
© Copyright 2014 IEEE - All rights reserved. Use of this web site signifies your agreement to the terms and conditions.