On New Multivariate Probability Distributions and Stochastic Processes with System Reliability and Maintenance Applications

Jerzy Filus () and Lidia Filus ()
Additional contact information
Jerzy Filus: Oakton Community College
Lidia Filus: Northeastern Illinois University

Methodology and Computing in Applied Probability, 2007, vol. 9, issue 3, 425-446

Abstract: Abstract Two distinct methods for construction of some interesting new classes of multivariate probability densities are described and applied. As common results of both procedures three n-variate pdf classes are obtained. These classes are considered as generalizations of the class of univariate Weibullian, gamma, and multivariate normal pdfs. An example of an application of the obtained n-variate pdfs to the problem of modeling the reliability of multicomponent systems with stochastically dependent life-times of their components is given. Obtaining sequences over n = 2, 3, ... of consistent n-variate pdfs, that obey a relatively simple common pattern, for each n, allows us to extend some of the constructions from random vectors to discrete time stochastic processes. Application of one, so obtained, class of highly non-Markovian, but still sufficiently simple, stochastic processes for modeling maintenance of systems with repair, is presented. These models allow us to describe and analyze repaired systems with histories of all past repairs.

Keywords: Multivariate probability density (pdf); Stochastic process; System reliability and maintenance modeling; Actuary modeling; Primary 60E99; Secondary 60K10; 60K15; 60K20; 62H99; 62N05; 62P05; 62P30 (search for similar items in EconPapers)
Date: 2007
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11009-007-9026-6 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

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:spr:metcap:v:9:y:2007:i:3:d:10.1007_s11009-007-9026-6

Ordering information: This journal article can be ordered from
https://www.springer.com/journal/11009

DOI: 10.1007/s11009-007-9026-6

Access Statistics for this article

Methodology and Computing in Applied Probability is currently edited by Joseph Glaz

More articles in Methodology and Computing in Applied Probability from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().