Extended Phase-type models for multistate competing risk systems

Lirong Cui and Bei Wu

Reliability Engineering and System Safety, 2019, vol. 181, issue C, 1-16

Abstract: Two extended Phase-type models with competing risks for failures of Markov repairable systems with absorbing states are presented in this article. We divide the states into three subsets: perfect, imperfect and failure (absorption) for a Markov repairable system. Two models are developed in terms of the proposed failure criteria of the repairable system. For model 1, the system failure criteria of the repairable system are, whichever occurs first, (1) when the system goes into the failure state (absorption state), or (2) when the system transfers from imperfect states to other states, and before that time the transitions from perfect to imperfect states reached a specified number. For model 2, there still are two criteria whichever occurs first. The first one is the same as failure criterion (1) in model 1, but failure criterion (2) is replaced by (3) which is when the sojourn time in imperfect states exceeds a given threshold. Under two models, two distributions are proposed, which are extensions of the well-known Phase-type distribution. Some reliability indexes under two models, such as the distributions of lifetimes, the point-wise availabilities, various interval availabilities, are given. Finally, some numerical examples are presented to illustrate the results obtained in this article.

Keywords: Phase-type distribution; Markov repairable system; Failure criterion; Point-wise availability; Interval availability; Lifetime (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (13)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0951832018302643
Full text for ScienceDirect subscribers only

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:eee:reensy:v:181:y:2019:i:c:p:1-16

DOI: 10.1016/j.ress.2018.08.015

Access Statistics for this article

Reliability Engineering and System Safety is currently edited by Carlos Guedes Soares

More articles in Reliability Engineering and System Safety from Elsevier
Bibliographic data for series maintained by Catherine Liu ().