Unavailability Analysis for k -out-of- n:G Systems with Multiple Failure Modes Based on Micro-Markov Models

Shengjin Tang, Xiaosong Guo, Xiaoyan Sun, Haijian Xue and Zhaofa Zhou

Mathematical Problems in Engineering, 2014, vol. 2014, 1-12

Abstract:

Markov models are commonly used for unavailability analysis of redundant systems. However, due to the exploding states of Markov models for redundant systems, the states need to be merged to simplify the computation, which is called micro-Markov models. However, how to derive the failure rates and repair rates of the newly developed micro-Markov models has not been studied thoroughly. Therefore, this paper proposes detailed explanations and rules to derive the static unavailability by the micro-Markov models for the k -out-of- n :G systems with multiple failure modes. Firstly, two properties about applying the Markov models to the repairable system with independent multiple failure modes are presented. Based on these two properties, two rules are proposed for implementing the micro-Markov models. The micro-Markov models provide the exact same results for the repairable k -out-of- n :G system with multiple independent failure modes and repair mechanisms and approximate results for systems with multiple hybrid failure modes. A case study of safety integrity verification for safety instrumented systems is provided to illustrate the application of the proposed method. The conceptual comparison and numerical examples demonstrate the reasonability and usefulness of the proposed micro-Markov models.

Date: 2014
References: Add references at CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
http://downloads.hindawi.com/journals/MPE/2014/740936.pdf (application/pdf)
http://downloads.hindawi.com/journals/MPE/2014/740936.xml (text/xml)

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:hin:jnlmpe:740936

DOI: 10.1155/2014/740936

Access Statistics for this article

More articles in Mathematical Problems in Engineering from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().