Unavailability Analysis for k-out-of-n:G Systems with Multiple Failure Modes Based on Micro-Markov Models. (24th April 2014)

• Record Type: Journal Article
• Authors: Tang, Shengjin; Guo, Xiaosong; Sun, Xiaoyan; Xue, Haijian; Zhou, Zhaofa
• Other Names: Proppe Carsten Academic Editor.
• Is Part Of: Mathematical problems in engineering. Volume 2014(2014)
• Publication Date: 2014-04-24
• Subjects: Engineering mathematics -- Periodicals; 510.2462
• DOI: 10.1155/2014/740936
• Languages: English
• ISSNs: 1024-123X

Abstract

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.