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首页> 外文期刊>Mathematical Problems in Engineering >Unavailability Analysis for k-out-of-n:G Systems with Multiple Failure Modes Based on Micro-Markov Models
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Unavailability Analysis for k-out-of-n:G Systems with Multiple Failure Modes Based on Micro-Markov Models

机译：基于微观马尔可夫模型的多失效模式k-out-of-n：G系统不可用性分析

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摘要

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.
机译：马尔可夫模型通常用于冗余系统的不可用性分析。但是，由于冗余系统的马尔可夫模型的爆炸状态，需要合并这些状态以简化计算，这被称为微马尔可夫模型。然而，如何得出新开发的微马尔可夫模型的失效率和修复率尚未得到充分研究。因此，本文提出了详细的解释和规则，以利用微马尔可夫模型推导具有多个失效模式的k-out-of-n：G系统的静态不可用性。首先，提出了将马尔可夫模型应用于具有独立多重故障模式的可修复系统的两个属性。基于这两个属性，提出了两个规则来实现微观马尔可夫模型。微观马尔可夫模型为具有多个独立故障模式和修复机制的可修复k-out-n：G系统提供了完全相同的结果，为具有多个混合故障模式的系统提供了近似的结果。提供了安全仪表系统安全完整性验证的案例研究，以说明所提出方法的应用。理论上的比较和数值例子证明了所提出的微观马尔可夫模型的合理性和实用性。

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  • 来源
    《Mathematical Problems in Engineering》 |2014年第8期|740936.1-740936.12|共12页
  • 作者

    Shengjin Tang; Xiaosong Guo; Xiaoyan Sun; Haijian Xue; Zhaofa Zhou;

  • 作者单位

    High-Tech Institute of Xi'an, Xi'an, Shaanxi 710025, China;

    High-Tech Institute of Xi'an, Xi'an, Shaanxi 710025, China;

    Suzhou INVO Automotive Electronics Co., Ltd., Suzhou, Jiangsu 215200, China;

    High-Tech Institute of Xi'an, Xi'an, Shaanxi 710025, China;

    High-Tech Institute of Xi'an, Xi'an, Shaanxi 710025, China;

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