Estimation of Dependability Measures and Parameter Sensitivities of a Consecutive-$k$-out-of-$n$: F Repairable System With $(k-1)$-Step Markov Dependence by Simulation
Estimation of Dependability Measures and Parameter Sensitivities of a Consecutive-$k$-out-of-$n$: F Repairable System With $(k-1)$-Step Markov Dependence by Simulation
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DOI：
10.1109/tr.2007.911252
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发表时间：
2008-03
影响因子：
5.9
通讯作者：
Gang Xiao;Zhizhong Li
中科院分区：
文献类型：
--
作者：
Gang Xiao;Zhizhong Li
本文提出了直接模拟法（DS）和条件期望估计法（CEE）两种估计方法，分别用于估计具有（k - 1）步马尔可夫依赖的n中取k：F可修系统的不可靠度、瞬态不可用度、稳态不可用度、平均故障前时间（MTTF）、平均故障间隔时间（MTBF）及其参数灵敏度。在引入参数灵敏度的似然比估计的表达式后，导出了参数灵敏度的直接估计和条件期望估计。Lam & Ng的一项研究中的分析结果被用来验证本文提出的算法。通过对高可靠性线性、循环C（4，50：F）和C（4，100：F）系统的数值算例，比较了DS算法的效率，发现CEE和CEE算法的效率明显高于DS算法.
In this paper, we present two methods, direct simulation (DS), and conditional expectation estimation (CEE), for estimating the unreliability, transient unavailability, steady unavailability, mean time to failure (MTTF), mean time between failure (MTBF), and their parameter sensitivities of consecutive-k-out-of-n: F repairable systems with (k - 1)-step Markov dependence. After an expression of the likelihood ratio estimator of parameter sensitivity is introduced, the direct estimators, and conditional expectation estimators are derived. The analytical results in a study by Lam & Ng were used to verify the algorithms presented in this paper. Numerical examples of highly reliable linear, and circular C (4, 50: F), and C (4,100: F) systems were illustrated to compare the algorithm efficiencies of DS, and CEE and CEE was found to be remarkably more efficient than DS.