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

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.