Reliability and Sensitivity Analysis of the k-out-of-n:G Warm Standby Parallel Repairable System with Replacement at Common-Cause Failure using Markov Mode

Standby redundancy is a technique that has been widely applied for improving system reliability and availability in system design. In this paper, probabilistic model for a redundant system with replacement at each common-cause failure has been developed to analyze the reliability measures using Markov models. We investigate the reliability and sensitivity analysis of k-out-of-n:G warm standby parallel repairable system. All failure and repair times of the system are exponentially distributed and when one of the operating primary units fails then it is instantaneously replaced by a warm standby unit if one is available. Comparative analysis of reliability measures between two dissimilar configurations has been developed. Configuration Ι is a 2-out-of-4:G warm standby parallel repairable system, while Configuration ΙΙ is a 2out-of-5:G warm standby parallel repairable system. We get a closed-form solution of the reliability measures of the system for the two configurations. Comparisons are performed for specific values of system parameter. Sensitivity analysis is also carried out to depict the effect of various parameters on the reliability function and mean time to failure of the system. Numerical example is given to illustrate the results obtained