Reliability of k-r-out-of-N:G system subject to random and common cause failure

This investigation deals with the reliability of k-r-out-of-N:G system having two types of system failures: (i) random failure and (ii) common cause failure (CCF). An optimality criterion leading to the optimal number of spare units for the system is established under the provision of repair after each system failure. The formulae for the cost ratios, expected total cost per unit time have been obtained explicitly. Some numerical results have also been tabulated.