In this paper we discuss the system failure probability of a k-out-of-n system considering common-cause failures. The conventional implicit technique is first introduced. Then the failure probabilities are formulated when the independence between common-cause failure events is assumed. We also provide algorithms to enumerate all the cut sets and the minimal cut sets, and to calculate the system failure probability. These methods are extendable to the case of systems with non-identical components. We verify the effectiveness of our method by comparison with the exact solution obtained by numerical calculation.

A one-shot system is a system that can be used only once during its life, and whose failures are detected only through inspections. In this paper, we discuss an inspection policy problem of one-shot system composed of multi-unit in series. Failed units are minimally repaired when failures are detected and all units in the system are replaced when the nth failure is detected after the last replacement. We derive the expected cost rate approximately. Our goal is to determine the optimal inspection policy that minimizes the expected cost rate.

This paper presents an approximation method for deriving the availability of a parallel redundant system with preventive maintenance (PM) and common-cause failures. The system discussed is composed of two identical units. A single service facility is available for PM and repair. The repair times, the PM times and the failure times except for common-cause failures are all assumed to be arbitrarily distributed. The presented method formulates the problem of the availability analysis of a parallel redundant system as a Markov renewal process which represents the state transitions of one specified unit in the system. This method derives the availability easily and accurately. Further, the availability obtained by this method is exact in a special case.