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.

A new method to obtain the availability of a cold standby series system with spare units is presented. Two models are considered. The first one is a series system with spare units. The other is m series systems with common spare units. The availabilities are solutions of nonlinear simultaneous equations and are obtained numerically.

A lattice system in this paper is a system whose components are ordered like the elements of (m, n) matrix. A representative example of a lattice system is a connected-(r, s)-out-of-(m, n):F lattice system which is treated as a model of supervision system. It fails if and only if all components in an (r, s) sub lattice fail. We modify the lattice system so as to include a maintenance action and a restriction on the number of failed components. Then, this paper presents availability and MTBF of the repairable system, and reliability when the system stocks spare parts on hand to ensure the specified reliability level.