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.

This paper considers an availability analysis and an optimal inventory problem for a repairable 1-out-ofN:G system assuming an ordering policy of (s, s+1) type. The system consists of N identical subsystems which constitute 1-out-ofN:G, and each subsystem is a m units series system. Since the system is repairable, the exact evaluation of the system availability is extremely difficult. In this paper, the system availability is obtained by an approximation analysis. The results are reasonably accurate and are much easier than the exact evaluation. Then the optimal inventory problem is discussed. The numerical example shows that the solution is obtained relatively easily when the system consists of highly reliable units.

This paper considers a fleet system which consists of n equipments. The system is operated intermittently repeating a system operation period and a system standby period alternatively. In each system operation period, any c of n equipments are required to operate. Each equipment undergoes overhaul (O/H) after prespecified periods (or numbers) of operation. We obtain the availability of the system assuming the following disciplines for the O/H interval and the failure probability. The O/H interval is scheduled by calendar time (Case 1) or actual operating time (Case 2). The failure probability of an equipment is constant in each operation (Model 1) or depends on the number of operations after O/H (Model 2). This analysis aims at the determination of the rational O/H interval and the number of the equipments in the system. Also it can be applied to the problem of spares provisioning for a system with O/H.

Determination of spare quantity assuming a general failure distribution is discussed. A new method is presented which is an extension of a usual normal approximation method. The original method is essentially a Normal distribution approximation" to a Poisson process of failure occurrence. On the other hand, the new method assumes a general failure distribution. The mean and the variance of the number of failures within for a given period of time are necessary for determining the spare quantity. The mean is obtained in a simple form. The variance is give as a solution of an integral equation. The solution of this equation for a general case is obtained by applying a discrete approximation technique. Some numerical examples are provided to discuss the difference between when assuming a general failure distribution and when assuming the exponential failure distribution.

This paper presents two approaches for computing the reliability of complex networks subject to two kinds of failure, open failure and shorted failure. The reliabilities of some series-parallel networks are considered by many analysts. However a practical system is more complex. The methods given in this paper can be applied not only to a series-parallel network but also to a non-series-parallel network which is composed of non-identical and independent components subject to two kinds of failure. This paper also deals with a network subject to flow quantity constraint such as the one which is required to control j or more separate paths. For such a system it is difficult to obtain system reliability because the number of states to be considered in this system is extremely large compared to a conventional 2-state device system. In this paper we obtain the reliabilities for such systems by a combinatorial approach and by a simulation approach.

This paper considers a repair system which includes several repair stations, many user sites and a great many identical equipments operated in these sites. The means and the variances of the numbers of the equipments in these user sites and repair stations are obtained using an approximation method. The proposed repair model is applicable to a complex repair system such as a multi-echelon repair system.

This paper considers a two-unit warm standby redundant system. Preventive maintenance (PM) for an active unit is scheduled after a certain period. When an active unit fails or undergoes PM while the other is in standby, the operation is switched to the standby unit. Probability of success in switchover is constant. If the system fails in switchover, the system stops the operation, and resumes it after a certain time. MTTFF, MTBF and steady state availability are obtained. Numerical examples show the effects of PM interval on them.

This paper considers a multi-base single repair station problem which is a reliability analysis for a system with a large number of equipments operated in their own bases and some repairmen in the repair station. In this problem, all the failed equipments are repaired in the repair station and are sent back to their own bases after completions of repair. The mean and the variance of the number of operative equipments in each base are obtained by a diffusion approximation method. Numerical examples of an approximation solution and a simulation solution are presented.

Mean Time Between Failures (MTBF) is an important measure of practical repairable systems, but it has not been obtained for a repairable linear consecutive-k-out-of-n: F system. We first present a general formula for the (steady-state) availability of a repairable linear consecutive-k-out-of-n: F system with nonidentical components by employing the cut set approach or a topological availability method. Second, we present a general formula for frequency of system failures of a repairable linear consecutive-k-out-of-n: F system with nonidentical components. Then the MTBF for the repairable linear consecutive-k-out-of-n: F system is shown by using the frequency of system failure and availability. Lastly, we derive some figures which show the relationship between the MTBF and repair rate µorρ(=λ/µ) in the repairable linear consecutive-k-out-of-n: F system. The figures can be easily used and are useful for reliability design.