Bounds on the reliability of binary coherent systems

The structure function of a binary coherent system is approximated by using only a few of its minimal path sets and minimal cut sets. These two incomplete structure functions are represented as disjoint sums. The average of each is a lower and upper bound, respectively, for the system reliability. The usefulness of these bounds is demonstrated on example networks     

Comment on `An improved Abraham-method for generating disjointsums'

The authors' earlier algorithm (see ibid., vol.R-36, p.70-74, Apr. 1987) yields relatively short disjoint sum forms of the structure functions of coherent binary systems. In the present paper, it is shown that, in applying this algorithm, still shorter disjoint sum forms can be obtained by proper arrangement of the path sets. This is demonstrated by some examples     

An Improved Abraham-Method for Generating Disjoint Sums

An algorithm, based on the Abraham-method, generates a disjoint-sum-form of the structure function. This algorithm contains two major improvements on the original method, and they considerably reduce the number of disjoint terms. The algorithm is more effective than the Abraham method with respect to the computation time for complex coherent systems. These statements are demonstrated by 2-terminal reliability analysis of example networks.     

A generalized reduction method for the connectedness probability ofstochastic networks

The connectedness probability of a stochastic network is computed by a generalized approach to network reduction. The approach is based on separating-vertex-sets and on introducing more than one replacement graph. Computational aspects are discussed, and examples are presented     

General Failure Model Applied to Preventive Maintenance Policies

The reliability behavior of systems is investigated if two types of failures can happen. Type 1 is removed by minimal repair, Type 2 by replacement. Reliability expressions are derived. The results are used for calculating the s-expected long-run cost rate for a generalized age replacement policy and repair limits.