Abstract
The main drawback of using the linear programming (LP) bounds method for computing bounds on the reliability of a general system is that the size of the LP problem increases exponentially with the number of components. Although a multi-scale approach has been proposed to deal with a system with a large number of components, the selection of the subsystems in a multi-scale approach could still be difficult or impossible for a general system. In order to overcome the main drawback of the LP bounds method, the relaxed linear programming (RLP) bounds method was developed for a pure series system and pure parallel system; it provides results comparable to that of the LP bounds method. This paper extends the applicability of linear programming by presenting an approach to handle a general system by decomposing the entire system into subsystems based on failure modes. The proposed approach relies on individual component state probabilities and joint probabilities of the states of a small number of components, and it can provide the bounds for the failure probability of large systems, especially when other methods are not applicable. This paper also presents a strategy for decreasing the number of constraints in the RLP bounds method.
