Determination of Reliability Bounds for Structural Systems Using Linear Programming

In reliability analysis of structural systems, what is of interest is intervals containing the survival probability when exact values cannot be obtained. There are analitical formulas to determinate the bounds of the system survival probability for series systems by employing biand higher-order component probabilities. For parallel systems, the bounds of the system survival probability cannot be found analytically only from marginal probabilities (first order component probabilities). Linear programming can be used to calculate the bounds of survival (or failure) system probability for any system with any amount of information available on the component probabilities. This paper considers two-state (intact or failure) component systems and uses the probabilities associated to these events as decision variables. The linear objective function is a sum containing some of these probabilities, with linear restrictions given by the individual probabilities and/or joint component probabilities and by the axioms of probability. The lower bound of the system probability is obtained as the minimum of the objective function and the upper bound is obtained as its maximum.