Optimization by Integer Programming of Constrained Reliability Problems with Several Modes of Failure

Reliability optimization problems with N stages or subsystems in series, utilizing parallel or series redundant units, can be formulated and solved as integer programming problems. The systems considered have subsystems with components which can fail in several modes and are subject to linear and nonlinear constraints. Two situations are considered in which components within the subsystem 1) all fail in the same mode, or 2) all may fail in different modes. Expressions are developed for the probability of failure in each case. Two examples are solved.