Linear programming and the reliability of multicomponent systems
Several problems in the assignment of parallel redundant components to systems composed of elements subject to failure are considered. In each case the problem is to make an assignment which maximizes the system reliability subject to system constraints. Three distinct problems are treated. The first is the classical problem of maximizing system reliability under total cost or weight constraints when components are subject to a single type of failure. The second problem deals with components which are subject to two types of failure and minimizes the probability of one mode of system failure subject to a constraint on the probability of the other mode of system failure. The third problem deals with components which may either fail to operate or may operate prematurely. System reliability is maximized subject to a constraint ori system safety.
In each case the problem is formulated as an integer linear program. This has an advantage over alternative dynamic programming formulations in that standard algorithms may be employed to obtain numerical results.
Source: Naval Research Logistics Quarterly
Kolesar, Peter. "Linear programming and the reliability of multicomponent systems." Naval Research Logistics Quarterly 14, no. 3 (1967): 317-327.