The design of optimum component test plans for system reliability

It is often necessary to conduct individual component tests for the prediction and verification of system reliability. Moreover, system testing can be economically infeasible or even impossible. The question then arises as to how component test plans should be designed so as to minimize test costs. Acceptance procedures based on the sum of failures during component tests have been previously suggested in the literature only for a series system, parallel system, and a serial connection of redundant subsystems. This line of research is extended by considering serial connection of standby redundant and k-out-of-n subsystems. It is shown that the serial connection of the mixture of all these systems can also be modelled. The optimal component testing problem is formulated as a semi-infinite linear program, and a procedure to compute optimum component test times is developed. The solution procedure is based on the well known cutting plane idea and column generation technique. Numerical examples are also provided.