A system-based component test plan for a series system, with type-II censoring

Acceptance testing is analyzed for a series system of n components, each having an unknown, different, constant failure rate. Components are tested individually, and tests are terminated when a preassigned number of failures is observed for each component. The total time-on-test for each component is noted, and a statistic is constructed using observed test times and the number of failures of the components; the statistic is based on the MLE of system reliability. This statistic is then used in specifying a decision rule for accepting or rejecting the entire system. The design of the test plan is stated as an optimization problem which minimizes test costs while ensuring that specified consumer & producer risks on system reliability are not exceeded. Numerical examples are provided, and implications of the test plan are discussed.