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 maximum likelihood estimation 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 and producer risks on system reliability are not exceeded. Numerical examples are provided, and implications of the test plan are discussed.