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

Reader Aids: Purpose: To widen state of the art Special math needed for explanation: Probability Special math needed to use results: None Results useful to: Reliability analysts and theoreticians Summary and Conclusions: We consider the problem of acceptance testing for a series system of n different components, each having an unknown, constant failure rate. Components are individually tested and the tests are terminated when a preassigned number of failures are observed for each component. The total time on test for each component is noted and a statistic is constructed by using the observed test times and the number of failures of the different components; the statistic is based on the MLE of system reliability. This statistic based on component test times 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 the system reliability are not exceeded. Numerical examples are provided and implications of the test plan are discussed.