A General Model for Start-Up Demonstration Tests

The commonly known consecutive successes total failures (CSTF) start-up demonstration test procedure is generalized to a total successes consecutive successes total failures consecutive failures (TSCSTFCF) procedure. Accordingly, a unit under test is accepted when either a total number of successful tests or a specified number of consecutive successes of tests are observed before both a total number of failures and any run of specified length of failures; otherwise the unit is rejected. The waiting time until termination (the length of the set of tests) of the general procedure is evaluated. A correct choice of parameters (e. g. the number of successes required for acceptance, or the length of a run of failures causing rejection) may yield a significantly shorter waiting time than that of the relevant CSTF procedure. Also, the new procedure is less sensitive to parameter changes, which is an obvious improvement in case the parameter values are miss-specified. We provide interval confidence bounds for the estimation of the reliability for the start-up demonstration test, which is based on maximum likelihood estimators. Then, we determine the minimum sample size needed in a demonstration test to achieve a certain precision of this reliability at a specified confidence level.