ABSTRACT
The total successes consecutive successes total failures consecutive failures (TSCSTFCF) procedure, and more simple procedures like consecutive successes total failures (CSTF) for reliability demonstration tests, are discussed. The expected number of required tests and the probability of accepting the tested unit are derived. First, a special private case is given to clarify the possibility of using a direct combinatorial approach. Further on, a system of difference equations is set up. They are solved with aid of certain auxiliary functions. In some cases, the method of generating functions may give closed-form expressions for the solution. A constrained optimization problem is solved for minimizing the number of required tests subject to some confidence-level requirements. The variables for this optimization include the total number of successes, failures, and the maximal lengths of runs of successes and failures. The TSCSTFCF procedure is observed to be the most worthwhile one, although it is the most complicated one. A generalization is presented to the possibility of testing several units in parallel.
