A Comparison of Start-Up Demonstration Test Procedures Based on a Combinatorial Approach

Abstract

A comparative study is presented of various start-up demonstration procedures based on a combinatorial approach. The expected number of required tests and the probability of accepting the tested unit are derived using a set of auxiliary functions. 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. Various extensions to scan statistic-based and weighted tests are included and also to the testing of several units in parallel. The alternative Markov Chain embedding approach might involve in some cases the inversion of very large matrices. This disadvantage does not exist here.