A Start-Up Demonstration Test Based on Exchangeable Binary Trials

We investigate several aspects of the recently introduced consecutive successes distance failures start-up demonstration test under an exchangeable model. By assuming that the probability of a successful start-up attempt p is a random variable, instead of a fixed value, the outcomes of the successive start-ups become s-dependent exchangeable binary random variables. From a practical point of view, this is a more realistic model than the ordinary model of s-independent start-ups. Critical quantities of the test such as the expected length of the test, the probability of acceptance of the equipment under test, as well as the distribution of the length of the test, are derived. Illustrative numerical examples based on a Beta-mixing distribution for p, and comparisons with the corresponding i.i.d. model, are presented. Furthermore, a comparison study is performed between the consecutive successes distance failures and other competitive start-up demonstration tests. Finally, inferential procedures for the estimation of the unknown parameter(s) of the Beta-mixing distribution are also discussed.