Start-up demonstration tests with three-level classification

In this paper, we introduce and study three new start-up demonstration tests with two types of unsuccessful start-ups. The proposed tests use run and frequency quotas acceptance/rejection criteria, providing extensions of binary start-up demonstration tests that have previously appeared in the literature. Using a Markov chain approach we establish general formulas for the distribution of the number of start-ups until the termination of the test, its mean and its variance, as well as for the acceptance probability of the equipment. Numerical results are presented in order to illustrate our method while a practical guidance for the determination of a good start-up demonstration test is also given. Finally, we discuss two inferential procedures for the estimation of the reliability of a single start-up of the test. Copyright Springer-Verlag Berlin Heidelberg 2015