Chapter 3 Binary start-up demonstration tests

In this chapter, we present in detail several binary start-up demonstration tests. The family of binary start-up demonstration tests includes models for which, the outcomes of the start-up procedure at each trial can be classified in two categories labeled as failure (F) or success (S). This family was the first one to be studied in the literature, and up to date a great number of models, with different acceptance and rejection criteria, has been considered. The most commonly used criteria are based (a) on uninterrupted sequences of successes and/or failures (runs), (b) on the total number of successes and/or failures (frequencies), (c) on sequences with high concentration of successes and/or failures (scans), and (d) on some alternative statistical functions of similar nature. We provide several formulas for the evaluation of their characteristics, namely the distribution and the moments of the time till a decision is reached.