First to signal criterion for comparing control chart performance

Control chart performance is often measured using average run length or median run length, which gives the expected or median number of samples to signal. It is often argued that on average, one chart will signal a process change quicker than another, and is therefore a better choice. Average and median run length do not, however, answer the question of which method will be more likely to signal first. We introduce the idea of “first to signal” and compare charts based on this criterion.