Monitoring a fraction with easy and reliable settings of the false alarm rate

Monitoring a fraction arises in many manufacturing applications and also in service applications. The traditional p‐chart is easy to use and design but is difficult to achieve the desired false alarm rate. We propose a two‐sided CUSUM Arcsine method that achieves both large and small desired false alarm rates for an in‐control probability anywhere between 0 and 1. The parameters of the new method are calculated easily, without tables, simulation, or Markov chain analysis used by many of the existing methods. The proposed method detects increases and decreases and works for constant and Poisson distributed sample sizes. The CUSUM Arcsine also has a superior sensitivity compared with other easily designed existing methods for monitoring Binomial distributed data. This paper includes an extensive literature review and a taxonomy of the existing monitoring methods for a fraction.