Phase I control charts for independent Bernoulli data

Phase I Shewhart p, np and runs of conforming charts are investigated. The performance of these charts are assessed using the probability of a false alarm. As with other Phase I Shewhart charts, the probability of a false alarm increases as the number, tn, of samples increases for a fixed sample size,n. For a fixed value of m, the probability of at least one signal decreases as the sample size n increases. The probability of a signal for a runs of conforming chart depends on the number of samplesm. Like the p and np charts, as tn increases the probability of a false alarm increases. Unlike the p and np charts, the false alarm rate for a runs of conforming chart does not depend on the in-control value of p.