Runs rules and p-charts for multistream binomial processes

Process control schemes for multistream binomial processes are described. A multistream process is one in which the streams are uncorrelated or very weakly correlated. When each of the J streams are identical (a homogeneous multistream process) one can use a group control chart (a k-sigma p-chart on which only the largest and smallest of the J sample proportions nonconforming are plotted). A test (runs rule) that signals when the same stream produces the largest proportion nonconforming R consecutive times is investigated. Methods using Markov chains are developed for determining the average run length (ARL) of a runs test. ARL tables useful for designing runs rule control schemes are provided for selected values of J, stream sample size n, proportion of nonconforming units p, and R.