A Cumulative Binomial Chart for Uni-variate Process Control

In this paper, a control method based on binomial distribution is proposed in which, by analyzing the cumulated data for a uni-variate quality characteristic, the possible mean shift is detected. In this method, the domain of observations is first divided into some specified intervals and then the number of observations in each interval is counted. Control statistics are next defined using the counted values based on the approximation methods. Necessary adaptations are made to form an appropriate statistic for the process monitoring. Using a simulation technique, the performance of the proposed method is compared with the ones of the optimal EWMA, GEWMA, CUSUM and GLR control charts. The results show that with an equal in-control average run length, the cumulative Binomial control method performs better than control charts in detecting a mean shift of any size less than 3 sigma. The analysis is also carried out for autocorrelated data, showing that the proposed method performs better than other methods for small to moderate values of autocorrelation coefficients.