A Cumulative Binomial Chart for Uni-variate Process Control


1 Department of Industrial Engineering,Sharif University of Technology

2 Department of Industrial Engineering,University of Yazd


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 rst divided into some speci ed intervals and then the number
of observations in each interval is counted. Control statistics are next de ned 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. 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 coecients.