Mehrnaz Noroozi Esfahani - Department of Industrial Engineering, Iran University of Science and Technology
Mohammad Hossein Abooie - Department of Industrial Engineering, University of Yazd

The shewhart p_chart or np_chart is commonly used for monitoring the number of non conforming items in a process with attribute data. Shewhart type control charts are not sensitive to small shifts in fraction non-conforming, instead, Cumulative Sum (CuSum) and Exponential Weighted Moving Average (EWMA) charts are more powerful tools for detecting small shifts in fraction nonconforming. The performance of a CuSum chart is depended on its values of parameters. This paper discusses about optimal values for CuSum parameters considering the standard deviation of average run length values. Results consist of the average run length values for out of control situations estimated by means of mathematical calculations, reveal a significant improvement in chart performance applying the appropriate values determined by rules acquired from simulation process. Furthermore, a linear model for estimating the parameters of the chart is also investigated that makes CuSum control chart more convenient for studies and industrial purposes. Numerical Example and diagram are also provided to illustrate how the rules affect the chart performance. Despite The optimal Shewhart chart parameters are well discussed in the literatures, very little studies done for optimizing CuSum chart, particularly it has been less considered to validate average run length by assessing the value of standard deviation of run length.

shewhart chart, fraction non-conforming, exponentially weighted moving average, cumulative sum, average run length