Some Study About Dynamic CUSUM Control Chart

With the increasingly fierce of the market competition, how to reduce the production costs and improve the quality of products effectively is particularly important. Control charts is an important tool of statistical process control, it is mainly used for analyzing the stability of the process and providing early warnings of abnormal factors existing in the process, so we can correct abnormal factors timely before a large number of the unqualified products produced and reduce the loss and the cost. Traditional control charts are static, that is to say, the sampling interval or the sample size is fixed, so the static control charts can not discover the abnormal factors existing in the process in time. Variable sampling interval control chart’s sampling interval and variable sampling size control chart’s sample size is based on the observation results of the sample, that control chart can find abnormity timely, so that the monitor can detect the abnormal factors and reduce the occurrence of unqualified products. In summary, dynamic control chart is more effectively than the static control chart in improving the production efficiency and reducing the occurrence of unqualified products. This paper mainly studied the dynamic cumulative sum control chart(CUSUM) in two aspects, that is:(1) This paper proposes the CUSUM median control charts with variable sampling intervals, and then compared with the CUSUM control chart with fixed sampling interval, we can use average time to signal(ATS) to measure the quality of the control chart. The main idea is that we choose the appropriate parameters to let them have the equal ATS when they under control, then compare the ATS when they out of control.(2) We also propose the CUSUM variance control charts with variable sampling sizes, and then compared with the CUSUM control chart with fixed sampling sizes, in order to measure the quality of the control chart, we can use average run length(ARL). The main idea is that we choose the appropriate parameters to let them have the equal ARL when they under control, then compare the ARL when they out of control.This paper uses Markov chain method to calculate ATS and ARL. According to the data results, the control chart we propose can effectively shorten the time of the out of control process, and improve the working efficiency.