The Optimal Design Of Cusum Charts For Joint Monitoring Mean And Variance

In order to reduce the quality loss of the production, quality controlchart should be quicker to find the problems happened in the process. Inthe modern production process, we require the characteristic value ofquality not only close to the target, but also have a small range. The vastmajority of control charts are designed to monitor a single processparameter, such as the mean or the variance, but it is often desirable tomonitor the mean and the variance simultaneously, since both may shift atthe same time.Because the classical Shewhart control chart is not sensitive indetecting small shifts, in this paper, the CUSUM chart is applied to detectsmall shift in monitoring both mean and variance. The proposed chart iscompared with other recently developed single charts. Comparisons arebased on the average run lengths. We use Markov chain to find the ARLof the new chart. The new chart detects small shifts in the mean andstandard deviation quicker than the other chart. Then the new model isimproved by introducing variable sampling intervals method. Bycomparative analysis, VSI model improve the ability of detect small shifteffectively. The combined scheme of an X-bar chart and a CUSUM chartin monitoring the mean and the variance is proposed in this paper. In thisscheme, the CUSUM feature will quickly detect small and moderateshifts, while the addition of the X-bar chart increases the speed ofdetecting large shifts. The method in this paper can greatly improve theability of detection and reduce the quality loss. In the conclusion, we summarize the future research possibilities following this subject.