HWMA Control Charts For Monitoring Process Mean And Variance

Product quality has been highly valued in the world.An efficient quality control chart is crucial to improve product quality and production efficiency.The quality control chart is used to monitor the mean value of the product during the production process.Control charts for monitoring the process variance and the combined control chart for monitoring the process mean and variance are equally important.Therefore,more and more researchers pay attention to design an efficient control chart to monitor the variance and monitor the mean and variance jointly.First,we briefly review a control chart,named as homogeneously weighted moving average(denoted as HWMA)control chart for monitoring the process mean.Then,four new HWMA charts are proposed for monitoring the process variance.The performance comparison is given.Furthermore,two kinds of control charts based on HWMA procedure are proposed for monitoring the process mean and variance simultaneously.One is the combined chart based on two single HWMA control chart which aimed at monitoring the process mean and variance.Another one is Max type chart,which combine the detection statistics of mean and variability to construct a control chart to monitor both the mean and the variability simultaneously.In this paper,The average run length(denoted as ARL)of the two joint control charts is calculated by Monte Carlo simulation.The ARL represent the monitoring performance of the control chart.Next,the combination of EWMA(denoted as CEWMA)control chart and MAX-EWMA control chart are compared with the combination of HWMA(denoted as CHWMA)control chart and MAX-HWMA control chart.Whereafter,the robustness analysis of MAX-HWMA control chart based on non-normal distribution samples is put forward.Gamma distribution,t distribution,Chi-square distribution and Uniform distribution are selected in this paper.It is found that the control chart based on non-normal samples can be more robust by adjusting the design parameters.Finally,a real data example is given to illustrate the application of the new chart.