Analysis for Dynamic Statistical Process Control with Interventions

Abstract

The assumption of normal distribution is questionable in Shewhart and Hotelling T2 statistical process control mainly because of the process dynamics. The method of analyzing the process dynamics in the statistical process is reported. The statistical process data are separated to the dynamic and static series in a chemical-mechanical polishing process. The dynamic series is the time series with interventions. The dynamic series is applied to fit the statistical process data and the mean average percentage errors are about 4.5 % in the univariate analysis and 3 % in the multivariate one. The static series is normal distribution taking the p-value of 0.05 as the criteria in the null hypothesis of Shapiro-Wilk test, which suggests the autocorrelation is mostly covered in the dynamic series.