Feasibility Study of a Moving Centerline Exponentially Weighted Moving Average Control Chart to Detect Real Warning for Daily Output QA in Proton

Abstract

The purpose of this study is to verify the usefulness of moving centerline exponentially weighted moving average (MCEWMA) chart, as compared an autoregressive integrated moving average (ARIMA) two-stage time series model, and MCEWMA chart approach, specific to detect the small variation detection in the daily output QA process. A total of 180 individual observations were taken on each of daily output measurements over a period of time in defined daily interval. The conventional control chart recommended for individual observation is primarily based on the assumption that the process data are independent and normally distributed. If the data set is correlated, conventional control charts can cause a substantial increase in the false alarm rate. For this reason, QA observations were analyzed using the autocorrelation function to find appropriate time series models. An ARIMA time series model and an MCEWMA variable control chart were both applied to identical output QA data. An autocorrelation function plot for daily output data at lag 1 and 2 result in r1=0.51 and r2=0.44, respectively. This is certainly large enough to severely distort control chart performance. In the ARIMA and MCEWMA control charts, 2 points fell out of the limits. This was the same result as the two-stage time series modeling and the special control chart, MCEWMA approach. Both indicate the output QA process is reasonably stable, with out-of-control signals where an assignable cause may be present. In the ARIMA model, applying control charts to several process variables and developing an explicit time series model for each variable of interest is potentially time-consuming. However, MCEWMA chart is simple and easy to implement with comparable results. The MCEWMA charts can detect meaningful, small shifts for individual data responses that are autocorrelated. This case study confirms the suitability of MCEWMA which is recommended as an alternative to the time series model and residual special control chart approach.