Double Moving Average Control Chart for Autocorrelated Data

Abstract

The assumption of normality and independence is necessary for statistical inference of control charts. Misleading results are obtained if the traditional control chart technique is applied on the auto-correlated data. When data is correlated, a time series model is employed to produce an optimum output. The objective is to create a new control chart methodology that takes the autocorrelation of observations into account. Charts of Moving Average, Exponentially Weighted and Cumulative Sum better perform in the existence of autocorrelation data for small and moderate changes. The proposed methodology is highly skilled and receptive to minor, moderate and major changes in the process. Propsed DMA chart increases  efficiency of  average run length (ARL) chart for  moving average (MA) to detect the  small to medium magnitude shifts in the mean. The simulation also demonstrates that the DMA chart with spans of w=10 and 15 generally performs well in terms of average run length (ARL) as compared to clasical MA. This research may be extended to a multivariate autocorrelated statistical process control, but it can also be used to recognise and categorise seven categories of traditional control chart patterns, such as Downward, Upward Shift, Normal Trend, Cyclic, Systematic patterns, Increasing and Decresing Trend. In order to identify and categorize a set of subclasses of abnormal patterns, this model (multivariate autocorrelated statistical process control chart) should employ a multilayer feed forward Artificial Neural Network (ANN) architecture controlled by a back-propagation learning rule.