EWMA Control Chart

The control charts discussed earlier are very useful in the diagnostic aspects of quality process improvement. They can be used to stabilize a process by identifying out-of-control situations. After the process is stabilized and brought in control, further improvement of the process can be achieved by using some special control charts such as the cumulative sum (CUSUM) control chart and the exponentially weighted moving average (EWMA) control chart. These control charts can be used when small shifts in a process are of interest. 

EWMA Control Chart An EWMA control chart plots weighted moving average values for variables data. A weighting factor is chosen by the user to determine how older data points affect the mean value compared to more recent ones. Because the EWMA chart uses information from all samples, it is a good alternative to the CUSUM chart in detecting smaller process shifts. 

Viinikka, J. and H. Debar, Monitoring IDS Background Noise Using EWMA Control Charts and Alert Information, in Proceedings of the 7th International Symposium on Recent Advances in Intrusion Detection (RAID 2004), Springer-Verlag, 2004. 

Two alternatives to the Shewhart control chart, which are more complicated to calculate but generally more effective to detect small shifts, are the Cumulative Sum (or Cusum) control chart and the Exponentially Weighted Moving Average (EWMA) control chart. These control charts will not be discussed here, but are described in standard references. ... 

Two approaches are typically followed in this case. The first approach involves the analysis of the underlying statistical model of the autocorrelation (e.g., ARIMA model) and the monitoring of the residuals with traditional control charts for independent observations. The second approach develops monitoring schemes directly on the correlated data (e.g., EWMA control charts). 

The EWMA Control Chart refers to the Exponentially Weighted Moving Average Chart. The common approach is plotting process data as a time series and... 

It should be noted that the cumulative sum (CUSUM) and exponential weighted moving average (EWMA) control charts have also been proposed for the use in high-quality processes (Yeh et al. 2008 Szarka and Woodall 2012). However, in some cases, they are very complex and complicated to understand for the practitioners. 

Yeh AB, Mcgrath RN, Sembowta- MA, Shen Q (2008) EWMA control charts for monitoring high-yield processes based on non-transfmmed observations. Int J Prod Res 46 5679-5699... 

Information about past measurements can also be included in the control chart calculations by exponentially weighting the data. This strategy provides the basis for the exponentially weighted moving-average (EWMA) control chart. Let x denote the sample mean of the measured variable and z denote the EWMA of X. A recursive equation is used to calculate z k),... 

The EWMA performance can be adjusted by specifying X. For example, X = 0.25 is a reasonable choice, because it results in an ARL of 493 for no mean shift (8 = 0) and an ARL of 11 for a mean shift of dx (8 = 1). EWMA control charts can also be constructed for measures of variability such as the range and standard deviation. 

In order to compare Shewhart, CUSUM, and EWMA control charts, consider simulated data for the tensile strength of a phenolic resin. It is assumed that the tensile strength x is normally distributed with a mean of x = 70 MPa and a standard deviation of a = 3 MPa. A single measurement is available at each sampling instant A constant (8 = 0.5a = 1.5) was added to x k) for A > 10 in order to evaluate each chart s ability to detect a small process shift. The CUSUM chart was designed using K = 0.5a and H = 5a, while the EWMA parameter was specified as X = 0.25. 

The relative performance of the Shewhart, CUSUM, and EWMA control charts is compared in Fig. 21.6. The Shewhart chart fails to detect the 0.5a shift in x. However, both the CUSUM and EWMA charts quickly detect this change, because limit violations occur about ten samples after the shift occurs (at k = 20 and A = 21, respectively). The mean shift can also be detected by applying the Western Electric Rules in the previous section. 

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