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## About this lesson

## Exercise files

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EWMA Chart.xlsx10.5 KB EWMA Chart - Solution.docx

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## Quick reference

### EWMA Chart

The EWMA chart (Exponentially Weighted Moving Average) is a variable data control chart that blends the current data point with an average of the previous data points. It can be created in either Microsoft Excel or Minitab.

### When to use

Use the EWMA Chart when seeking to ensure a stable process stays very close to its current mean. Also, this chart will dampen the effects of high system noise and common cause variation to quickly reveal shifts in the mean.

### Instructions

The EWMA chart is combining two effects. It is using the weighted moving average to dampen out oscillations in the data and identify trends in the mean. It is using an exponential function in the calculation of the control limits to contain potential shifts until the chart has enough data to reach a point of stability. This gives the EWMA chart a distinctive look with the control limits, as though a funnel was opening.

A key parameter that must be selected for this chart is the λ value. This value is used both in the calculation of the EWMA value and the calculation of the control limits. This value must be between zero and one. If the value is zero, the plot becomes void. If the value is one, the plot becomes essentially an I-MR plot. Normally the λ value is set between 0.2 and 0.4. The smaller the value, the smaller the shift it will likely detect.

The math for this chart is far more complex than any other chart we have discussed. While doing the math is easy for Microsoft Excel or Minitab.; it is difficult to do by hand.

Within Minitab, control charts are created by using the “Stat” pull down menu, then selecting “Control Charts.” Within the Control Charts window, select “Time Weighted” and then finally select “EWMA” In the Minitab EWMA Chart panel, you will need to select the data columns with your data and set the EWMA weight.

If creating the EWMA Chart in Excel:

- Determine the λ value you will use and establish your subgroup plan.
- Measure the attribute and record it in Excel column(s). If the subgroup has multiple items, calculate a subgroup mean.
- Calculate a global mean for all the data values you have.
- Calculate a global standard deviation for all the data values you have. Adjust this standard deviation by dividing it by the square root of the number of items in a subgroup. (If 4 items in the subgroup divide by the square root of 4, which is 2.)
- Calculate the EWMA value (Z) for each subgroup. This is a weighted average of the subgroup value and the EWMA value from the previous subgroup. The weight for the subgroup value is the λ value and the weight for the previous EWMA value is then 1 minus λ. For the first data value, use your global mean as the previous EWMA value.

This is the value you will be plotting on the EWMA chart.

- Calculate the upper and lower control limits using the equations shown. The standard deviation is the adjusted standard deviation from step 4.
- Plot the EWMA, global mean and the control limits.
- Take appropriate actions to remove special causes or to center your data within the customer spec limits.

### Hints & tips

- If doing this in Minitab, it is easy to run the chart with several λ’s to see which provides the best insight.
- There are several other moving average control charts, but this one is the most widely adopted.

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