The EWMA – Exponentially Weighted Moving Average chart is used in statistical process control to monitor variables (or attributes that act like variables) that make use of the entire history of a given output. This is different from other control charts that tend to treat each data point individually.

Each output (previous sample mean) is given a weighting by the user. The most recent samples are weighted the highest. This means the oldest data is given the least amount of weight. The chart displays the data geometrically. This gives the advantage of the chart not being greatly affected when a small or large value enters the calculation.

The EWMA chart will detect shifts of .5 sigma to 2 sigma much faster than Shewhart charts with the same sample size. They are, however, slower in detecting large shifts in the process mean.

Another advantage is that each data point plotted on the chart is represents a moving average of points. Thus you can use the Central Limit Theorem to say that the plotted points (the moving average of the subgroups) is normally distributed and the control limits are clearly defined.

## Use EWMA Charts When:

- When you have continuous data from the entire life of a process.
- You want to detect small shifts in the process. For larger shifts, use Shewart style charts like the X Bar R and the X Bar S charts.
- When you want to measure the mean. Monitoring the process variability requires the use of some other technique.
- The subgroup sample size should be > 1. If the sample size in the subgroup is 1, try using an Individual X chart.
- When you want to smooth out the effect of uncontrollable noise in the data.

## How to Use EWMA Control Charts

- Decide the weightings
- Use smaller weightings to discern smaller shifts.
- Set between 0 and 1.
- If you pick a weighting of 1, you have an xbar chart.

- Based on user experience and preference.

- Create the control limits
- Generally default to 3 standard deviations for six sigma quality purposes and to match what other charts generally do.
- May need to change the control limits to something smaller if the weightings are very small.

- Plot the points
- Can be either subgroups or individual observations.
- When plotting a subgroup, use the mean of that subgroup.

- Can be either subgroups or individual observations.
- See if the points are within the control limits.
- Look for trends or patterns.

## Examples of Uses of EWMA Control Charts

- Detecting drift that is caused by tool wear.
- Ex. Manufacturer produces a widget of a certain diameter. If the diameters of the widget are off, there are consequences. Measuring using an EWMA Chart helps understand the manufacturing machine wear and it’s impact to the creation of the widgets.

- Accounting processes
- Ex. Day-to-day fluctuations in accounting processes may be large but may not necessarily mean the process is unstable. The choice of lambda can be determined to make the chart more or less sensitive to these daily fluctuations.

- Chemical processes
- Website visitors that fluctuate depending on the day of the week.
- Ex. This website gets far more visitors when people are at work Monday through Thursday compared to even Friday, the weekends or during holidays.

## Important Notes on EWMA Charts

- Your data must be time-ordered.
- Consecutive points have the highest chance of being alike – so default to a range of 2 when possible.
- Created for normal data but is robust enough for non-normal data sets.

## ASQ Six Sigma Black Belt Moving Average Questions

**Question: ** Which of the following charts plots the mean of a set of values and recalculates the mean with each new value?

(A) Moving range

(B) Moving average

(C) X Bar and s

(D) c

**Answer: **B. The moving average chart plots the mean of a set of values (subgroups) with each new value.

X Bar and s is a good choice because the X Bar is a moving average. However, simply the moving average is a better choice as it doesn’t have the s (standard deviation) component.

The moving range doesn’t make sense for this question as there is no charting of the mean. And the c chart is an attribute chart for a fixed sample size and doesn’t pertain to our question here.

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