Locked lesson.
About this lesson
Exercise files
Download this lesson’s related exercise files.
EWMA Chart.xlsx10.5 KB EWMA Chart - Solution.docx
64.3 KB
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.
- 00:04 Hi, I'm Ray Sheen.
- 00:06 Let's look now at another category of time-weighted control charts,
- 00:10 the EWMA chart.
- 00:12 I suppose you're wondering what the EWMA stands for.
- 00:16 The Exponentially Weighted Moving Average chart doesn't plot the precise data value.
- 00:22 It uses a moving average of the current value and
- 00:25 the previous average value to create the data plot.
- 00:28 The EWMA plot can be tuned for various types of sensitivity,
- 00:31 based upon the exponential decay factor of lambda.
- 00:35 A lambda of 0.2 will be tuned to detect small shifts in the mean,
- 00:39 because it relies heavily on the historic weighted average.
- 00:43 A lambda of 0.4 will quickly identify larger shifts in the mean,
- 00:47 because it puts more emphasis on the current value.
- 00:49 And a lambda of 1 essentially eliminates the exponential weighting.
- 00:54 It would bring us back to an I-MR chart or Xbar-R chart,
- 00:57 as depending upon the subgroup size.
- 00:59 So, we use the EWMA chart to focus in on shifts to the mean of a stable process.
- 01:04 Once you have a process running really well and you wanna keep it in tight
- 01:07 control, you can switch from whatever variable data chart you were using,
- 01:11 initially, and now use an EWMA chart.
- 01:14 Through the exponential waiting,
- 01:16 noise factors are dampened and the true shift becomes obvious.
- 01:20 So let's take a look at an example of EWMA chart, and
- 01:24 you can see it has a very distinctive appearance.
- 01:26 The plot is of the weighted value of the data item, or subgroup data mean, and
- 01:30 the previous weighted average.
- 01:32 What makes this chart distinctive is the way the control limits start out narrow
- 01:36 and then widen out until they stabilize.
- 01:38 And a characteristic of how this chart is drawn is that the mean is always at
- 01:42 the center of the chart, which gives it part of its distinctive appearance.
- 01:46 Now, we went through the steps of creating a control chart on a previous module, but
- 01:50 let's take a look at some of the specifics about the EWMA chart.
- 01:55 Like so many others, we want to set up our subgroup definition in the sample plan.
- 02:00 Do this in the same way you would have done it for an I-MR or Xbar R chart.
- 02:04 Next is to select the lambda value.
- 02:07 The value you select is based upon what you are trying to do.
- 02:10 The lambda affects the weight of the most current value as compared to the last
- 02:13 view points.
- 02:14 The lambda must between 0 and 1.
- 02:17 If not sure what value to use, start with 0.2.
- 02:20 Now collect your data points, and
- 02:22 if there's a subgroup with multiple data points, calculate your subgroup mean.
- 02:26 Using the formulas on the next slide, you can calculate the EWMA (z) value.
- 02:31 Next, calculate a global mean, or a target value, and the global standard deviation.
- 02:36 This will also need to be adjusted.
- 02:39 Calculate the control limits, and plot everything.
- 02:42 Of course, if the chart shows an out of control situation, stop, investigate, and
- 02:46 take appropriate action.
- 02:48 Let's look at how we do the calculations, manually, or in Excel.
- 02:52 As with the other modules, formulas are on the right side of the screen, and
- 02:55 the calculation steps will be discussed on the left side.
- 02:58 First, if there is a subgroup with more than one data point, calculate its mean.
- 03:02 Then consider all of the data values in your data set, and
- 03:05 calculate a global mean.
- 03:07 Now, calculate the standard deviation for
- 03:09 the entire data set, then adjust the standard deviation for
- 03:12 the subgroup size by dividing it by the square root of the subgroup size.
- 03:17 So, if the subgroup size was 1, you're just dividing by 1.
- 03:20 But if the subgroup size was 4, you would be dividing by 2.
- 03:24 Next, pick your lambda value.
- 03:26 I talked about this in the previous slide.
- 03:28 Now, we can calculate the EWMA z value.
- 03:31 It is a weighted average of the current value and the previous z value.
- 03:35 Multiply the current value times lambda, and
- 03:38 add that to the product of the previous z value times 1 minus lambda.
- 03:43 For the first data point, use the global mean for the previous value.
- 03:47 That part was easy.
- 03:49 The control limits are a pain.
- 03:51 Start by taking 1 minus lambda and raising that to a power
- 03:55 that is two times the number of the subgroup for that data point.
- 03:59 Subtract that value from 1, and then multiply that times lambda, and
- 04:04 divide everything by 2 minus lambda.
- 04:08 Now take that result and find the square root.
- 04:11 Then multiply the square root times 3 times the adjusted standard deviation.
- 04:16 Now this is the most difficult math in the entire course,
- 04:19 which is why I saved it till the last module.
- 04:21 To get to the control limits, add that product to the mean value for
- 04:24 the upper control limit, and subtract that product from the mean value for
- 04:28 the lower control limit.
- 04:30 Finally if using Excel, you can plot your EWMA z value, the mean value, and
- 04:34 the upper and lower control limits, using the line chart graphics option.
- 04:38 Now let’s look at creating this chart in Minitab.
- 04:41 Go to the Start menu, select Control Charts, then select Time Weighted Charts,
- 04:45 and, finally, select the EWMA chart.
- 04:47 When you do that, you should see a panel that looks like this.
- 04:50 Select your data entry approach, either one column, or
- 04:53 multiple columns if you have subgroups.
- 04:56 Click in the Variables window, then highlight your column names with the data.
- 05:00 Hit Select.
- 05:01 Your column should now be in the Variable window.
- 05:04 You'll need to set your EWMA weighting, or lambda value.
- 05:07 Now click on the OK button on the bottom of the panel, and
- 05:11 Minitab will generate your control chart.
- 05:14 The EWMA control chart will weight the most recent value in a manner that
- 05:19 minimizes noise and maximizes your ability to see small shifts in the mean.
Lesson notes are only available for subscribers.
PMI, PMP, CAPM and PMBOK are registered marks of the Project Management Institute, Inc.