The formula used for the EWMA statistic is given as:

- Click
**SigmaXL > Templates & Calculators > Control Chart Templates > Time Weighted > EWMA**. This template is also located at**SigmaXL > Control Charts > Control Chart Templates > Time Weighted > EWMA**. - Open Montgomery Table 9.1.xlsx (Sheet 1 tab). This is
simulated data from Montgomery, D.C. (2013),
*Introduction to Statistical Quality Control*, Seventh Ed., Wiley, pp. 415. Table 9.1. Samples 1 to 20 are drawn from a random normal distribution with population mean µ = 10 and population standard deviation σ = 1. Samples 21 to 30 have a mean = 11 and standard deviation = 1, so the process has shifted by 1 sigma and is “out-of-control”. While this is a small shift in process mean, it is something that we want to be able to detect and correct as quickly as possible. - Copy cells
**A1:B21**and Paste Values to the template at**A1**. Use the default**Weight (Lambda)**= 0.1,**K**= 2.7. Specify**Historical Mean**= 10 and**Historical StDev**= 1 as shown: - Click the
**EWMA Control Chart**button to create the EWMA Control Chart: - This confirms that the process is “in-control”.
- Switch back to
**Montgomery Table 9.1.xlsx**(**Sheet 1**tab). Select and copy cells**A22: B31**as shown. This is the data with shifted mean. - Switch to the EWMA template and Paste
Values to cell
**A22**as shown. - Click the
**Add Data**button to add the new data to the EWMA Control Chart: - This confirms that the process is now “out-of-control” with signals at samples 29 and 30. This matches Figure 9.7 in Montgomery.

1. This Exponentially Weighted Moving Average (EWMA) Control
Chart template should be used with continuous data. The data must be
in chronological time-sequence order.

2. You can replace the **X-Axis Label** and **
Data** column headings with any headings that you wish. Enter
your data in the Data column.

3. Enter labels in **X-Axis Label** column. Labels can
be Date, Time, Name, or other text information. These labels are
optional and will appear on the horizontal X-Axis of the EWMA
Control Chart.

4. Enter the EWMA **Weight** in cell D1. This is also
known as Lambda and is a value between 0 and 1.

5. Enter the EWMA **K** StDev multiplier in cell D2.
This is a value between 2 and 4. This is also referred to as L, but
SigmaXL uses K to avoid confusion with Lambda.

6. **Weight** and **K** values affect the
Average Run Length (ARL) characteristics. For ARL tables, see
**SigmaXL > Templates and Calculators > Control Chart
Templates > Time Weighted > Average Run Length (ARL) Tables**
and the SigmaXL workbook.

7. **Historical Mean** (D3) and **Historical
StDev** (D4) are optional. Enter values if process mean and
standard deviation are known.

8. Click the **EWMA Control Chart** button to create an
EWMA Control Chart.

9. After the control chart has been created and additional new data
entered into the **Data** column, click the **Add
Data** button to add the data to the existing chart. Control
limits will be calculated using the original chart mean and stdev or
specified Historical Mean/StDev.

10. **Add Data** should only be used if there are at
least 20 observations in the original chart, or Historical Mean and
StDev have been specified.

11. **Weight** and **K** StDev. parameters
are dynamic. If they are modified, the chart will automatically
update with the new parameters. However, they should be selected
prior to creating the EWMA chart. Data values and out-of-control
formatting are refreshed only when the buttons are used.

12. Reference: Montgomery, D.C. (2013), *Introduction to
Statistical Quality Control*, Seventh Ed., Wiley, pp. 433-438.

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