- Click
**SigmaXL > Templates & Calculators > Control Chart Templates > Time Weighted > Tabular CUSUM.**This template is also located at**SigmaXL > Control Charts > Control Chart Templates > Time Weighted >****Tabular CUSUM**.

- 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**k**= 0.5,**h**= 5,**FIR**= 0. Specify**Target**= 10 and**Historical StDev**= 1 as shown:

- Click the
**Tabular CUSUM Chart**button to create the Tabular CUSUM 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 Tabular CUSUM template and Paste
Values to cell
**A22**as shown.

- Click the
**Add Data**button to add the new data to the Tabular CUSUM Control Chart:

- This confirms that the process is now “out-of-control” with signals at samples 29 and 30.

The CUSUM chart plots the cumulative sums of deviations of sample values from a target value. Because they combine information from several samples, cumulative sum charts are more effective than Shewhart charts for detecting small process shifts. There are two ways to represent CUSUMs: the tabular (or algorithmic) CUSUM, and the V-mask form of the CUSUM (see Montgomery, 2013). SigmaXL utilizes the Tabular CUSUM.

1. This Tabular Cumulative Sum (CUSUM) 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 the **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 Tabular
CUSUM Control Chart.

4. Enter the CUSUM **k** parameter in cell D1. This is
the reference (or slack) value, typically set to 0.5. It sets the
size of mean shift (2k sigma) that you would like to detect quickly,
so 0.5 denotes rapid detection of a shift in mean = 1 sigma.

5. Enter the CUSUM **h** parameter in cell D2. This is
the decision interval, typically set to 4 or 5. The upper and lower
control limits = +/- h*StDev (MR-bar/d2). The center line = 0.

6. Enter the CUSUM **FIR** parameter in cell D3. This
is the fast initial response (or headstart) value, typically set to
h/2 if used, 0 otherwise. This sets the initial CUSUM statistic so
that it improves the sensitivity to a mean shift at startup.

7. Optionally enter the CUSUM **Target** in cell D4.
This is your process target value, typically the midpoint of your
specification limits or historical mean. If you do not specify a
Target, the data average will be used.

8. Optionally enter the CUSUM **Historical StDev** in
cell D5. If you do not specify a Historical StDev, it will be
estimated using MR-bar/d2.

9. The **h**,** k** and **FIR**
parameters affect the Average Run Length (ARL) characteristics. For
example, h=4 will detect a small shift more quickly than h=5, but
has a shorter ARL(0) run length (higher false alarm rate).

10. To determine optimal CUSUM parameter values and calculate ARL,
click **SigmaXL > Templates and Calculators > Control Chart
Templates > Average Run Length (ARL) Calculators > CUSUM ARL**.

11. Click the **Tabular CUSUM Chart** button to create
a Tabular CUSUM Control Chart.

12. 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 Target and Historical StDev.

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

14. The **k**, **h** and **FIR**
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 Tabular CUSUM chart. Data values
and out-of-control formatting are refreshed only when the buttons
are used.

15. Reference: Montgomery, D.C. (2013), *Introduction to
Statistical Quality Control*, Seventh Ed., Wiley, pp. 418-427.

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