Time Series Analysis (CUSUM): Difference between revisions

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== Excel ==
== Excel ==


{{Under construction|section}}
The '''CUSUM''' control chart may be invoked from the Excel formula bar with the following function calls:
 
The CUSUM control chart may be invoked from the Excel formula bar with the following function calls:


<syntaxhighlight lang="vb">=mdTimeSeries_CUSUM(TimeSeriesData as Range, T as Double, Optional k as Double = 0)</syntaxhighlight>
<syntaxhighlight lang="vb">=mdTimeSeries_CUSUM(TimeSeriesData as Range, T as Double, Optional k as Double = 0)</syntaxhighlight>


{{Excel (Text, Help, No Arguments)}}
{{Excel (Text, Help, No Arguments)}}
The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:
{|
|- style="vertical-align:top;"
|
{|
  |- style="vertical-align:top;"
  |
:<math>
  \begin{align}
  \mathit{TimeSeriesData} & =
\begin{bmatrix}
y_1\\
\vdots\\
y_t\\
\end{bmatrix}\\
\\
  \mathit{T} & = \big [ T \big ]\\
\\
  \mathit{k} & = \big [ k \big ]\\
  \end{align}</math>
  |
::<math>
\begin{align}
  \mathit{mdTimeSeries\_CUSUM}  & = 
\begin{bmatrix}
\begin{bmatrix}
C_{1}\\
\vdots\\
C_{t}\\
\end{bmatrix}
&
\begin{bmatrix}
S_{\rm H,1}\\
\vdots\\
S_{\rm H,t}\\
\end{bmatrix}^*
&
\begin{bmatrix}
S_{\rm L,1}\\
\vdots\\
S_{\rm L,t}\\
\end{bmatrix}^*
\end{bmatrix}
\end{align}
</math>
  |-  style="vertical-align:top;"
  |colspan="2"|
where:
* <math>y_t</math> is the original observation (data point) at time <math>t</math>
* <math>T</math> is a constant, typically a target value or the mean of historical data
* <math>k</math> is the slope of the V-Mask arm, an optional parameter (V-Mask limits <math>S_{\rm H}</math> and <math>S_{\rm L}</math> are not returned if <math>k</math> is omitted)
* <math>C_t</math> is the value of the cumulative sum (CUSUM) at time <math>t</math>
* <math>S_{\rm H}</math> and <math>S_{\rm L}</math> are the high and low V-Mask parameters, respectively, and the <math>^*</math> superscripts indicate they are optionally-returned
  |}
|
:[[File:TimeSeriesAnalysis2.png|frame|Figure 1. Example showing the selection of the '''TimeSeriesData''' (blue frame), '''T''' (red frame), '''k''' (purple frame), and Results (light blue frame) arrays in Excel. The <math>S_{\rm L}</math> and <math>S_{\rm L}</math> parameters are returned in this example as '''k''' is specified.]]
|}


== References ==
== References ==

Latest revision as of 04:44, 19 May 2023

Description

This article describes a method for preparing a Cumulative Sum (CUSUM) control chart.[1][2]

Model theory

Under construction icon-blue.svg.png This section is currently under construction. Please check back later for updates and revisions.

Excel

The CUSUM control chart may be invoked from the Excel formula bar with the following function calls:

=mdTimeSeries_CUSUM(TimeSeriesData as Range, T as Double, Optional k as Double = 0)

Invoking the function with no arguments will print Help text associated with the model, including a link to this page.

The input parameters and calculation results are defined below in matrix notation, along with an example image showing the selection of the same cells and arrays in the Excel interface:

where:

  • is the original observation (data point) at time
  • is a constant, typically a target value or the mean of historical data
  • is the slope of the V-Mask arm, an optional parameter (V-Mask limits and are not returned if is omitted)
  • is the value of the cumulative sum (CUSUM) at time
  • and are the high and low V-Mask parameters, respectively, and the superscripts indicate they are optionally-returned
Figure 1. Example showing the selection of the TimeSeriesData (blue frame), T (red frame), k (purple frame), and Results (light blue frame) arrays in Excel. The and parameters are returned in this example as k is specified.

References

  1. NIST/SEMATECH, 2012. e-Handbook of Statistical Methods, http://www.itl.nist.gov/div898/handbook/, accessed 24 March 2022.
  2. Napier-Munn, T.J., 2014. Cunning solutions to process improvement. 12th Mill Operators' Conference, Townsville, Qld, 1-3 September 2014.