View source for Time Series Analysis (CUSUM)

== Description ==

This article describes a method for preparing a Cumulative Sum ('''CUSUM''') control chart.{{NIST/SEMATECH (2012)}}{{Napier-Munn (2014)}}

== Model theory ==

{{Under construction|section}}

== Excel ==

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>

{{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 ==