Cumulative Sum (CUSUM)

Local Algorithm - One-Dimensional Algorithm

Cumulative Sum algorithm calculates the cumulative sum of an input data sequence. The basic formula is stated as follows:

\[S_0 = 0 \, \text{,}\]

\[S_n = max(0, S_{n-1} + Y_n - k) \, \text{,}\]

where \(Y\) is the input data sequence and \(S\) represents the cumulative sums. \(k\) is a user-given reference value.

Input Parameters

Parameter	Type	Constraint	Description	Remarks
\(Y\)	\(Y \in \mathbb R^N\)	\(N \in \mathbb{N}\)	Input data sequence of length \(N\)
\(k\)	\(k \in \mathbb R\)

Output Parameters

Parameter	Type	Constraint	Description	Remarks
\(S\)	\(S \in \mathbb R^N\)	\(N \in \mathbb{N}\)

Tool Support

• Matlab

Single Steps using the Algorithm

• Computing CUSUM Values with CUSUM (Cumulative Sum) Algorithm

References

• E.S. Page, Continuous Inspection Scheme, Biometrika, vol. 41(1/2), pp. 100-115, 1954.