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.