Cumulative Sum (CUSUM)ΒΆ

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 \(N\) None
\(k\) \(k \in \mathbb R\) None None None

Output Parameters

Parameter Type Constraint Description Remarks
\(S\) \(S \in \mathbb R^N\) \(N \in \mathbb{N}\) None None

Single Steps using the Algorithm

References

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