# cusum: Calculates a sequence of Cusum statistics In Smisc: Sego Miscellaneous

## Description

Calculates a sequence of one-sided upper Cusum statistics given the reference value and the control limit.

## Usage

 ``` 1 2 3 4 5 6 7 8 9 10``` ```cusum(X, k, h, initial = 0, reset = TRUE) ## S3 method for class 'cusum' print(x, ...) ## S3 method for class 'cusum' plot(x, indexes = NULL, emphOOC = TRUE, ...) ## S3 method for class 'cusum' signal(object, ...) ```

## Arguments

 `X` A numeric vector. `k` The reference value. `h` The upper control limit. `initial` The starting value of the Cusum (C[0]). `reset` Logical indicating whether the Cusum is reset to 0 after crossing the control limit. `x` Object of class `cusum` `indexes` A vector of indexes that select the elements of the cusum statistics that will be plotted. `emphOOC` A logical indicating whether out of control points should be emphasized in red. `object` Object of class `cusum` `...` Additional arguments to `print.default` or `plot.default`. Ignored by the `signal` method.

## Details

Cusum is assumed to be of the form: C[i] = max(0, C[i-1] + X[i] - k), where the signal occurs when C[i] > h. Note that `X` can be the Cusum scores, or weights, given by the log-likelihood ratio, in which case `k = 0` would make sense.

## Value

A object of class `cusum`, which is a vector of the Cusum statistics, along with the following attributes: `X`, `k`, `h`, `initial`, and `reset` (which correspond to the original arguments provided to the function) and `resetCounter`, a vector of integers corresponding to `cusum` that indicates when the Cusum resets.

## Methods (by generic)

• `print`: Prints the `cusum` object by only showing the Cusum statistics and suppressing the attributes.

• `plot`: Plots the `cusum` object.

• `signal`: Prints the indexes in a `cusum` object that exceed the control limit

## References

Hawkins DM and Olwell DH. (1998) Cumulative Sum Charts and Charting for Quality Improvement. Springer.

## Examples

 ``` 1 2 3 4 5 6 7 8 9 10 11``` ```y <- cusum(rnorm(50), 0.2, 2) y # Plot the cusum plot(y) # Show the indexes where the chart signaled signal(y) # A look at the attributes attributes(y) ```

Smisc documentation built on May 30, 2017, 1:55 a.m.