Smisc (version 0.3.9.1)

cusum: Calculates a sequence of Cusum statistics

Description

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

Usage

cusum(X, k, h, initial = 0, reset = TRUE)
# S3 method for cusum
print(x, ...)
# S3 method for cusum
plot(x, indexes = NULL, emphOOC = TRUE, ...)
# S3 method for 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

…

Additional arguments to print.default or plot.default. Ignored by the signal method.

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

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

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.

References

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

Examples

# NOT RUN {
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)
# }