cusum {qcc}

Cusum chart

Description

Create an object of class 'cusum.qcc' to compute a Cusum chart for statistical quality control.

Usage

cusum(data, sizes, center, std.dev, head.start = 0,
      decision.interval = 5, se.shift = 1, data.name, labels,
      newdata, newsizes, newlabels, plot = TRUE, ...)

## S3 method for class 'cusum.qcc'
print(x, ...)

## S3 method for class 'cusum.qcc'
summary(object, digits = getOption("digits"), ...)

## S3 method for class 'cusum.qcc'
plot(x, add.stats = TRUE, chart.all = TRUE, 
     label.bounds = c("LDB", "UDB"), title, xlab, ylab, ylim, 
     axes.las = 0, digits =  getOption("digits"),
     restore.par = TRUE, ...)

Arguments

data

a data frame, a matrix or a vector containing observed data for the variable to chart. Each row of a data frame or a matrix, and each value of a vector, refers to a sample or ”rationale group”.

sizes

a value or a vector of values specifying the sample sizes associated with each group. If not provided the sample sizes are obtained counting the non-NA elements of each row of a data frame or a matrix; sample sizes are set all equal to one if data is a vector.

center

a value specifying the center of group statistics or the ”target” value of the process.

std.dev

a value or an available method specifying the within-group standard deviation(s) of the process.
Several methods are available for estimating the standard deviation. See sd.xbar and sd.xbar.one for, respectively, the grouped data case and the individual observations case.

head.start

The initializing value for the above-target and below-target cumulative sums, measured in standard errors of the summary statistics. Use zero for the traditional Cusum chart, or a positive value less than the decision.interval for a Fast Initial Response.

decision.interval

A numeric value specifying the number of standard errors of the summary statistics at which the cumulative sum is out of control.

se.shift

The amount of shift to detect in the process, measured in standard errors of the summary statistics.

data.name

a string specifying the name of the variable which appears on the plots. If not provided is taken from the object given as data.

labels

a character vector of labels for each group.

newdata

a data frame, matrix or vector, as for the data argument, providing further data to plot but not included in the computations.

newsizes

a vector as for the sizes argument providing further data sizes to plot but not included in the computations.

newlabels

a character vector of labels for each new group defined in the argument newdata.

plot

logical. If TRUE a Cusum chart is plotted.

add.stats

a logical value indicating whether statistics and other information should be printed at the bottom of the chart.

chart.all

a logical value indicating whether both statistics for data and for newdata (if given) should be plotted.

label.bounds

a character vector specifying the labels for the the decision interval boundaries.

title

a string giving the label for the main title.

xlab

a string giving the label for the x-axis.

ylab

a string giving the label for the y-axis.

ylim

a numeric vector specifying the limits for the y-axis.

axes.las

numeric in {0,1,2,3} specifying the style of axis labels. See help(par).

digits

the number of significant digits to use.

restore.par

a logical value indicating whether the previous par settings must be restored. If you need to add points, lines, etc. to a control chart set this to FALSE.

object

an object of class 'cusum.qcc'.

x

an object of class 'cusum.qcc'.

...

additional arguments to be passed to the generic function.

Details

Cusum charts display how the group summary statistics deviate above or below the process center or target value, relative to the standard errors of the summary statistics. Useful to detect small and permanent variation on the mean of the process.

Value

Returns an object of class 'cusum.qcc'.

Author(s)

Luca Scrucca

References

Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.
Montgomery, D.C. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Ryan, T. P. (2000), Statistical Methods for Quality Improvement, 2nd ed. New York: John Wiley & Sons, Inc.
Scrucca, L. (2004). qcc: an R package for quality control charting and statistical process control. R News 4/1, 11-17.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc, ewma

Examples

##
## Grouped-data
##
data(pistonrings)
attach(pistonrings)
diameter <- qcc.groups(diameter, sample)

q <- cusum(diameter[1:25,], decision.interval = 4, se.shift = 1)
summary(q)

q <- cusum(diameter[1:25,], newdata=diameter[26:40,])
summary(q)
plot(q, chart.all=FALSE)

detach(pistonrings)