Multivariate Quality Control Charts

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Description

Create an object of class 'mqcc' to perform multivariate statistical quality control.

Usage

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mqcc(data, type = c("T2", "T2.single"), center, cov,
     limits = TRUE, pred.limits = FALSE,
     data.name, labels, newdata, newlabels, 
     confidence.level = (1 - 0.0027)^p, rules = shewhart.rules,
     plot = TRUE, ...)

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

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

## S3 method for class 'mqcc'
plot(x, add.stats = TRUE, chart.all = TRUE,
     label.limits = c("LCL", "UCL"), label.pred.limits = c("LPL", "UPL"),
     title, xlab, ylab, ylim, axes.las = 0, 
     digits = getOption("digits"), restore.par = TRUE, ...)

Arguments

data

For subgrouped data a list with a data frame or a matrix for each variable to monitor. Each row of the data frame or matrix refers to a sample or ”rationale” group. For individual observations, where each sample has a single observation, users can provide a list with a data frame or a matrix having a single column, or a data frame or a matrix where each rows refer to samples and columns to variables. See examples.

type

a character string specifying the type of chart:

Chart description
"T2" Hotelling T^2 chart for subgrouped data
"T2.single" Hotelling T^2 chart for individual observations
center

a vector of values to use for center of input variables.

cov

a matrix of values to use for the covariance matrix of input variables.

limits

a logical indicating if control limits (Phase I) must be computed (by default using limits.T2 or limits.T2.single) and plotted, or a two-values vector specifying control limits.

pred.limits

a logical indicating if prediction limits (Phase II) must be computed (by default using limits.T2 or limits.T2.single) and plotted, or a two-values vector specifying prediction limits.

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.

newlabels

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

confidence.level

a numeric value between 0 and 1 specifying the confidence level of the computed probability limits. By default is set at (1 - 0.0027)^p where p is the number of variables, and 0.0027 is the probability of Type I error for a single Shewhart chart at the usual 3-sigma control level.

rules

a function of rules to apply to the chart. By default, the shewhart.rules function is used.

plot

logical. If TRUE a quality 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.limits

a character vector specifying the labels for control limits (Phase I).

label.pred.limits

a character vector specifying the labels for prediction control limits (Phase II).

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 when add.stats = TRUE.

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 'mqcc'.

x

an object of class 'mqcc'.

...

additional arguments to be passed to the generic function.

Value

Returns an object of class 'mqcc'.

Author(s)

Luca Scrucca luca@stat.unipg.it

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

stats.T2, stats.T2.single, limits.T2, limits.T2.single, ellipseChart, qcc

Examples

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##
##  Subgrouped data
##

# Ryan (2000, Table 9.2) data with p = 2 variables, m = 20 samples, n = 4 sample size:
X1 = matrix(c(72, 56, 55, 44, 97, 83, 47, 88, 57, 26, 46, 
49, 71, 71, 67, 55, 49, 72, 61, 35, 84, 87, 73, 80, 26, 89, 66, 
50, 47, 39, 27, 62, 63, 58, 69, 63, 51, 80, 74, 38, 79, 33, 22, 
54, 48, 91, 53, 84, 41, 52, 63, 78, 82, 69, 70, 72, 55, 61, 62, 
41, 49, 42, 60, 74, 58, 62, 58, 69, 46, 48, 34, 87, 55, 70, 94, 
49, 76, 59, 57, 46), ncol = 4)
X2 = matrix(c(23, 14, 13, 9, 36, 30, 12, 31, 14, 7, 10, 
11, 22, 21, 18, 15, 13, 22, 19, 10, 30, 31, 22, 28, 10, 35, 18, 
11, 10, 11, 8, 20, 16, 19, 19, 16, 14, 28, 20, 11, 28, 8, 6, 
15, 14, 36, 14, 30, 8, 35, 19, 27, 31, 17, 18, 20, 16, 18, 16, 
13, 10, 9, 16, 25, 15, 18, 16, 19, 10, 30, 9, 31, 15, 20, 35, 
12, 26, 17, 14, 16), ncol = 4)
X = list(X1 = X1, X2 = X2)

q = mqcc(X, type = "T2")
summary(q)
ellipseChart(q)
ellipseChart(q, show.id = TRUE)

q = mqcc(X, type = "T2", pred.limits = TRUE)

# Ryan (2000) discussed Xbar-charts for single variables computed adjusting the 
# confidence level of the T^2 chart:
q1 = qcc(X1, type = "xbar", confidence.level = q$confidence.level^(1/2))
summary(q1)
q2 = qcc(X2, type = "xbar", confidence.level = q$confidence.level^(1/2))
summary(q2)


require(MASS)
# generate new "in control" data
Xnew = list(X1 = matrix(NA, 10, 4), X2 =  matrix(NA, 10, 4))
for(i in 1:4)
   { x = mvrnorm(10, mu = q$center, Sigma = q$cov)
     Xnew$X1[,i] = x[,1]
     Xnew$X2[,i] = x[,2] 
   }
qq = mqcc(X, type = "T2", newdata = Xnew, pred.limits = TRUE)
summary(qq)

# generate new "out of control" data
Xnew = list(X1 = matrix(NA, 10, 4), X2 =  matrix(NA, 10, 4))
for(i in 1:4)
   { x = mvrnorm(10, mu = 1.2*q$center, Sigma = q$cov)
     Xnew$X1[,i] = x[,1]
     Xnew$X2[,i] = x[,2] 
   }
qq = mqcc(X, type = "T2", newdata = Xnew, pred.limits = TRUE)
summary(qq)

##
## Individual observations data
##

data(boiler)

q = mqcc(boiler, type = "T2.single", confidence.level = 0.999)
summary(q)

# generate new "in control" data
boilerNew = mvrnorm(10, mu = q$center, Sigma = q$cov)
qq = mqcc(boiler, type = "T2.single", confidence.level = 0.999, 
          newdata = boilerNew, pred.limits = TRUE)
summary(qq)

# generate new "out of control" data
boilerNew = mvrnorm(10, mu = 1.01*q$center, Sigma = q$cov)
qq = mqcc(boiler, type = "T2.single", confidence.level = 0.999, 
          newdata = boilerNew, pred.limits = TRUE)
summary(qq)

# provides "robust" estimates of means and covariance matrix
library(MASS)
rob = cov.rob(boiler)
qrob = mqcc(boiler, type = "T2.single", center = rob$center, cov = rob$cov)
summary(qrob)

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