mqcc: Multivariate Quality Control Charts

Description

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

Usage

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, ...)
"print"(x, ...)
"summary"(object, digits = getOption("digits"), ...)
"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'.

...

additional arguments to be passed to the generic function.

Value

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.

Examples

Run this code

##
##  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)

Run the code above in your browser using DataCamp Workspace