# Multivariate Quality Control Charts Create an object of class 'mqcc' to perform multivariate statistical quality control. ```r 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. ## Returns Returns an object of class 'mqcc'. ## 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. ## Author(s) Luca Scrucca ## See Also `stats.T2`, `stats.T2.single`, `limits.T2`, `limits.T2.single`, `ellipseChart`, `qcc` ## Examples ```r ## ## 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) ```

mqcc function