Package 'qcc' reference manual

Title:	Quality Control Charts
Description:	Shewhart quality control charts for continuous, attribute and count data. Cusum and EWMA charts. Operating characteristic curves. Process capability analysis. Pareto chart and cause-and-effect chart. Multivariate control charts.
Authors:	Luca Scrucca [aut, cre] , Greg Snow [ctb], Peter Bloomfield [ctb]
Maintainer:	Luca Scrucca <[email protected]>
License:	GPL (>= 2)
Version:	3.0
Built:	2025-02-01 05:29:43 UTC
Source:	https://github.com/luca-scr/qcc

Quality Control Charts

Description

Shewhart quality control charts for continuous, attribute and count data. Cusum and EWMA charts. Operating characteristic curves. Process capability analysis. Pareto chart and cause-and-effect chart. Multivariate control charts.

Details

See vignette and documentation accompanying the package.

Author(s)

Luca Scrucca

References

Scrucca, L. (2004). qcc: an R package for quality control charting and statistical process control. R News 4/1, 11-17.

Water content of antifreeze data

Description

Water content (in ppm) of batches of antifreeze.

Usage

data(antifreeze)data(antifreeze)

Format

A data frame with observations on 34 successive batches of antifreeze:

water: water content (in ppm)

References

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall, p. 120

Examples

data(antifreeze)
describe(antifreeze)
data(antifreeze)
describe(antifreeze)

Boiler temperature data

Description

Temperature readings from the eight configured burners on a boiler.

Usage

data(boiler)data(boiler)

Format

A data frame with 25 observations on the following 8 variables:

t1: temperature reading 1
t2: temperature reading 2
t3: temperature reading 3
t4: temperature reading 4
t5: temperature reading 5
t6: temperature reading 6
t7: temperature reading 7
t8: temperature reading 8

References

Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM, p. 86.

Examples

data(boiler)
describe(boiler)
boxplot(boiler)
data(boiler)
describe(boiler)
boxplot(boiler)

Cause and Effect Diagram

Description

Draw a basic cause and effect diagram.

Usage

causeEffectDiagram(cause, effect, title,
                   cex = c(1, 0.9, 1), 
                   font = c(1, 3, 2))
causeEffectDiagram(cause, effect, title,
                   cex = c(1, 0.9, 1), 
                   font = c(1, 3, 2))

Arguments

`cause`	a list of causes and branches providing descriptive labels (see the example below).
`effect`	a string label or the effect.
`title`	a character string specifying the main title. Set `title = NULL` to remove the title.
`cex`	a vector of values for the graphical character expansion. The values refer, in order, to branches, causes and effect.
`font`	a vector of values for the font to use. The values refer, in order, to branches, causes and effect.

Author(s)

Luca Scrucca

References

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

Examples

causeEffectDiagram(cause = list(Measurements = c("Micrometers", 
                                                 "Microscopes", 
                                                 "Inspectors"),
                                Materials = c("Alloys", 
                                              "Lubricants", 
                                              "Suppliers"),
                                Personnel = c("Shifts", 
                                              "Supervisors", 
                                              "Training", 
                                              "Operators"),
                                Environment = c("Condensation", 
                                                "Moisture"),
                                Methods = c("Brake",
                                            "Engager", 
                                            "Angle"),
                                Machines = c("Speed", 
                                             "Lathes", 
                                             "Bits", 
                                             "Sockets")),
                   effect = "Surface Flaws")
causeEffectDiagram(cause = list(Measurements = c("Micrometers", 
                                                 "Microscopes", 
                                                 "Inspectors"),
                                Materials = c("Alloys", 
                                              "Lubricants", 
                                              "Suppliers"),
                                Personnel = c("Shifts", 
                                              "Supervisors", 
                                              "Training", 
                                              "Operators"),
                                Environment = c("Condensation", 
                                                "Moisture"),
                                Methods = c("Brake",
                                            "Engager", 
                                            "Angle"),
                                Machines = c("Speed", 
                                             "Lathes", 
                                             "Bits", 
                                             "Sockets")),
                   effect = "Surface Flaws")

Circuit boards data

Description

Number of nonconformities observed in 26 successive samples of 100 printed circuit boards. Sample 6 and 20 are outside the control limits. Sample 6 was examined by a new inspector and he did not recognize several type of nonconformities that could have been present. Furthermore, the unusually large number of nonconformities in sample 20 resulted from a temperature control problem in the wave soldering machine, which was subsequently repaired. The last 20 samples are further samples collected on inspection units (each formed by 100 boards).

Usage

data(circuit)data(circuit)

Format

A data frame with 46 observations on the following 4 variables.

sample: sample number
x: number of defectives in 100 printed circuit boards (inspection unit)
size: sample size
trial: trial sample indicator (TRUE/FALSE)

References

Montgomery, D.C. (1991) Introduction to Statistical Quality Control, 2nd ed, New York, John Wiley & Sons, pp. 173–175

Examples

data(circuit)
describe(circuit, by = trial)
boxplot(x/size ~ trial, data = circuit)
plot(x/size ~ sample, data = circuit, type="b")
data(circuit)
describe(circuit, by = trial)
boxplot(x/size ~ trial, data = circuit)
plot(x/size ~ sample, data = circuit, type="b")

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, 
      decision.interval = 5, se.shift = 1,
      head.start = 0,
      newdata, newsizes, ...)

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

## S3 method for class 'cusum.qcc'
plot(x, 
     xtime = NULL,
     add.stats = qcc.options("add.stats"), 
     chart.all = qcc.options("chart.all"), 
     fill = qcc.options("fill"),
     label.bounds = c("LDB", "UDB"),
     title, xlab, ylab, xlim, ylim, 
     digits =  getOption("digits"), ...)
cusum(data, sizes, center, std.dev, 
      decision.interval = 5, se.shift = 1,
      head.start = 0,
      newdata, newsizes, ...)

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

## S3 method for class 'cusum.qcc'
plot(x, 
     xtime = NULL,
     add.stats = qcc.options("add.stats"), 
     chart.all = qcc.options("chart.all"), 
     fill = qcc.options("fill"),
     label.bounds = c("LDB", "UDB"),
     title, xlab, ylab, xlim, ylim, 
     digits =  getOption("digits"), ...)

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.
`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.
`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.
`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.
`xtime`	a vector of date-time values as returned by `Sys.time` and `Sys.Date`. If provided it is used for x-axis so it must be of the same length as the statistic charted.
`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.
`fill`	a logical value specifying if the in-control area should be filled with the color specified in `qcc.options("zones")$fill`.
`label.bounds`	a character vector specifying the labels for the the decision interval boundaries.
`title`	a character string specifying the main title. Set `title = NULL` to remove the title.
`xlab`, `ylab`	a string giving the label for the x-axis and the y-axis.
`xlim`, `ylim`	a numeric vector specifying the limits for the x-axis and the y-axis.
`digits`	the number of significant digits to use.
`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. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Ryan, T. P. (2011), Statistical Methods for Quality Improvement, 3rd 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

##
## Grouped-data
##
data(pistonrings)
diameter <- qccGroups(data = pistonrings, diameter, sample)

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

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

##
## Individual observations
##
data(viscosity)
q <- with(viscosity, cusum(viscosity[trial], newdata = viscosity[!trial]))
plot(q)
##
## Grouped-data
##
data(pistonrings)
diameter <- qccGroups(data = pistonrings, diameter, sample)

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

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

##
## Individual observations
##
data(viscosity)
q <- with(viscosity, cusum(viscosity[trial], newdata = viscosity[!trial]))
plot(q)

Descriptive statistics

Description

Compute and print descriptive statistics for a matrix or data frame, eventually conditioning on another variable.

Usage

describe(data, by, detailed = FALSE, ...)
## S3 method for class 'describe'
print(x, digits = getOption("digits") - 3, ...)
describe(data, by, detailed = FALSE, ...)
## S3 method for class 'describe'
print(x, digits = getOption("digits") - 3, ...)

Arguments

`data`	a matrix or data frame.
`by`	a factor or character vector specifying the conditioning variable. This may be a variable included in `data` or an object defined in the current environment.
`detailed`	a logical specifying if detailed statistics should be provided.
`...`	additional arguments to be passed to the generic function.
`x`	an object of class `'describe'`.
`digits`	the number of significant digits to use.

Details

This function provides simple descriptive statistics for different types of variables, such as numeric, factor, and logical, conditioning or not on another variable.

Author(s)

Luca Scrucca

Examples

data(warpbreaks)
describe(warpbreaks)
describe(warpbreaks, detail = TRUE)
describe(warpbreaks, by = wool)
data(warpbreaks)
describe(warpbreaks)
describe(warpbreaks, detail = TRUE)
describe(warpbreaks, by = wool)

Dyed cloth data

Description

In a textile finishing plant, dyed cloth is inspected for the occurrence of defects per 50 square meters. The data on ten rolls of cloth are presented.

Usage

data(dyedcloth)data(dyedcloth)

Format

A data frame with 10 observations on the following 2 variables.

x: number of nonconformities per 50 square meters (inspection units)
size: number of inspection units in roll (variable sample size)

References

Montgomery, D.C. (1991) Introduction to Statistical Quality Control, 2nd ed, New York, John Wiley & Sons, pp. 183–184

Examples

data(dyedcloth)
describe(dyedcloth)
dyedcloth <- transform(dyedcloth, sample = seq(nrow(dyedcloth)))
plot(x/size ~ sample, data = dyedcloth, type="b")
data(dyedcloth)
describe(dyedcloth)
dyedcloth <- transform(dyedcloth, sample = seq(nrow(dyedcloth)))
plot(x/size ~ sample, data = dyedcloth, type="b")

Multivariate Quality Control Charts

Description

Plot an ellipse chart for a bivariate quality control data.

Usage

ellipseChart(object, chart.all = TRUE, show.id = FALSE, ngrid = 50,
             confidence.level, correct.multiple = TRUE, 
             title, xlim, ylim, xlab, ylab,
             restore.par = TRUE, ...)
ellipseChart(object, chart.all = TRUE, show.id = FALSE, ngrid = 50,
             confidence.level, correct.multiple = TRUE, 
             title, xlim, ylim, xlab, ylab,
             restore.par = TRUE, ...)

Arguments

`object`	an object of class `'mqcc'`.
`chart.all`	a logical value indicating whether both statistics for `data` and for `newdata` (if given) should be plotted.
`show.id`	a logical value indicating whether to plot point labels (`TRUE`) or symbols (`FALSE`) for group means.
`ngrid`	a value for the size of the grid over which the ellipse is evaluated.
`confidence.level`	a numeric value between 0 and 1 specifying the confidence level of the computed probability limits.
`correct.multiple`	a logical value indicating whether to correct or not for multiple comparisons.
`title`	a character string specifying the main title. Set `title = FALSE` or `title = NA` to remove the title.
`xlim`	a numeric vector specifying the limits for the x-axis.
`ylim`	a numeric vector specifying the limits for the y-axis.
`xlab`	a string giving the label for the x-axis.
`ylab`	a string giving the label for the y-axis.
`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`.
`...`	additional arguments to be passed to the generic `points` function.

Author(s)

Luca Scrucca

References

Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Ryan, T. P. (2011), Statistical Methods for Quality Improvement, 3rd ed. New York: John Wiley & Sons, Inc.

Examples

# See examples in help(mqcc)
# See examples in help(mqcc)

EWMA chart

Description

Create an object of class 'ewma.qcc' to compute and draw an Exponential Weighted Moving Average (EWMA) chart for statistical quality control.

Usage

ewma(data, sizes, center, std.dev, 
     lambda = 0.2, nsigmas = 3, 
     newdata, newsizes, ...)

## S3 method for class 'ewma.qcc'
print(x, digits = getOption("digits"), ...)

## S3 method for class 'ewma.qcc'
plot(x, 
     xtime, 
     add.stats = qcc.options("add.stats"), 
     chart.all = qcc.options("chart.all"), 
     fill = qcc.options("fill"),
     label.center = "CL",
     label.limits = c("LCL", "UCL"), 
     title, xlab, ylab, xlim, ylim, 
     digits = getOption("digits"), ...)
ewma(data, sizes, center, std.dev, 
     lambda = 0.2, nsigmas = 3, 
     newdata, newsizes, ...)

## S3 method for class 'ewma.qcc'
print(x, digits = getOption("digits"), ...)

## S3 method for class 'ewma.qcc'
plot(x, 
     xtime, 
     add.stats = qcc.options("add.stats"), 
     chart.all = qcc.options("chart.all"), 
     fill = qcc.options("fill"),
     label.center = "CL",
     label.limits = c("LCL", "UCL"), 
     title, xlab, ylab, xlim, ylim, 
     digits = getOption("digits"), ...)

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 target.
`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.
`lambda`	the smoothing parameter $0 \le \lambda \le 1$
`nsigmas`	a numeric value specifying the number of sigmas to use for computing control limits.
`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.
`xtime`	a vector of date-time values as returned by `Sys.time` and `Sys.Date`. If provided it is used for x-axis so it must be of the same length as the statistic charted.
`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.
`fill`	a logical value specifying if the in-control area should be filled with the color specified in `qcc.options("zones")$fill`.
`label.center`	a character specifying the label for center line.
`label.limits`	a character vector specifying the labels for control limits.
`title`	a character string specifying the main title. Set `title = NULL` to remove the title.
`xlab`, `ylab`	a string giving the label for the x-axis and the y-axis.
`xlim`, `ylim`	a numeric vector specifying the limits for the x-axis and the y-axis.
`digits`	the number of significant digits to use.
`x`	an object of class 'ewma.qcc'.
`...`	additional arguments to be passed to the generic function.

Details

EWMA chart smooths a series of data based on a moving average with weights which decay exponentially. Useful to detect small and permanent variation on the mean of the process.

Value

Returns an object of class 'ewma.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. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Ryan, T. P. (2011), Statistical Methods for Quality Improvement, 3rd 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

##
## Grouped-data
##
data(pistonrings)
diameter <- qccGroups(data = pistonrings, diameter, sample)

q = ewma(diameter[1:25,], lambda=0.2, nsigmas=3)
summary(q)
plot(q)

ewma(diameter[1:25,], lambda=0.2, nsigmas=2.7, newdata=diameter[26:40,]) 

##
## Individual observations
##
data(viscosity)
with(viscosity, 
     ewma(viscosity[trial], lambda = 0.2, nsigmas = 2.7,
          newdata = viscosity[!trial]))
##
## Grouped-data
##
data(pistonrings)
diameter <- qccGroups(data = pistonrings, diameter, sample)

q = ewma(diameter[1:25,], lambda=0.2, nsigmas=3)
summary(q)
plot(q)

ewma(diameter[1:25,], lambda=0.2, nsigmas=2.7, newdata=diameter[26:40,]) 

##
## Individual observations
##
data(viscosity)
with(viscosity, 
     ewma(viscosity[trial], lambda = 0.2, nsigmas = 2.7,
          newdata = viscosity[!trial]))

EWMA smoothing function

Description

Compute Exponential Weighted Moving Average.

Usage

ewmaSmooth(x, y, lambda = 0.2, start, ...)
ewmaSmooth(x, y, lambda = 0.2, start, ...)

Arguments

`x`	a vector of x-values.
`y`	a vector of y-values.
`lambda`	the smoothing parameter.
`start`	the starting value.
`...`	additional arguments (currently not used).

Details

EWMA function smooths a series of data based on a moving average with weights which decay exponentially.

For each $y_t$ value the smoothed value is computed as

$z_t = \lambda y_t + (1-\lambda) z_{t-1}$

where $0 \le \lambda \le 1$ is the parameter which controls the weights applied.

Value

Returns a list with elements:

`x`	ordered x-values
`y`	smoothed y-values
`lambda`	the smoothing parameter
`start`	the starting value

Author(s)

Luca Scrucca

References

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

Examples

x <- 1:50
y <- rnorm(50, sin(x/5), 0.5)
plot(x,y)
lines(ewmaSmooth(x,y,lambda=0.1), col="red")
x <- 1:50
y <- rnorm(50, sin(x/5), 0.5)
plot(x,y)
lines(ewmaSmooth(x,y,lambda=0.1), col="red")

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,
     plot = TRUE, ...)

## S3 method for class 'mqcc'
print(x, digits = getOption("digits"), ...)

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

## S3 method for class 'mqcc'
print(x, digits = getOption("digits"), ...)

## S3 method for class 'mqcc'
plot(x, 
     add.stats = qcc.options("add.stats"), 
     chart.all = qcc.options("chart.all"), 
     fill = qcc.options("fill"),
     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.

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.

fill

a logical value specifying if the in-control area should be filled with the color specified in qcc.options("zones")$fill.

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 character string specifying the main title. Set title = FALSE or title = NA to remove the 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.

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

References

Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Ryan, T. P. (2011), Statistical Methods for Quality Improvement, 3rd 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

##
##  Subgrouped data
##

data(RyanMultivar)
str(RyanMultivar)

q <- mqcc(RyanMultivar, type = "T2")
summary(q)
ellipseChart(q)
ellipseChart(q, show.id = TRUE)
q <- mqcc(RyanMultivar, type = "T2", pred.limits = TRUE)

# Xbar-charts for single variables computed adjusting the 
# confidence level of the T^2 chart:
q1 <- with(RyanMultivar, 
           qcc(X1, type = "xbar", confidence.level = q$confidence.level^(1/2)))
summary(q1)
q2 <- with(RyanMultivar,
           qcc(X2, type = "xbar", confidence.level = q$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(RyanMultivar, 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(RyanMultivar, type = "T2", newdata = Xnew, pred.limits = TRUE)
summary(qq)

##
## Individual observations data
##

data(boiler)
str(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
rob <- cov.rob(boiler)
qrob <- mqcc(boiler, type = "T2.single", center = rob$center, cov = rob$cov)
summary(qrob)
##
##  Subgrouped data
##

data(RyanMultivar)
str(RyanMultivar)

q <- mqcc(RyanMultivar, type = "T2")
summary(q)
ellipseChart(q)
ellipseChart(q, show.id = TRUE)
q <- mqcc(RyanMultivar, type = "T2", pred.limits = TRUE)

# Xbar-charts for single variables computed adjusting the 
# confidence level of the T^2 chart:
q1 <- with(RyanMultivar, 
           qcc(X1, type = "xbar", confidence.level = q$confidence.level^(1/2)))
summary(q1)
q2 <- with(RyanMultivar,
           qcc(X2, type = "xbar", confidence.level = q$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(RyanMultivar, 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(RyanMultivar, type = "T2", newdata = Xnew, pred.limits = TRUE)
summary(qq)

##
## Individual observations data
##

data(boiler)
str(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
rob <- cov.rob(boiler)
qrob <- mqcc(boiler, type = "T2.single", center = rob$center, cov = rob$cov)
summary(qrob)

Operating Characteristic Function

Description

Draws the operating characteristic curves for a 'qcc' object.

Usage

ocCurves(object, ...)

ocCurves.xbar(object, 
              size = c(1, 5, 10, 15, 20), 
              shift = seq(0, 5, by = 0.1),
              nsigmas = object$nsigmas, ...)

ocCurves.R(object, 
           size = c(2, 5, 10, 15, 20), 
           multiplier = seq(1, 6, by = 0.1),
           nsigmas = object$nsigmas, ...)

ocCurves.S(object, 
           size = c(2, 5, 10, 15, 20), 
           multiplier = seq(1, 6, by = 0.1),
           nsigmas = object$nsigmas, ...) 

ocCurves.p(object, ...)

ocCurves.c(object, ...)
					 
## S3 method for class 'ocCurves'
print(x, digits = getOption("digits"), ...)

## S3 method for class 'ocCurves'
plot(x, what = c("beta", "ARL"), 
     title, xlab, ylab, lty, lwd, col, ...)				 
ocCurves(object, ...)

ocCurves.xbar(object, 
              size = c(1, 5, 10, 15, 20), 
              shift = seq(0, 5, by = 0.1),
              nsigmas = object$nsigmas, ...)

ocCurves.R(object, 
           size = c(2, 5, 10, 15, 20), 
           multiplier = seq(1, 6, by = 0.1),
           nsigmas = object$nsigmas, ...)

ocCurves.S(object, 
           size = c(2, 5, 10, 15, 20), 
           multiplier = seq(1, 6, by = 0.1),
           nsigmas = object$nsigmas, ...) 

ocCurves.p(object, ...)

ocCurves.c(object, ...)
					 
## S3 method for class 'ocCurves'
print(x, digits = getOption("digits"), ...)

## S3 method for class 'ocCurves'
plot(x, what = c("beta", "ARL"), 
     title, xlab, ylab, lty, lwd, col, ...)

Arguments

`object`	an object of class `'qcc'`.
`size`	a vector of values specifying the sample sizes for which to draw the OC curves.
`shift`, `multiplier`	a vector of values specifying the shift or multiplier values (in units of sigma).
`nsigmas`	a numeric value specifying the number of sigmas to use for computing control limits; if `nsigmas` is `NULL`, `object$conf` is used to set up probability limits.
`x`	an object of class `'ocCurves'`.
`digits`	the number of significant digits to use.
`what`	a string specifying the quantity to plot on the y-axis. Possible values are `"beta"` for the probability of not detecting a shift, and `"ARL"` for the average run length.
`title`	a character string specifying the main title. Set `title = NULL` to remove the title.
`xlab`, `ylab`	a string giving the label for the x-axis and the y-axis.
`lty`, `lwd`, `col`	values or vector of values controlling the line type, line width and colour of curves.
`...`	catches further ignored arguments.

Details

An operating characteristic curve graphically provides information about the probability of not detecting a shift in the process. ocCurves is a generic function which calls the proper function depending on the type of 'qcc' object. Further arguments provided through ... are passed to the specific function depending on the type of chart.

The probabilities are based on the conventional assumptions about process distributions: the normal distribution for "xbar", "R", and "S", the binomial distribution for "p" and "np", and the Poisson distribution for "c" and "u". They are all sensitive to departures from those assumptions, but to varying degrees. The performance of the "S" chart, and especially the "R" chart, are likely to be seriously affected by longer tails.

Value

The function returns an object of class 'ocCurves' which contains a matrix or a vector of beta values (the probability of type II error) and ARL (average run length).

Author(s)

Luca Scrucca

References

Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Ryan, T. P. (2011), Statistical Methods for Quality Improvement, 3rd 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

data(pistonrings)
diameter <- qccGroups(diameter, sample, data = pistonrings)
oc <- ocCurves.xbar(qcc(diameter, type="xbar", nsigmas=3))
oc
plot(oc)

data(orangejuice)
oc <- with(orangejuice,
           ocCurves(qcc(D[trial], sizes=size[trial], type="p")))
oc
plot(oc)

data(circuit)
oc <- with(circuit,
           ocCurves(qcc(x[trial], sizes=size[trial], type="c")))
oc
plot(oc)
data(pistonrings)
diameter <- qccGroups(diameter, sample, data = pistonrings)
oc <- ocCurves.xbar(qcc(diameter, type="xbar", nsigmas=3))
oc
plot(oc)

data(orangejuice)
oc <- with(orangejuice,
           ocCurves(qcc(D[trial], sizes=size[trial], type="p")))
oc
plot(oc)

data(circuit)
oc <- with(circuit,
           ocCurves(qcc(x[trial], sizes=size[trial], type="c")))
oc
plot(oc)

Orange juice data

Description

Frozen orange juice concentrate is packed in 6-oz cardboard cans. These cans are formed on a machine by spinning them from cardboard stock and attaching a metal bottom panel. A can is then inspected to determine whether, when filled, the liquid could possible leak either on the side seam or around the bottom joint. If this occurs, a can is considered nonconforming. The data were collected as 30 samples of 50 cans each at half-hour intervals over a three-shift period in which the machine was in continuous operation. From sample 15 used a new batch of cardboard stock was punt into production. Sample 23 was obtained when an inexperienced operator was temporarily assigned to the machine. After the first 30 samples, a machine adjustment was made. Then further 24 samples were taken from the process.

Usage

data(orangejuice)data(orangejuice)

Format

A data frame with 54 observations on the following 4 variables:

sample: sample id
D: number of defectives
size: sample sizes
trial: trial samples (TRUE/FALSE)

References

Montgomery, D.C. (1991) Introduction to Statistical Quality Control, 2nd ed, New York, John Wiley & Sons, pp. 152–155.

Examples

data(orangejuice)
orangejuice <- transform(orangejuice, d = D/size)
describe(orangejuice, by = trial)
boxplot(d ~ trial, data = orangejuice)
plot(d ~ sample, data = orangejuice, type = "b", pch = ifelse(trial, 1, 19))
data(orangejuice)
orangejuice <- transform(orangejuice, d = D/size)
describe(orangejuice, by = trial)
boxplot(d ~ trial, data = orangejuice)
plot(d ~ sample, data = orangejuice, type = "b", pch = ifelse(trial, 1, 19))

Orange juice data – Part 2

Description

A full description of the problem is given in orangejuice.

This dataset contains samples taken after the machine adjustment was made.

Usage

data(orangejuice)data(orangejuice)

Format

A data frame with 64 observations on the following 4 variables:

sample: sample id
D: number of defectives
size: sample sizes
trial: trial samples (TRUE/FALSE)

References

Montgomery, D.C. (1991) Introduction to Statistical Quality Control, 2nd ed, New York, John Wiley & Sons, pp. 155–159.

Examples

data(orangejuice2)
orangejuice2 <- transform(orangejuice2, d = D/size)
describe(orangejuice2, by = trial)
boxplot(d ~ trial, data = orangejuice2)
plot(d ~ sample, data = orangejuice2, type = "b", pch = ifelse(trial, 1, 19))
data(orangejuice2)
orangejuice2 <- transform(orangejuice2, d = D/size)
describe(orangejuice2, by = trial)
boxplot(d ~ trial, data = orangejuice2)
plot(d ~ sample, data = orangejuice2, type = "b", pch = ifelse(trial, 1, 19))

Pareto chart

Description

Computes a table of statistics and plot a Pareto chart.

Usage

paretoChart(data, ...)

## S3 method for class 'paretoChart'
plot(x, title, xlab, 
     ylab = "Frequency", ylab2 = "Cumulative percentage", 
     ylim, col = blues.colors(nlevels), ...) 
paretoChart(data, ...)

## S3 method for class 'paretoChart'
plot(x, title, xlab, 
     ylab = "Frequency", ylab2 = "Cumulative percentage", 
     ylim, col = blues.colors(nlevels), ...)

Arguments

`data`	a vector of values. `names(data)` are used for labelling the bars.
`plot`	a logical specifying if the chart should be provided (`TRUE`, default).
`x`	an object of class `'paretoChart'` returned by a call to `paretoChart()` function.
`title`	a character string specifying the main title. Set `title = NULL` to remove the title.
`xlab`	a string specifying the label for the x-axis.
`ylab`	a string specifying the label for the y-axis.
`ylab2`	a string specifying the label for the second y-axis on the right side.
`ylim`	a numeric vector specifying the limits for the y-axis.
`col`	a value for the color, a vector of colors, or a palette for the bars. See the help for `colors` and `palette`.
`...`	catch other optional arguments.

Details

A Pareto chart is a barplot where the categories are ordered in non increasing order, and a line is also added to show the cumulative sum.

Value

Returns an object of class 'paretoChart' containing the descriptive statistics used to draw the Pareto chart. This object has associated a print and plot method.

Author(s)

Luca Scrucca

References

Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Ryan, T. P. (2011), Statistical Methods for Quality Improvement, 3rd 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

defect <- c(80, 27, 66, 94, 33)
names(defect) <- c("price code", "schedule date", "supplier code", "contact num.", "part num.")
pc = paretoChart(defect, ylab = "Error frequency")
pc
plot(pc)

plot(paretoChart(defect, ylab = "Error frequency"), col=rainbow(length(defect)))
defect <- c(80, 27, 66, 94, 33)
names(defect) <- c("price code", "schedule date", "supplier code", "contact num.", "part num.")
pc = paretoChart(defect, ylab = "Error frequency")
pc
plot(pc)

plot(paretoChart(defect, ylab = "Error frequency"), col=rainbow(length(defect)))

Personal computer manufacturer data

Description

A personal computer manufacturer counts the number of nonconformities per unit on the final assembly line. He collects data on 20 samples of 5 computers each.

Usage

data(pcmanufact)data(pcmanufact)

Format

A data frame with 10 observations on the following 2 variables.

x: number of nonconformities (inspection units)
size: number of computers inspected

References

Montgomery, D.C. (1991) Introduction to Statistical Quality Control, 2nd ed, New York, John Wiley & Sons, pp. 181–182

Examples

data(pcmanufact)
describe(pcmanufact)
pcmanufact <- transform(pcmanufact, sample = seq(nrow(pcmanufact)))
plot(x/size ~ sample, data = pcmanufact, type="b")
data(pcmanufact)
describe(pcmanufact)
pcmanufact <- transform(pcmanufact, sample = seq(nrow(pcmanufact)))
plot(x/size ~ sample, data = pcmanufact, type="b")

Piston rings data

Description

Piston rings for an automotive engine are produced by a forging process. The inside diameter of the rings manufactured by the process is measured on 25 samples, each of size 5, for the control phase I, when preliminary samples from a process being considered 'in control' are used to construct control charts. Then, further 15 samples, again each of size 5, are obtained for phase II.

Usage

data(pistonrings)data(pistonrings)

Format

A data frame with 200 observations on the following 3 variables.

diameter: a numeric vector
sample: sample ID
trial: preliminary sample indicator (TRUE/FALSE)

References

Montgomery, D.C. (1991) Introduction to Statistical Quality Control, 2nd ed, New York, John Wiley & Sons, pp. 206–213

Examples

data(pistonrings)
describe(pistonrings, by = trial)
boxplot(diameter ~ trial, data = pistonrings)
plot(diameter ~ sample, data = pistonrings, cex=0.7)
with(pistonrings, lines(tapply(diameter,sample,mean)))
data(pistonrings)
describe(pistonrings, by = trial)
boxplot(diameter ~ trial, data = pistonrings)
plot(diameter ~ sample, data = pistonrings, cex=0.7)
with(pistonrings, lines(tapply(diameter,sample,mean)))

Process capability analysis

Description

Computes process capability indices for a 'qcc' object of type "xbar" and plot the histogram.

Usage

processCapability(object, spec.limits, target, 
                  std.dev, nsigmas, 
                  confidence.level = 0.95,  ...)
                   
## S3 method for class 'processCapability'
print(x, digits = getOption("digits"), ...)

## S3 method for class 'processCapability'
plot(x, 
     add.stats = qcc.options("add.stats"), 
     breaks = nclass.scott, 
     fill = adjustcolor(qcc.options("zones")$fill, alpha.f = 0.5),
     color = "white", title, xlab, 
     digits = getOption("digits"), ...)
processCapability(object, spec.limits, target, 
                  std.dev, nsigmas, 
                  confidence.level = 0.95,  ...)
                   
## S3 method for class 'processCapability'
print(x, digits = getOption("digits"), ...)

## S3 method for class 'processCapability'
plot(x, 
     add.stats = qcc.options("add.stats"), 
     breaks = nclass.scott, 
     fill = adjustcolor(qcc.options("zones")$fill, alpha.f = 0.5),
     color = "white", title, xlab, 
     digits = getOption("digits"), ...)

Arguments

`object`	a `'qcc'` object of type `"xbar"`
`spec.limits`	a two-values vector specifying the lower and upper specification limits. For one-sided specification limits, the value of the missing limit must be set to `NA`.
`target`	a value specifying the target of the process. If missing the value from the `'qcc'` object is used if not `NULL`, otherwise the target is set at the middle value between specification limits.
`std.dev`	a value specifying the within-group standard deviation. If not provided is taken from the `'qcc'` object.
`nsigmas`	a numeric value specifying the number of sigmas to use. If not provided is taken from the `'qcc'` object.
`confidence.level`	a numeric value between 0 and 1 specifying the level to use for computing confidence intervals.
`x`	an object of class 'processCapability'.
`add.stats`	a logical value indicating whether statistics and capability indices should be added at the bottom of the chart.
`breaks`	a value or a function used to select the number of bins in a histogram. See the help for `nclass.scott` for more details.
`fill`, `color`	values specifying the colour of the filled area and the border used for drawing the histogram.
`title`	a character string specifying the plot title. Set `title = NULL` to remove the title.
`xlab`	a character string specifying the label for the x-axis.
`digits`	the number of significant digits to use.
`...`	catches further ignored arguments.

Details

This function calculates confidence limits for $C_p$ using the method described by Chou et al. (1990). Approximate confidence limits for $C_{pl}$ , $C_{pu}$ and $C_{pk}$ are computed using the method in Bissell (1990). Confidence limits for $C_{pm}$ are based on the method of Boyles (1991); this method is approximate and it assumes that the target is midway between the specification limits.

Value

Invisibly returns a list with components:

`nobs`	number of observations
`center`	center
`std.dev`	standard deviation
`target`	target
`spec.limits`	a vector of values giving the lower specification limit (LSL) and the upper specification limit (USL)
`indices`	a matrix of capability indices ( $C_p$ , $C_{pl}$ , $C_{pu}$ , $C_{pk}$ , $C_{pm}$ ) and the corresponding confidence limits.
`exp`	a vector of values giving the expected fraction, based on a normal approximation, of the observations less than LSL and greater than USL.
`obs`	a vector of values giving the fraction of observations less than LSL and greater than USL.

Author(s)

Luca Scrucca

References

Bissell, A.F. (1990) How reliable is your capability index?, Applied Statistics, 39, 331-340.

Boyles, R.A. (1991) The Taguchi capability index, Journal of Quality Technology, 23, 107-126.

Chou, Y., Owen D.B. and Borrego S.A. (1990) Lower Confidence Limits on Process Capability Indices, Journal of Quality Technology, 22, 223-229.

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

Examples

data(pistonrings)
diameter <- qccGroups(data = pistonrings, diameter, sample)
q <- qcc(diameter[1:25,], type="xbar", nsigmas=3)
pc <- processCapability(q, spec.limits=c(73.95,74.05))
pc
plot(pc)
plot(processCapability(q, spec.limits=c(73.95,74.05), target=74.02))
plot(processCapability(q, spec.limits=c(73.99,74.01)))
plot(processCapability(q, spec.limits = c(73.99, 74.1)))
data(pistonrings)
diameter <- qccGroups(data = pistonrings, diameter, sample)
q <- qcc(diameter[1:25,], type="xbar", nsigmas=3)
pc <- processCapability(q, spec.limits=c(73.95,74.05))
pc
plot(pc)
plot(processCapability(q, spec.limits=c(73.95,74.05), target=74.02))
plot(processCapability(q, spec.limits=c(73.99,74.01)))
plot(processCapability(q, spec.limits = c(73.99, 74.1)))

Quality Control Charts

Description

Create an object of class 'qcc' to perform statistical quality control. This object may then be used to plot Shewhart charts, drawing OC curves, computes capability indices, and more.

Usage

qcc(data, 
    type = c("xbar", "R", "S", "xbar.one", "p", "np", "c", "u", "g"), 
    sizes, center, std.dev, limits,
    newdata, newsizes, 
    nsigmas = 3, confidence.level, 
    rules = c(1,4), ...)

## S3 method for class 'qcc'
print(x, digits = getOption("digits"), ...)

## S3 method for class 'qcc'
plot(x,
     xtime = NULL,
     add.stats = qcc.options("add.stats"), 
     chart.all = qcc.options("chart.all"), 
     fill = qcc.options("fill"),
     label.center = "CL",
     label.limits = c("LCL ", "UCL"),
     title, xlab, ylab, xlim, ylim,
     digits = getOption("digits"), ...)
qcc(data, 
    type = c("xbar", "R", "S", "xbar.one", "p", "np", "c", "u", "g"), 
    sizes, center, std.dev, limits,
    newdata, newsizes, 
    nsigmas = 3, confidence.level, 
    rules = c(1,4), ...)

## S3 method for class 'qcc'
print(x, digits = getOption("digits"), ...)

## S3 method for class 'qcc'
plot(x,
     xtime = NULL,
     add.stats = qcc.options("add.stats"), 
     chart.all = qcc.options("chart.all"), 
     fill = qcc.options("fill"),
     label.center = "CL",
     label.limits = c("LCL ", "UCL"),
     title, xlab, ylab, xlim, ylim,
     digits = getOption("digits"), ...)

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”.

type

a character string specifying the group statistics to compute.
Available methods are:

	Statistic charted	Chart description
`"xbar"`	mean	means of a continuous process variable
`"R"`	range	ranges of a continuous process variable
`"S"`	standard deviation	standard deviations of a continuous variable
`"xbar.one"`	mean	one-at-time data of a continuous process variable
`"p"`	proportion	proportion of nonconforming units
`"np"`	count	number of nonconforming units
`"c"`	count	nonconformities per unit
`"u"`	count	average nonconformities per unit
`"g"`	count	number of non-events between events

Furthermore, a user specified type of chart, say "newchart", can be provided. This requires the definition of "stats.newchart", "sd.newchart", and "limits.newchart". As an example, see stats.xbar.

sizes

a value or a vector of values specifying the sample sizes associated with each group. For continuous data provided as data frame or matrix the sample sizes are obtained counting the non-NA elements of each row. For "p", "np" and "u" charts the argument sizes is required.

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 in case of a continuous process variable; see sd.xbar, sd.xbar.one, sd.R, sd.S.

limits

a two-values vector specifying control limits.

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.

nsigmas

a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the confidence.level argument is provided.

confidence.level

a numeric value between 0 and 1 specifying the confidence level of the computed probability limits.

rules

a value or a vector of values specifying the rules to apply to the chart. See qccRules for possible values and their meaning.

xtime

a vector of date-time values as returned by Sys.time and Sys.Date. If provided it is used for x-axis so it must be of the same length as the statistic charted.

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.

fill

a logical value specifying if the in-control area should be filled with the color specified in qcc.options("zones")$fill.

label.center

a character specifying the label for center line.

label.limits

a character vector specifying the labels for control limits.

title

a character string specifying the main title. Set title = NULL to remove the title.

xlab, ylab

a string giving the label for the x-axis and the y-axis.

xlim, ylim

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

digits

the number of significant digits to use.

x

an object of class 'qcc'.

...

additional arguments to be passed to the generic function.

Value

Returns an object of class '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. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Ryan, T. P. (2011), Statistical Methods for Quality Improvement, 3rd 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

##
##  Continuous data 
##
data(pistonrings)
diameter <- qccGroups(data = pistonrings, diameter, sample)

(q <- qcc(diameter[1:25,], type="xbar"))
plot(q)

(q <- qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,]))
plot(q)

q <- qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,])
plot(q, chart.all=FALSE)

plot(qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], nsigmas=2))

plot(qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], confidence.level=0.99))

q <- qcc(diameter[1:25,], type="R")
q
plot(q)

plot(qcc(diameter[1:25,], type="R", newdata=diameter[26:40,]))

plot(qcc(diameter[1:25,], type="S"))

plot(qcc(diameter[1:25,], type="S", newdata=diameter[26:40,]))

plot(qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], rules = 1:4))

# variable control limits
out <- c(9, 10, 30, 35, 45, 64, 65, 74, 75, 85, 99, 100)
diameter <- qccGroups(data = pistonrings[-out,], diameter, sample)
plot(qcc(diameter[1:25,], type="xbar"))
plot(qcc(diameter[1:25,], type="R"))
plot(qcc(diameter[1:25,], type="S"))
plot(qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,]))
plot(qcc(diameter[1:25,], type="R", newdata=diameter[26:40,]))
plot(qcc(diameter[1:25,], type="S", newdata=diameter[26:40,]))

##
##  Attribute data 
##

data(orangejuice)

q <- with(orangejuice, 
          qcc(D[trial], sizes=size[trial], type="p"))
q
plot(q)

# remove out-of-control points (see help(orangejuice) for the reasons)
outofctrl <- c(15,23)
q1 <- with(orangejuice[-outofctrl,], 
           qcc(D[trial], sizes=size[trial], type="p"))
plot(q1)
q1 <- with(orangejuice[-outofctrl,], 
           qcc(D[trial], sizes=size[trial], type="p",
               newdata=D[!trial], newsizes=size[!trial]))
plot(q1)

data(orangejuice2)
q2 <- with(orangejuice2, 
           qcc(D[trial], sizes=size[trial], type="p"))
plot(q2)
q2 <- with(orangejuice2, 
           qcc(D[trial], sizes=size[trial], type="p", 
               newdata=D[!trial], newsizes=size[!trial]))
plot(q2)

data(circuit)
plot(with(circuit, qcc(x[trial], sizes=size[trial], type="c")))

# remove out-of-control points (see help(circuit) for the reasons)
outofctrl <- c(15,23)
q1 <- with(orangejuice[-outofctrl,], 
           qcc(D[trial], sizes=size[trial], type="p"))
plot(q1)
q1 <- with(orangejuice[-outofctrl,], 
           qcc(D[trial], sizes=size[trial], type="p",
               newdata=D[!trial], newsizes=size[!trial]))
plot(q1)

outofctrl <- c(6,20)
q1 <- with(circuit[-outofctrl,], 
           qcc(x[trial], sizes=size[trial], type="c"))
plot(q1)
q1 <- with(circuit[-outofctrl,], 
           qcc(x[trial], sizes=size[trial], type="c", 
               newdata = x[!trial], newsizes = size[!trial]))
plot(q1)
q1 <- with(circuit[-outofctrl,], 
           qcc(x[trial], sizes=size[trial], type="u", 
           newdata = x[!trial], newsizes = size[!trial]))
plot(q1)

data(pcmanufact)
q1 <- with(pcmanufact, qcc(x, sizes=size, type="u"))
q1
plot(q1)

data(dyedcloth)
# variable control limits
plot(with(dyedcloth, qcc(x, sizes=size, type="u")))
# standardized control chart
q <- with(dyedcloth, qcc(x, sizes=size, type="u"))
z <- (q$statistics - q$center)/sqrt(q$center/q$size)
plot(qcc(z, sizes = 1, type = "u", center = 0, std.dev = 1, limits = c(-3,3)),
     title = "Standardized u chart")
    
##
##  Continuous one-at-time data 
##

data(viscosity)
q <- with(viscosity, 
          qcc(viscosity[trial], type = "xbar.one"))
q
plot(q)
# batch 4 is out-of-control because of a process temperature controller
# failure; remove it and recompute
viscosity <- viscosity[-4,]
plot(with(viscosity, 
          qcc(viscosity[trial], type = "xbar.one", newdata = viscosity[!trial])))
##
##  Continuous data 
##
data(pistonrings)
diameter <- qccGroups(data = pistonrings, diameter, sample)

(q <- qcc(diameter[1:25,], type="xbar"))
plot(q)

(q <- qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,]))
plot(q)

q <- qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,])
plot(q, chart.all=FALSE)

plot(qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], nsigmas=2))

plot(qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], confidence.level=0.99))

q <- qcc(diameter[1:25,], type="R")
q
plot(q)

plot(qcc(diameter[1:25,], type="R", newdata=diameter[26:40,]))

plot(qcc(diameter[1:25,], type="S"))

plot(qcc(diameter[1:25,], type="S", newdata=diameter[26:40,]))

plot(qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], rules = 1:4))

# variable control limits
out <- c(9, 10, 30, 35, 45, 64, 65, 74, 75, 85, 99, 100)
diameter <- qccGroups(data = pistonrings[-out,], diameter, sample)
plot(qcc(diameter[1:25,], type="xbar"))
plot(qcc(diameter[1:25,], type="R"))
plot(qcc(diameter[1:25,], type="S"))
plot(qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,]))
plot(qcc(diameter[1:25,], type="R", newdata=diameter[26:40,]))
plot(qcc(diameter[1:25,], type="S", newdata=diameter[26:40,]))

##
##  Attribute data 
##

data(orangejuice)

q <- with(orangejuice, 
          qcc(D[trial], sizes=size[trial], type="p"))
q
plot(q)

# remove out-of-control points (see help(orangejuice) for the reasons)
outofctrl <- c(15,23)
q1 <- with(orangejuice[-outofctrl,], 
           qcc(D[trial], sizes=size[trial], type="p"))
plot(q1)
q1 <- with(orangejuice[-outofctrl,], 
           qcc(D[trial], sizes=size[trial], type="p",
               newdata=D[!trial], newsizes=size[!trial]))
plot(q1)

data(orangejuice2)
q2 <- with(orangejuice2, 
           qcc(D[trial], sizes=size[trial], type="p"))
plot(q2)
q2 <- with(orangejuice2, 
           qcc(D[trial], sizes=size[trial], type="p", 
               newdata=D[!trial], newsizes=size[!trial]))
plot(q2)

data(circuit)
plot(with(circuit, qcc(x[trial], sizes=size[trial], type="c")))

# remove out-of-control points (see help(circuit) for the reasons)
outofctrl <- c(15,23)
q1 <- with(orangejuice[-outofctrl,], 
           qcc(D[trial], sizes=size[trial], type="p"))
plot(q1)
q1 <- with(orangejuice[-outofctrl,], 
           qcc(D[trial], sizes=size[trial], type="p",
               newdata=D[!trial], newsizes=size[!trial]))
plot(q1)

outofctrl <- c(6,20)
q1 <- with(circuit[-outofctrl,], 
           qcc(x[trial], sizes=size[trial], type="c"))
plot(q1)
q1 <- with(circuit[-outofctrl,], 
           qcc(x[trial], sizes=size[trial], type="c", 
               newdata = x[!trial], newsizes = size[!trial]))
plot(q1)
q1 <- with(circuit[-outofctrl,], 
           qcc(x[trial], sizes=size[trial], type="u", 
           newdata = x[!trial], newsizes = size[!trial]))
plot(q1)

data(pcmanufact)
q1 <- with(pcmanufact, qcc(x, sizes=size, type="u"))
q1
plot(q1)

data(dyedcloth)
# variable control limits
plot(with(dyedcloth, qcc(x, sizes=size, type="u")))
# standardized control chart
q <- with(dyedcloth, qcc(x, sizes=size, type="u"))
z <- (q$statistics - q$center)/sqrt(q$center/q$size)
plot(qcc(z, sizes = 1, type = "u", center = 0, std.dev = 1, limits = c(-3,3)),
     title = "Standardized u chart")
    
##
##  Continuous one-at-time data 
##

data(viscosity)
q <- with(viscosity, 
          qcc(viscosity[trial], type = "xbar.one"))
q
plot(q)
# batch 4 is out-of-control because of a process temperature controller
# failure; remove it and recompute
viscosity <- viscosity[-4,]
plot(with(viscosity, 
          qcc(viscosity[trial], type = "xbar.one", newdata = viscosity[!trial])))

Deprecated Functions in qcc package

Description

These functions are provided for compatibility with older versions of the package qcc, and they will likely be removed in the future.

Usage

qcc.groups(...)
pareto.chart(...)
process.capability(...)
oc.curves(...)
cause.and.effect(...)
qcc.overdispersion.test(...)
qcc.groups(...)
pareto.chart(...)
process.capability(...)
oc.curves(...)
cause.and.effect(...)
qcc.overdispersion.test(...)

Arguments

...

all arguments are passed down.

Set or return options for the qcc package.

Description

This function can be used to control the behavior of the 'qcc' library such as the background color, out-of-control points appearance, and many others.

Usage

qcc.options(...)qcc.options(...)

Arguments

...

the option to be set or retrieved. See details.

Details

The available options are:

exp.R.unscaled: a vector specifying, for each sample size, the expected value of the relative range (i.e. $R/\sigma$ ) for a normal distribution. This appears as $d_2$ on most tables containing factors for the construction of control charts.
se.R.unscaled: a vector specifying, for each sample size, the standard error of the relative range (i.e. $R/\sigma$ ) for a normal distribution. This appears as $d_3$ on most tables containing factors for the construction of control charts.
beyond.limits$pch: plotting character used to highlight points beyond control limits.
beyond.limits$col: color used to highlight points beyond control limits.
violating.runs$pch: plotting character used to highlight points violating runs.
violating.runs$col: color used to highlight points violating runs.
run.length: the maximum value of a run before to signal a point as out of control.
bg.margin: background color used to draw the margin of the charts.
bg.figure: background color used to draw the figure of the charts.
cex: character expansion used to draw plot annotations (labels, title, tickmarks, etc.).
font.stats: font used to draw text at the bottom of control charts.
cex.stats: character expansion used to draw text at the bottom of control charts.

Value

If the functions is called with no argument return a list of available options.

If an option argument is provided the corresponding value is returned.

If a value is associated with an option argument, such option is set and the list of updated option values is invisibly returned. In this case the list .qcc.options is modified and any modification will remain in effect for the rest of the session.

Author(s)

Luca Scrucca

Examples

old <- qcc.options()			# save defaults
qcc.options("cex.stats")		# get a single parameter
qcc.options("cex.stats"=1.2)	# change parameters
qcc.options(bg.margin="azure2")
qcc.options("violating.runs" = list(pch = 15, col = "purple"))
qcc.options("beyond.limits" = list(pch = 15, col = "orangered"))
qcc(rnorm(100), type = "xbar.one", std.dev = 0.7)	# see the results
qcc.options(old)				# restore old defaults 
old <- qcc.options()			# save defaults
qcc.options("cex.stats")		# get a single parameter
qcc.options("cex.stats"=1.2)	# change parameters
qcc.options(bg.margin="azure2")
qcc.options("violating.runs" = list(pch = 15, col = "purple"))
qcc.options("beyond.limits" = list(pch = 15, col = "orangered"))
qcc(rnorm(100), type = "xbar.one", std.dev = 0.7)	# see the results
qcc.options(old)				# restore old defaults

Grouping data based on a sample indicator

Description

This function allows to easily group data to use as input to the qcc() function.

Usage

qccGroups(data, x, sample)
qccGroups(data, x, sample)

Arguments

`data`	a data frame (or a similar structure which can be coerced to be a `data.frame`) providing the observed data. If not provided, the input to the following arguments must be objects defined in the calling environment.
`x`	a name from `data` or a vector of observed data values.
`sample`	a name from `data` or a vector of sample indicators defining the rationale subgroups of data values.

Value

The function returns a matrix of suitable dimensions. If one or more group have fewer observations than others, NA values are used to fill empty values.

Author(s)

Luca Scrucca

Examples

data(pistonrings)
# create a matrix of 40 samples made of 5 observations each
qccGroups(data = pistonrings, diameter, sample)
# remove some observations to get still a 40x5 matrix but filled with NAs 
qccGroups(data = pistonrings[-c(1,2,50,52,199),], diameter, sample)
data(pistonrings)
# create a matrix of 40 samples made of 5 observations each
qccGroups(data = pistonrings, diameter, sample)
# remove some observations to get still a 40x5 matrix but filled with NAs 
qccGroups(data = pistonrings[-c(1,2,50,52,199),], diameter, sample)

Overdispersion test for binomial and poisson data

Description

This function allows to test for overdispersed data in the binomial and poisson case.

Usage

qccOverdispersionTest(x, size, 
  type = ifelse(missing(size), "poisson", "binomial"))
qccOverdispersionTest(x, size, 
  type = ifelse(missing(size), "poisson", "binomial"))

Arguments

`x`	a vector of observed data values
`size`	for binomial data, a vector of sample sizes
`type`	a character string specifying the distribution for testing, either `"poisson"` or `"binomial"`. By default, if `size` is provided a binomial distribution is assumed, otherwise a poisson distribution.

Details

This very simple test amounts to compute the test statistic

$D = s^2 / \sigma^2 \times (n - 1)$

where $s^2$ is the observed variance, $\sigma^2$ is the theoretical variance, and $n$ is the number of observations. The test statistic is the compared to the critical value of a Chi-square distribution with $n-1$ degrees of freedom.

Value

The function returns a matrix of results.

Author(s)

Luca Scrucca

References

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control, New York, Chapman and Hall, pp. 216–218

Examples

# data from Wetherill and Brown (1991) pp. 212--213, 216--218:
x <- c(12,11,18,11,10,16,9,11,14,15,11,9,10,13,12,
       8,12,13,10,12,13,16,12,18,16,10,16,10,12,14)
size <- rep(50, length(x))
qccOverdispersionTest(x, size)

x <- c(11,8,13,11,13,17,25,23,11,16,9,15,10,16,12,
       8,9,15,4,12,12,12,15,17,14,17,12,12,7,16)
qccOverdispersionTest(x)
# data from Wetherill and Brown (1991) pp. 212--213, 216--218:
x <- c(12,11,18,11,10,16,9,11,14,15,11,9,10,13,12,
       8,12,13,10,12,13,16,12,18,16,10,16,10,12,14)
size <- rep(50, length(x))
qccOverdispersionTest(x, size)

x <- c(11,8,13,11,13,17,25,23,11,16,9,15,10,16,12,
       8,9,15,4,12,12,12,15,17,14,17,12,12,7,16)
qccOverdispersionTest(x)

Rules for Shewhart charts

Description

Function which implements rules to signal out of control points in Shewhart charts.

Usage

qccRules(object, rules = object$rules)
qccRules(object, rules = object$rules)

Arguments

object

an object of class 'qcc'.

rules

a vector of values specifying the rules used to declare a process out-of-control. Possible values are:

1.: One point plots outside 3-sigma control limits.
2.: Two of three consecutive points plot beyond a 2-sigma limit.
3.: Four of five consecutive points plot beyond a 1-sigma limit.
4.: Eight consecutive points plot on one side of the center line.

These are often known as Western Electric rules.

Value

The function returns a vector of the same length as the statistics charted with value NA if no rule is violated, and numerical values corresponding to the violated rule. If more than one rule is violated, the value returned corresponds to the most serious violation.

Author(s)

Luca Scrucca

Ryan's (2011) multivariate data for quality control

Description

Multivariate data from Ryan (2011, Table 9.2).

Usage

data(RyanMultivar)data(RyanMultivar)

Format

Multivariate data on 20 samples of size 4 for two variables.

RyanMultivar: a list of two data frames, X1 and X2, one for each variable.

References

Ryan, T. P. (2011), Statistical Methods for Quality Improvement, 3rd ed. New York: John Wiley & Sons, Inc.

Examples

data(RyanMultivar)
str(RyanMultivar)
data(RyanMultivar)
str(RyanMultivar)

Functions to plot Shewhart c chart

Description

Statistics used in computing and drawing a Shewhart c chart.

Usage

stats.c(data, sizes)
sd.c(data, sizes, ...)
limits.c(center, std.dev, sizes, nsigmas = NULL, conf = NULL)
stats.c(data, sizes)
sd.c(data, sizes, ...)
limits.c(center, std.dev, sizes, nsigmas = NULL, conf = NULL)

Arguments

`data`	the observed data values
`center`	sample/group center statistic.
`sizes`	samples sizes.
`std.dev`	within group standard deviation.
`nsigmas`	a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the `conf` argument is provided.
`conf`	a numeric value in $(0,1)$ specifying the confidence level to use for computing control limits.
`...`	catches further ignored arguments.

Value

The function stats.c returns a list with components statistics and center.

The function sd.c returns std.dev the standard deviation of the statistic charted.

The function limits.c returns a matrix with lower and upper control limits.

Author(s)

Luca Scrucca

References

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

Statistics used in computing and drawing a Shewhart g chart

Description

These functions are used to compute statistics required by the g chart (geometric distribution) for use with the qcc package.

Usage

stats.g(data, sizes)
sd.g(data, sizes, ...)
limits.g(center, std.dev, sizes, nsigmas = NULL, conf = NULL)
stats.g(data, sizes)
sd.g(data, sizes, ...)
limits.g(center, std.dev, sizes, nsigmas = NULL, conf = NULL)

Arguments

`data`	the observed data values
`center`	sample center statistic
`sizes`	sample sizes (not used)
`std.dev`	standard deviation of geometric distribution
`nsigmas`	a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the `conf` argument is provided.
`conf`	a numeric value in $(0,1)$ specifying the confidence level to use for computing control limits.
`...`	catches further ignored arguments.

Details

The g chart plots the number of non-events between events. np charts do not work well when the probability of an event is rare (see example below). Instead of plotting the number of events, the g chart plots the number of non-events between events.

Value

The function stats.g() returns a list with components statistics and center.

The function sd.g() returns std.dev the standard deviation $sqrt(1-p)/p$ .

The function limits.g() returns a matrix with lower and upper control limits.

Note

The geometric distribution is quite skewed so it is best to set conf at the required confidence interval (0 < conf < 1) rather than as a multiplier of sigma.

Author(s)

Greg Snow [email protected]

References

Kaminsky, FC et. al. (1992) Statistical Control Charts Based on a Geometric Distribution, Journal of Quality Technology, 24, pp 63–69.

Yang, Z et. al. (2002) On the Performance of Geometric Charts with Estimated Control Limits, Journal of Quality Technology, 34, pp 448–458.

Examples

success <- rbinom(1000, 1, 0.01)
num.noevent <- diff(which(c(1,success)==1))-1
qcc(success, type = "np", sizes = 1)
qcc(num.noevent, type = "g")
success <- rbinom(1000, 1, 0.01)
num.noevent <- diff(which(c(1,success)==1))-1
qcc(success, type = "np", sizes = 1)
qcc(num.noevent, type = "g")

Statistics used in computing and drawing a Shewhart np chart

Description

These functions are used to compute statistics required by the np chart.

Usage

stats.np(data, sizes)
sd.np(data, sizes, ...)
limits.np(center, std.dev, sizes, nsigmas = NULL, conf = NULL)
stats.np(data, sizes)
sd.np(data, sizes, ...)
limits.np(center, std.dev, sizes, nsigmas = NULL, conf = NULL)

Arguments

`data`	the observed data values
`center`	sample/group center statistic.
`sizes`	samples sizes.
`std.dev`	within group standard deviation.
`nsigmas`	a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the `conf` argument is provided.
`conf`	a numeric value in $(0,1)$ specifying the confidence level to use for computing control limits.
`...`	catches further ignored arguments.

Value

The function stats.np returns a list with components statistics and center.

The function sd.np returns std.dev the standard deviation of the statistic charted.

The function limits.np returns a matrix with lower and upper control limits.

Author(s)

Luca Scrucca

References

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

Statistics used in computing and drawing a Shewhart p chart

Description

These functions are used to compute statistics required by the p chart.

Usage

stats.p(data, sizes)
sd.p(data, sizes, ...)
limits.p(center, std.dev, sizes, nsigmas = NULL, conf = NULL)
stats.p(data, sizes)
sd.p(data, sizes, ...)
limits.p(center, std.dev, sizes, nsigmas = NULL, conf = NULL)

Arguments

`data`	the observed data values
`center`	sample/group center statistic.
`sizes`	samples sizes.
`std.dev`	within group standard deviation.
`nsigmas`	a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the `conf` argument is provided.
`conf`	a numeric value in $(0,1)$ specifying the confidence level to use for computing control limits.
`...`	catches further ignored arguments.

Value

The function stats.p returns a list with components statistics and center.

The function sd.p returns std.dev the standard deviation of the statistic charted.

The function limits.p returns a matrix with lower and upper control limits.

Author(s)

Luca Scrucca

References

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

Statistics used in computing and drawing a Shewhart R chart

Description

These functions are used to compute statistics required by the R chart.

Usage

stats.R(data, sizes)
sd.R(data, sizes, std.dev = c("UWAVE-R", "MVLUE-R"), ...)
limits.R(center, std.dev, sizes, nsigmas = NULL, conf = NULL)
stats.R(data, sizes)
sd.R(data, sizes, std.dev = c("UWAVE-R", "MVLUE-R"), ...)
limits.R(center, std.dev, sizes, nsigmas = NULL, conf = NULL)

Arguments

`data`	the observed data values
`center`	sample/group center statistic.
`sizes`	samples sizes. Optional
`std.dev`	within group standard deviation. Optional for `sd.R` function, required for `limits.R`. See `sd.xbar`.
`nsigmas`	a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the `conf` argument is provided.
`conf`	a numeric value in $(0,1)$ specifying the confidence level to use for computing control limits.
`...`	catches further ignored arguments.

Value

The function stats.R returns a list with components statistics and center.

The function sd.R returns std.dev the standard deviation of the statistic charted.

The function limits.R returns a matrix with lower and upper control limits.

Author(s)

Luca Scrucca

References

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

Functions to plot Shewhart S chart

Description

These functions are used to compute statistics required by the S chart.

Usage

stats.S(data, sizes)
sd.S(data, sizes, std.dev = c("UWAVE-SD", "MVLUE-SD", "RMSDF"), ...)
limits.S(center, std.dev, sizes, nsigmas = NULL, conf = NULL)
stats.S(data, sizes)
sd.S(data, sizes, std.dev = c("UWAVE-SD", "MVLUE-SD", "RMSDF"), ...)
limits.S(center, std.dev, sizes, nsigmas = NULL, conf = NULL)

Arguments

`data`	the observed data values
`center`	sample/group center statistic.
`sizes`	samples sizes. Optional
`std.dev`	within group standard deviation. Optional for `sd.S` function, required for `limits.S`. See `sd.xbar`.
`nsigmas`	a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the `conf` argument is provided.
`conf`	a numeric value in $(0,1)$ specifying the confidence level to use for computing control limits.
`...`	catches further ignored arguments.

Value

The function stats.S returns a list with components statistics and center.

The function sd.S returns std.dev the standard deviation of the statistic charted.

The function limits.S returns a matrix with lower and upper control limits.

Author(s)

Luca Scrucca

References

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

Statistics used in computing and drawing the Hotelling T^2 chart for subgrouped data

Description

These functions are used to compute statistics required by the $T^2$ chart.

Usage

stats.T2(data, center = NULL, cov = NULL)

limits.T2(ngroups, size, nvars, conf) 
stats.T2(data, center = NULL, cov = NULL)

limits.T2(ngroups, size, nvars, conf)

Arguments

`data`	the observed data values
`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.
`ngroups`	number of groups
`size`	sample size
`nvars`	number of variables
`conf`	confidence level (0 < `conf` < 1)

Value

The function stats.T2 returns a list with components:

`statistics`	a vector of values for the $T^2$ statistic
`means`	a matrix of within group means for each variable
`center`	sample/group center statistic
`S`	covariance matrix

The function limits.T2 returns a list with components:

`control`	control limits
`prediction`	pred.limits

Author(s)

Luca Scrucca

References

Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Ryan, T. P. (2011), Statistical Methods for Quality Improvement, 3rd ed. New York: John Wiley & Sons, Inc.

Statistics used in computing and drawing the Hotelling T^2 chart for individual observations data

Description

These functions are used to compute statistics required by the $T^2$ chart for individual observations.

Usage

stats.T2.single(data, center = NULL, cov = NULL)

limits.T2.single(ngroups, size, nvars, conf) 
stats.T2.single(data, center = NULL, cov = NULL)

limits.T2.single(ngroups, size, nvars, conf)

Arguments

`data`	the observed data values
`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.
`ngroups`	number of groups
`size`	sample size
`nvars`	number of variables
`conf`	confidence level (0 < `conf` < 1)

Value

The function stats.T2.single returns a list with components:

`statistics`	a vector of values for the $T^2$ statistic
`means`	a matrix of within group means for each variable (which is equal to `data` since sample are of sizes one)
`center`	sample/group center statistic
`S`	covariance matrix

The function limits.T2.single returns a list with components:

`control`	control limits
`prediction`	pred.limits

Author(s)

Luca Scrucca

References

Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Ryan, T. P. (2011), Statistical Methods for Quality Improvement, 3rd ed. New York: John Wiley & Sons, Inc.

Statistics used in computing and drawing a Shewhart u chart

Description

These functions are used to compute statistics required by the u chart.

Usage

stats.u(data, sizes)
sd.u(data, sizes, ...)
limits.u(center, std.dev, sizes, nsigmas = NULL, conf = NULL)
stats.u(data, sizes)
sd.u(data, sizes, ...)
limits.u(center, std.dev, sizes, nsigmas = NULL, conf = NULL)

Arguments

`data`	the observed data values
`center`	sample/group center statistic.
`sizes`	samples sizes.
`std.dev`	within group standard deviation.
`nsigmas`	a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the `conf` argument is provided.
`conf`	a numeric value in $(0,1)$ specifying the confidence level to use for computing control limits.
`...`	catches further ignored arguments.

Value

The function stats.u returns a list with components statistics and center.

The function sd.u returns std.dev the standard deviation of the statistic charted.

The function limits.u returns a matrix with lower and upper control limits.

Author(s)

Luca Scrucca

References

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

Statistics used in computing and drawing a Shewhart xbar chart

Description

These functions are used to compute statistics required by the xbar chart.

Usage

stats.xbar(data, sizes)
sd.xbar(data, sizes, 
        std.dev = c("UWAVE-R", "UWAVE-SD", "MVLUE-R", "MVLUE-SD", "RMSDF"), 
        ...)
limits.xbar(center, std.dev, sizes, nsigmas = NULL, conf = NULL)
stats.xbar(data, sizes)
sd.xbar(data, sizes, 
        std.dev = c("UWAVE-R", "UWAVE-SD", "MVLUE-R", "MVLUE-SD", "RMSDF"), 
        ...)
limits.xbar(center, std.dev, sizes, nsigmas = NULL, conf = NULL)

Arguments

`data`	the observed data values
`center`	sample/group center statistic
`sizes`	samples sizes. Optional
`std.dev`	within group standard deviation. Optional for `sd.xbar` function, required for `limits.xbar`. See details.
`nsigmas`	a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the `conf` argument is provided.
`conf`	a numeric value in $(0,1)$ specifying the confidence level to use for computing control limits.
`...`	catches further ignored arguments.

Details

The following methods are available for estimating the process standard deviation:

"UWAVE-R": UnWeighted AVErage of within-group estimates based on within-group Ranges
"UWAVE-SD": UnWeighted AVErage of within-group estimates based on within-group Standard Deviations
"MVLUE-R": Minimum Variance Linear Unbiased Estimator computed as a weighted average of within-group estimates based on within-group Ranges
"MVLUE-SD": Minimum Variance Linear Unbiased Estimator computed as a weighted average of within-group estimates based on within-group Standard Deviations
"RMSDF": Root-Mean-Square estimator computed as a weighted average of within-group estimates based on within-group Standard Deviations

Depending on the chart, a method may be available or not, or set as the default according to the following table:

Detailed definitions of formulae implemented are available in the SAS/QC User's Guide.

Value

The function stats.xbar returns a list with components statistics and center.

The function sd.xbar returns std.dev the standard deviation of the statistic charted. This is based on results from Burr (1969).

The function limits.xbar returns a matrix with lower and upper control limits.

Author(s)

Luca Scrucca

References

Burr, I.W. (1969) Control charts for measurements with varying sample sizes. Journal of Quality Technology, 1(3), 163-167.

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

Statistics used in computing and drawing a Shewhart xbar chart for one-at-time data

Description

These functions are used to compute statistics required by the xbar chart for one-at-time data.

Usage

stats.xbar.one(data, sizes)
sd.xbar.one(data, sizes, std.dev = c("MR", "SD"), r = 2, ...)
limits.xbar.one(center, std.dev, sizes, nsigmas = NULL, conf = NULL)
stats.xbar.one(data, sizes)
sd.xbar.one(data, sizes, std.dev = c("MR", "SD"), r = 2, ...)
limits.xbar.one(center, std.dev, sizes, nsigmas = NULL, conf = NULL)

Arguments

`data`	the observed data values
`center`	sample/group center statistic.
`sizes`	samples sizes. Not needed, `size = 1` is used.
`r`	number of successive pairs of observations for computing the standard deviation based on moving ranges of r points.
`std.dev`	within group standard deviation. Optional for `sd.xbar.one` function, required for `limits.xbar.one`. See details.
`nsigmas`	a numeric value specifying the number of sigmas to use for computing control limits. It is ignored when the `conf` argument is provided.
`conf`	a numeric value in $(0,1)$ specifying the confidence level to use for computing control limits.
`...`	catches further ignored arguments.

Details

Methods available for estimating the process standard deviation:

"MR" = moving range: this is estimate is based on the scaled mean of moving ranges
"SD" = sample standard deviation: this estimate is defined as sd(x)/cd(n), where n is the number of individual measurements of x.

Value

The function stats.xbar.one returns a list with components statistics and center.

The function sd.xbar.one returns std.dev the standard deviation of the statistic charted.

The function limits.xbar.one returns a matrix with lower and upper control limits.

Author(s)

Luca Scrucca

References

Montgomery, D.C. (2013) Introduction to Statistical Quality Control, 7th ed. New York: John Wiley & Sons.

Ryan, T. P. (2011), Statistical Methods for Quality Improvement, 3rd ed. New York: John Wiley & Sons, Inc.

Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

Examples

# Water content of antifreeze data (Wetherill and Brown, 1991, p. 120)
x <- c(2.23, 2.53, 2.62, 2.63, 2.58, 2.44, 2.49, 2.34, 2.95, 2.54, 2.60, 2.45,
       2.17, 2.58, 2.57, 2.44, 2.38, 2.23, 2.23, 2.54, 2.66, 2.84, 2.81, 2.39,
       2.56, 2.70, 3.00, 2.81, 2.77, 2.89, 2.54, 2.98, 2.35, 2.53)
# the Shewhart control chart for one-at-time data
# 1) using MR (default)
qcc(x, type="xbar.one", data.name="Water content (in ppm) of batches of antifreeze")
# 2) using SD
qcc(x, type="xbar.one", std.dev = "SD", data.name="Water content (in ppm) of batches of antifreeze")

# "as the size increases further, we would expect sigma-hat to settle down
#  at a value close to the overall sigma-hat" (Wetherill and Brown, 1991,
# p. 121)
sigma <- NA
k <- 2:24
for (j in k)
    sigma[j] <- sd.xbar.one(x, k=j)
plot(k, sigma[k], type="b")     # plot estimates of sigma for 
abline(h=sd(x), col=2, lty=2)   # different values of k
# Water content of antifreeze data (Wetherill and Brown, 1991, p. 120)
x <- c(2.23, 2.53, 2.62, 2.63, 2.58, 2.44, 2.49, 2.34, 2.95, 2.54, 2.60, 2.45,
       2.17, 2.58, 2.57, 2.44, 2.38, 2.23, 2.23, 2.54, 2.66, 2.84, 2.81, 2.39,
       2.56, 2.70, 3.00, 2.81, 2.77, 2.89, 2.54, 2.98, 2.35, 2.53)
# the Shewhart control chart for one-at-time data
# 1) using MR (default)
qcc(x, type="xbar.one", data.name="Water content (in ppm) of batches of antifreeze")
# 2) using SD
qcc(x, type="xbar.one", std.dev = "SD", data.name="Water content (in ppm) of batches of antifreeze")

# "as the size increases further, we would expect sigma-hat to settle down
#  at a value close to the overall sigma-hat" (Wetherill and Brown, 1991,
# p. 121)
sigma <- NA
k <- 2:24
for (j in k)
    sigma[j] <- sd.xbar.one(x, k=j)
plot(k, sigma[k], type="b")     # plot estimates of sigma for 
abline(h=sd(x), col=2, lty=2)   # different values of k

Viscosity for aircraft primer paint data

Description

"The viscosity of an aircraft primer paint is an important quality characteristic. The product is produced in batches, and because each batch takes several hours to produce, the production rate is too slow to allow for rational subgroups of size greater than one." (Montgomery, 2005, p. 232)

Usage

data(viscosity)data(viscosity)

Format

A data frame with 35 observations on the following 3 variables.

batch: batch number
viscosity: viscosity measure
trial: preliminary sample indicator (TRUE/FALSE)

References

Montgomery, D.C. (2005) Introduction to Statistical Quality Control, 5th ed, New York, John Wiley & Sons, pp. 232-235

Examples

data(viscosity)
describe(viscosity, by = trial)
plot(viscosity ~ batch, data = viscosity, type = "o", 
     pch = ifelse(trial, 19, 1))
data(viscosity)
describe(viscosity, by = trial)
plot(viscosity ~ batch, data = viscosity, type = "o", 
     pch = ifelse(trial, 19, 1))

Package 'qcc'

Help Index

Quality Control Charts

Description

Details

Author(s)

References

See Also

Water content of antifreeze data

Description

Usage

Format

References

Examples

Boiler temperature data

Description

Usage

Format

References

Examples

Cause and Effect Diagram

Description

Usage

Arguments

Author(s)

References

Examples

Circuit boards data

Description

Usage

Format

References

Examples

Cusum chart

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

Descriptive statistics

Description

Usage

Arguments

Details

Author(s)

See Also

Examples

Dyed cloth data

Description

Usage

Format

References

Examples

Multivariate Quality Control Charts

Description

Usage

Arguments

Author(s)

References

See Also

Examples

EWMA chart

Description

Usage

Arguments

Details

Value

Author(s)

References

See Also

Examples

EWMA smoothing function

Description

Usage

Arguments

Details