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.

See Also

qcc, mqcc, cusum, ewma, oc.curves, process.capability, pareto.chart, cause.and.effect.

Boiler temperature data

Description

Temperature readings from the eight configured burners on a boiler.

Usage

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)
summary(boiler)
boxplot(boiler)

Cause and effect diagram

Description

Draw a basic cause and effect diagram.

Usage

cause.and.effect(cause, effect, title = "Cause-and-Effect diagram", 
                 cex = c(1, 0.9, 1), font = c(1, 3, 2))

Arguments

Author(s)

Luca Scrucca

References

Montgomery, D.C. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

Examples

cause.and.effect(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)

Format

A data frame with 46 observations on the following 3 variables.

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)
attach(circuit)
summary(circuit)
boxplot(x ~ trial)
plot(x, type="b")
detach(circuit)

Cusum chart

Description

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

Usage

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

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

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

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

Arguments

Details

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

Value

Returns an object of class 'cusum.qcc'.

Author(s)

Luca Scrucca

References

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

See Also

qcc, ewma

Examples

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

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

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

detach(pistonrings)

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)

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)
attach(dyedcloth)
summary(dyedcloth)
plot(x/size, type="b")
detach(dyedcloth)

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, ...)

Arguments

Author(s)

Luca Scrucca

References

Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.
Montgomery, D.C. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Ryan, T. P. (2000), Statistical Methods for Quality Improvement, 2nd ed. New York: John Wiley & Sons, Inc.

See Also

mqcc, stats.T2, stats.T2.single

Examples

# 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, 
     data.name, labels, newdata, newsizes, newlabels, 
     plot = TRUE, ...)

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

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

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

Arguments

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

See Also

qcc, ewmaSmooth, cusum

Examples

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

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

q <-  ewma(diameter[1:25,], lambda=0.2, nsigmas=2.7, newdata=diameter[26:40,], plot = FALSE) 
summary(q)
plot(q)

detach(pistonrings)

##
## Individual observations: viscosity data (Montgomery, pag. 242)
##
x <- c(33.75, 33.05, 34, 33.81, 33.46, 34.02, 33.68, 
33.27, 33.49, 33.20, 33.62, 33.00, 33.54, 33.12, 33.84)
q <-  ewma(x, lambda=0.2, nsigmas=2.7)
summary(q)

EWMA smoothing function

Description

Compute Exponential Weighted Moving Average.

Usage

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

Arguments

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:

Author(s)

Luca Scrucca

References

Montgomery, D.C. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc, cusum

Examples

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, 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

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

See Also

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

Examples

##
##  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)

Operating Characteristic Function

Description

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

Usage

oc.curves(object, ...)

oc.curves.xbar(object, n, c = seq(0, 5, length=101), 
               nsigmas = object$nsigmas, identify=FALSE, restore.par=TRUE)

oc.curves.R(object, n, c = seq(1, 6, length=101),
            nsigmas = object$nsigmas, identify = FALSE, restore.par=TRUE)

oc.curves.S(object, n, c = seq(1, 6, length=101),
            nsigmas = object$nsigmas, identify = FALSE, restore.par=TRUE)

oc.curves.p(object, nsigmas = object$nsigmas, identify = FALSE, restore.par=TRUE)

oc.curves.c(object, nsigmas = object$nsigmas, identify = FALSE, restore.par=TRUE)

Arguments

Details

An operating characteristic curve graphically provides information about the probability of not detecting a shift in the process. oc.curves 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 invisibly returns a matrix or a vector of beta values, the probability of type II error.

Author(s)

Luca Scrucca

References

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

See Also

qcc

Examples

data(pistonrings)
attach(pistonrings)
diameter <- qcc.groups(diameter, sample)
beta <- oc.curves.xbar(qcc(diameter, type="xbar", nsigmas=3, plot=FALSE))
print(round(beta, digits=4))
# or to identify points on the plot use
## Not run: oc.curves.xbar(qcc(diameter, type="xbar", nsigmas=3, plot=FALSE), identify=TRUE)
detach(pistonrings)

data(orangejuice)
attach(orangejuice)
beta <- oc.curves(qcc(D[trial], sizes=size[trial], type="p", plot=FALSE))
print(round(beta, digits=4))
# or to identify points on the plot use
## Not run: oc.curves(qcc(D[trial], sizes=size[trial], type="p", plot=FALSE), identify=TRUE)
detach(orangejuice)

data(circuit)
attach(circuit)
q <- qcc(x[trial], sizes=size[trial], type="c", plot=FALSE)
beta <- oc.curves(q)
print(round(beta, digits=4))
# or to identify points on the plot use
## Not run: oc.curves(qcc(x[trial], sizes=size[trial], type="c", plot=FALSE), identify=TRUE)
detach(circuit)

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)

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$d <- orangejuice$D/orangejuice$size
attach(orangejuice)
summary(orangejuice)
boxplot(d ~ trial)
mark <- ifelse(trial, 1, 2)
plot(sample, d, type="b", col=mark, pch=mark)
detach(orangejuice)

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)

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$d <- orangejuice2$D/orangejuice2$size
attach(orangejuice2)
summary(orangejuice2)
boxplot(d ~ trial)
mark <- ifelse(trial, 1, 2)
plot(sample, d, type="b", col=mark, pch=mark)
detach(orangejuice2)

Pareto chart

Description

Computes a table of statistics and plot a Pareto chart.

Usage

pareto.chart(data, plot = TRUE, ...)

## S3 method for class 'pareto.chart'
plot(x, xlab = NULL, ylab = "Frequency", 
     ylab2 = "Cumulative Percentage", 
     cumperc = seq(0, 100, by = 25), 
     ylim = NULL, main = NULL,
     col = blues.colors(nlevels), 
     ...) 

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 'pareto.chart' containing the descriptive statistics used to draw the Pareto chart. This object has associated a print and plot mehod.

Author(s)

Luca Scrucca

References

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

See Also

barplot

Examples

defect <- c(80, 27, 66, 94, 33)
names(defect) <- c("price code", "schedule date", "supplier code", "contact num.", "part num.")
pareto.chart(defect, ylab = "Error frequency")
pareto.chart(defect, ylab = "Error frequency", xlab = "Error causes", las=1)
pareto.chart(defect, ylab = "Error frequency", col=rainbow(length(defect)))
pareto.chart(defect, cumperc = seq(0, 100, by = 5), ylab2 = "A finer tickmarks grid")

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)

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)
attach(pcmanufact)
summary(pcmanufact)
plot(x/size, type="b")
detach(pcmanufact)

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)

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)
attach(pistonrings)
summary(pistonrings)
boxplot(diameter ~ sample)
plot(sample, diameter, cex=0.7)
lines(tapply(diameter,sample,mean))
detach(pistonrings)

Process capability analysis

Description

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

Usage

process.capability(object,spec.limits, target, std.dev, nsigmas, 
                   confidence.level = 0.95, breaks = "scott", 
                   add.stats = TRUE, print = TRUE, 
                   digits = getOption("digits"), restore.par = TRUE)

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:

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. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc

Examples

data(pistonrings)
attach(pistonrings)
diameter <- qcc.groups(diameter, sample)
q <- qcc(diameter[1:25,], type="xbar", nsigmas=3, plot=FALSE)
process.capability(q, spec.limits=c(73.95,74.05))
process.capability(q, spec.limits=c(73.95,74.05), target=74.02)
process.capability(q, spec.limits=c(73.99,74.01))
process.capability(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, sizes, center, std.dev, limits,
    data.name, labels, newdata, newsizes, newdata.name,
    newlabels, nsigmas = 3, confidence.level,
    rules = shewhart.rules, plot = TRUE, ...)

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

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

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

Arguments

Value

Returns an object of class 'qcc'.

Note

For a nice blog post discussing the qcc package, in particular how to implement the Western Eletric Rules (WER), see http://blog.yhathq.com/posts/quality-control-in-r.html.

Author(s)

Luca Scrucca

References

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

See Also

shewhart.rules, cusum, ewma, oc.curves, process.capability, qcc.groups

Examples

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

qcc(diameter[1:25,], type="xbar")
qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,])
q <- qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], plot=FALSE)
plot(q, chart.all=FALSE)
qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], nsigmas=2)
qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], confidence.level=0.99)

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

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

# add warning limits at 2 std. deviations
q <- qcc(diameter[1:25,], type="xbar", newdata=diameter[26:40,], plot=FALSE)
(warn.limits <- limits.xbar(q$center, q$std.dev, q$sizes, 2))
plot(q, restore.par = FALSE)
abline(h = warn.limits, lty = 3, col = "chocolate")

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

detach(pistonrings)

##
##  Attribute data 
##

data(orangejuice)
attach(orangejuice)
qcc(D[trial], sizes=size[trial], type="p")

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

data(orangejuice2)
attach(orangejuice2)
names(D) <- sample
qcc(D[trial], sizes=size[trial], type="p")
q2 <- qcc(D[trial], sizes=size[trial], type="p", newdata=D[!trial], newsizes=size[!trial])
detach(orangejuice2)

# put on the same graph the two orange juice samples
oldpar <- par(no.readonly = TRUE)
par(mfrow=c(1,2), mar=c(5,5,3,0))
plot(q1, title="First samples", ylim=c(0,0.5), add.stats=FALSE, restore.par=FALSE)
par("mar"=c(5,0,3,3), yaxt="n")
plot(q2, title="Second samples", add.stats=FALSE, ylim=c(0,0.5))
par(oldpar)

data(circuit)
attach(circuit)
qcc(x[trial], sizes=size[trial], type="c")
# remove out-of-control points (see help(circuit) for the reasons)
inc <- setdiff(which(trial), c(6,20))
qcc(x[inc], sizes=size[inc], type="c", labels=inc)
qcc(x[inc], sizes=size[inc], type="c", labels=inc, 
    newdata=x[!trial], newsizes=size[!trial], newlabels=which(!trial))
qcc(x[inc], sizes=size[inc], type="u", labels=inc, 
    newdata=x[!trial], newsizes=size[!trial], newlabels=which(!trial))
detach(circuit)

data(pcmanufact)
attach(pcmanufact)
qcc(x, sizes=size, type="u")
detach(pcmanufact)

data(dyedcloth)
attach(dyedcloth)
qcc(x, sizes=size, type="u")
# standardized control chart
q <- qcc(x, sizes=size, type="u", plot=FALSE)
z <- (q$statistics - q$center)/sqrt(q$center/q$size)
plot(z,  type="o", ylim=range(z,3,-3), pch=16)
abline(h=0, lty=2)
abline(h=c(-3,3), lty=2)
detach(dyedcloth)

##
##  Continuous one-at-time data 
##

# viscosity data (Montgomery, pag. 242)
x <- c(33.75, 33.05, 34, 33.81, 33.46, 34.02, 33.68, 33.27, 33.49, 33.20,
       33.62, 33.00, 33.54, 33.12, 33.84)
qcc(x, type="xbar.one")
qcc(x, type="xbar.one", std.dev = "SD")

Internal 'qcc' functions

Description

Internal functions for package 'qcc'.

Usage

.printShortMatrix(x, head = 2, tail = 1, chead = 5, ctail = 1, ...)

Details

These functions are not intended to be called by the user.

Author(s)

Luca Scrucca

Grouping data based on a sample indicator

Description

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

Usage

qcc.groups(data, sample)

Arguments

Value

The function returns a matrix of suitable dimensions. If one or more group have few observations than others, NA values are appended.

Author(s)

Luca Scrucca

See Also

qcc

Examples

data(pistonrings)
attach(pistonrings)
# 40 sample of 5 obs each
qcc.groups(diameter, sample)
# some obs are removed, the result is still a 40x5 matrix but with NAs added
qcc.groups(diameter[-c(1,2,50,52, 199)], sample[-c(1,2,50,52, 199)])

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(...)

Arguments

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

See Also

qcc

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 

Overdispersion test for binomial and poisson data

Description

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

Usage

qcc.overdispersion.test(x, size, type=ifelse(missing(size), "poisson", "binomial"))

Arguments

Details

This very simple test amounts to compute the statistic

and refer this to a Chi-square distribution with (no. observations - 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))
qcc.overdispersion.test(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)
qcc.overdispersion.test(x)

Functions specifying rules for Shewhart charts

Description

These functions are used to signal out of control points in Shewhart charts.

Usage

shewhart.rules(object, limits = object$limits, run.length = qcc.options("run.length"))
beyond.limits(object, limits = object$limits)
violating.runs(object, run.length = qcc.options("run.length"))

Arguments

Details

The function shewhart.rules simply calls the beyond.limits and violating.runs functions which actually do the real calculations.

Value

The shewhart.rules function returns a list with components:

Author(s)

Luca Scrucca

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, conf)

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. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc

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, conf)

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. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc

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) 

Arguments

Value

The function stats.T2 returns a list with components:

The function limits.T2 returns a list with components:

Author(s)

Luca Scrucca

References

Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.
Montgomery, D.C. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Ryan, T. P. (2000), Statistical Methods for Quality Improvement, 2nd ed. New York: John Wiley & Sons, Inc.

See Also

mqcc, stats.T2.single

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) 

Arguments

Value

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

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

Author(s)

Luca Scrucca

References

Mason, R.L. and Young, J.C. (2002) Multivariate Statistical Process Control with Industrial Applications, SIAM.
Montgomery, D.C. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Ryan, T. P. (2000), Statistical Methods for Quality Improvement, 2nd ed. New York: John Wiley & Sons, Inc.

See Also

mqcc, stats.T2

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, conf)

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. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc

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, conf)

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 greg.snow@ihc.com

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.

See Also

qcc

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")

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, conf)

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. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc

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, conf)

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. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc

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, conf)

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. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc

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, conf)

Arguments

Details

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

"UWAVE-R"

UnWeighted AVErage of subgroup estimates based on subgroup Ranges

"UWAVE-SD"

UnWeighted AVErage of subgroup estimates based on subgroup Standard Deviations

"MVLUE-R"

Minimum Variance Linear Unbiased Estimator computed as a weighted average of subgroups estimates based on subgroup Ranges

"MVLUE-SD"

Minimum Variance Linear Unbiased Estimator computed as a weighted average of subgroup estimates based on subgroup Standard Deviations

"RMSDF"

Root-Mean-Square estimator computed as a weighted average of subgroup estimates based on subgroup 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 9.2 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. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc

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"), k=2)
limits.xbar.one(center, std.dev, sizes, conf)

Arguments

Details

Methods available for estimating the process standard deviation:

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. (2005) Introduction to Statistical Quality Control, 5th ed. New York: John Wiley & Sons.
Ryan T.P. (2000) Statistical Methods for Quality Improvement, New York: John Wiley & Sons.
Wetherill, G.B. and Brown, D.W. (1991) Statistical Process Control. New York: Chapman & Hall.

See Also

qcc

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