Type:	Package
Title:	Six Sigma Tools for Quality Control and Improvement
Version:	0.11.1
Encoding:	UTF-8
Maintainer:	Emilio L. Cano <emilio@lcano.com>
BugReports:	https://github.com/emilopezcano/SixSigma/issues/
Description:	Functions and utilities to perform Statistical Analyses in the Six Sigma way. Through the DMAIC cycle (Define, Measure, Analyze, Improve, Control), you can manage several Quality Management studies: Gage R&R, Capability Analysis, Control Charts, Loss Function Analysis, etc. Data frames used in the books "Six Sigma with R" [ISBN 978-1-4614-3652-2] and "Quality Control with R" [ISBN 978-3-319-24046-6], are also included in the package.
URL:	https://www.sixsigmawithr.com/, http://emilopezcano.github.io/SixSigma/, https://github.com/emilopezcano/SixSigma/
License:	GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Depends:	R (≥ 3.5.0)
Imports:	grDevices, stats, graphics, lattice, ggplot2, reshape2, nortest, e1071, scales, testthat, xtable
LazyLoad:	yes
LazyData:	yes
RoxygenNote:	7.2.3
Config/testthat/edition:	3
Suggests:	covr
NeedsCompilation:	no
Packaged:	2023-08-21 16:30:45 UTC; emilio.lcano
Author:	Emilio L. Cano [aut, cre], Javier M. Moguerza [aut], Mariano Prieto [aut], Andrés Redchuk [aut], Karl Tatgenhorst [ctb], Paula Martínez [ctb], Manuel Alfaro [ctb]
Repository:	CRAN
Date/Publication:	2023-08-22 04:50:02 UTC

SixSigma: Six Sigma Tools for Quality Control and Improvement

Description

Functions and utilities to perform Statistical Analyses in the Six Sigma way. Through the DMAIC cycle (Define, Measure, Analyze, Improve, Control), you can manage several Quality Management studies: Gage R&R, Capability Analysis, Control Charts, Loss Function Analysis, etc. Data frames used in the books "Six Sigma with R" [ISBN 978-1-4614-3652-2] and "Quality Control with R" [ISBN 978-3-319-24046-6], are also included in the package.

Six Sigma Tools for Quality and Process Improvement

Details

This package contains functions and utilities to perform Statistical Analyses in the Six Sigma way. Through the DMAIC cycle (Define, Measure, Analyze, Improve, Control), you can manage several Quality Management studies: Gage R&R, Capability Analysis, Control Charts, Loss Function Analysis, etc. Data frames used in "Six Sigma with R" (Springer, 2012) are also included in the package. Use the package to perform Six Sigma Methodology tasks, throughout its breakthrough strategy: Define, Measure, Analyze, Improve, Control (DMAIC)
Define: Process Map (ss.pMap), Cause and effect Diagram (ss.ceDiag);
Measure: Gage R&R study (ss.rr); Capability Analysis (ss.study.ca); Loss Function Analysis (ss.lfa)
Analyze: Confidence Intervals (ss.ci)
Control: Moving Average Control Chart
Soon: further functions

Note

The current version includes Loss Function Analysis, Gage R&R Study, confidence intervals, Process Map and Cause-and-Effect diagram. We plan to regularly upload updated versions, with new functions and improving those previously deployed. The subsequent versions will cover tools for the whole cycle:

• Define

• Measure

• Analyze

• Improve

• Control

Author(s)

Maintainer: Emilio L. Cano emilio@lcano.com (ORCID)

Authors:

• Javier M. Moguerza

• Mariano Prieto

• Andrés Redchuk

Other contributors:

• Karl Tatgenhorst (ORCID) [contributor]

• Paula Martínez [contributor]

• Manuel Alfaro [contributor]

Emilio L. Cano, Javier M. Moguerza, Mariano Prieto Corcoba and Andrés Redchuk;

Maintainer: Emilio L. Cano emilio.lopez@urjc.es

References

Allen, T. T. (2010) Introduction to Engineering Statistics and Lean Six Sigma - Statistical Quality Control and Design of Experiments and Systems (Second Edition ed.). London: Springer.

Box, G. (1991). Teaching engineers experimental design with a paper helicopter. Report 76, Center for Quality and Productivity Improvement. University of Wisconsin.

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Cano, Emilio L., Moguerza, Javier M. and Prieto Corcoba, Andrés. 2015. Quality Control with R. An ISO Standards approach, Use R!, Springer, New York.

Chambers, J. M. (2008) Software for data analysis. Programming with R New York: Springer.

Montgomery, DC (2008) Introduction to Statistical Quality Control (Sixth Edition). New York: Wiley&Sons

Wikipedia, https://en.wikipedia.org/wiki/Six_Sigma

See Also

Useful links:

• https://www.sixsigmawithr.com/

• http://emilopezcano.github.io/SixSigma/

• https://github.com/emilopezcano/SixSigma/

• Report bugs at https://github.com/emilopezcano/SixSigma/issues/

ss.pMap, ss.rr, ss.ceDiag, ss.ci, ss.heli, ss.lfa

Compute profiles limits

Description

Function to compute prototype profile and confidence bands for a set of profiles (Phase I)

Usage

climProfiles(
  profiles,
  x = 1:nrow(profiles),
  smoothprof = FALSE,
  smoothlim = FALSE,
  alpha = 0.01
)

Arguments

Value

a matrix with three profiles: prototype and confidence bands

Author(s)

Javier M. Moguerza and Emilio L. Cano

References

Cano, E.L. and Moguerza, J.M. and Prieto Corcoba, M. (2015) Quality Control with R. An ISO Standards Approach. Springer.

Examples

wby.phase1 <- ss.data.wby[, 1:35]
wb.limits <- climProfiles(profiles = wby.phase1,
    x = ss.data.wbx,
    smoothprof = FALSE,
    smoothlim = FALSE)
    plotProfiles(profiles = wby.phase1,
                 x = ss.data.wbx, 
                 cLimits = wb.limits)

Get out-of-control profiles

Description

Returns a list with information about the out-of-control profiles given a set of profiles and some control limits

Usage

outProfiles(profiles, x = 1:nrow(profiles), cLimits, tol = 0.5)

Arguments

Value

a list with the following elements:

References

Cano, E.L. and Moguerza, J.M. and Prieto Corcoba, M. (2015) Quality Control with R. An ISO Standards Approach. Springer.

Examples

wby.phase1 <- ss.data.wby[, 1:35]
wb.limits <- climProfiles(profiles = wby.phase1,
    x = ss.data.wbx,
    smoothprof = TRUE,
    smoothlim = TRUE)
wby.phase2 <- ss.data.wby[, 36:50]
wb.out.phase2 <- outProfiles(profiles = wby.phase2,
    x = ss.data.wbx,
    cLimits = wb.limits,
    tol = 0.8)
wb.out.phase2
plotProfiles(wby.phase2,
    x = ss.data.wbx,
    cLimits = wb.limits,
    outControl = wb.out.phase2$idOut,
    onlyout = TRUE)

Profiles control plot

Description

Plots the proportion of times that each profile remains out of the confidence bands

Usage

plotControlProfiles(pOut, tol = 0.5)

Arguments

Value

There is only graphical output

Author(s)

Javier M. Moguerza and Emilio L. Cano

References

Cano, E.L. and Moguerza, J.M. and Prieto Corcoba, M. (2015) Quality Control with R. An ISO Standards Approach. Springer.

Examples

wby.phase1 <- ss.data.wby[, 1:35]
wb.limits <- climProfiles(profiles = wby.phase1,
    x = ss.data.wbx,
    smoothprof = TRUE,
    smoothlim = TRUE)
wby.phase2 <- ss.data.wby[, 36:50]
wb.out.phase2 <- outProfiles(profiles = wby.phase2,
    x = ss.data.wbx,
    cLimits = wb.limits,
    tol = 0.8)
plotControlProfiles(wb.out.phase2$pOut, tol = 0.8)

Plot Profiles

Description

Plot profiles and optionally control limits

Usage

plotProfiles(
  profiles,
  x = 1:nrow(profiles),
  cLimits = NULL,
  outControl = NULL,
  onlyout = FALSE
)

Arguments

Value

Only graphical output with the profiles

Author(s)

Javier M. Moguerza and Emilio L. Cano

References

Cano, E.L. and Moguerza, J.M. and Prieto Corcoba, M. (2015) Quality Control with R. An ISO Standards Approach. Springer.

Examples

plotProfiles(profiles = ss.data.wby,
    x = ss.data.wbx)     

Regularise set of profiles

Description

This function takes a set of profiles and regularise them by means of a SVM

Usage

smoothProfiles(
  profiles,
  x = 1:nrow(profiles),
  svm.c = NULL,
  svm.eps = NULL,
  svm.gamma = NULL,
  parsvm.unique = TRUE
)

Arguments

Value

Regularized profiles

Note

The package e1071 is needed in order to be able to use this function. SVM Parameters can be vectors of the same lenght as number of profiles, or a single value for all of them

Author(s)

Javier M. Moguerza and Emilio L. Cano

References

Cano, E.L. and Moguerza, J.M. and Prieto Corcoba, M. (2015) Quality Control with R. An ISO Standards Approach. Springer.

Examples

wby.smooth <- smoothProfiles(profiles = ss.data.wby,
    x = ss.data.wbx)
plotProfiles(profiles = wby.smooth,
    x = ss.data.wbx)     

Main calculations regarding The Voice of the Process in SixSigma: Yield, FTY, RTY, DPMO

Description

Computes the Yield, First Time Yield, Rolled Throughput Yield and Defects per Million Opportunities of a process.

Usage

ss.ca.yield(defects = 0, rework = 0, opportunities = 1)

Arguments

Details

The arguments defects and rework must have the same length.

Value

Author(s)

Emilio L. Cano

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Gygi C, DeCarlo N, Williams B (2005) Six sigma for dummies. –For dummies, Wiley Pub.

Examples

ss.ca.yield(c(3,5,12),c(1,2,4),1915)

Capability Indices

Description

Compute the Capability Indices of a process, Z (Sigma Score), C_p and C_{pk}.

Usage

ss.ca.cp(x, LSL = NA, USL = NA, LT = FALSE, f.na.rm = TRUE, 
  ci = FALSE, alpha = 0.05)

ss.ca.cpk(x, LSL = NA, USL = NA, LT = FALSE, f.na.rm = TRUE, 
  ci = FALSE, alpha = 0.05)

ss.ca.z(x, LSL = NA, USL = NA, LT = FALSE, f.na.rm = TRUE)

Arguments

Value

A numeric value for the index, or a vector with the limits of the Confidence Interval

Author(s)

EL Cano

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Montgomery, DC (2008) Introduction to Statistical Quality Control (Sixth Edition). New York: Wiley&Sons

See Also

ss.study.ca

Examples

ss.ca.cp(ss.data.ca$Volume,740, 760)
ss.ca.cpk(ss.data.ca$Volume,740, 760)
ss.ca.z(ss.data.ca$Volume,740,760)

Control Charts

Description

Plot control charts

Usage

ss.cc(type, data, cdata, CTQ = names(data)[1], groups, climits, nsigmas = 3)

Arguments

Details

If control limits are provided, cdata is dismissed and a message is shown. If there are no control limits nor controlled data, the limits are computed using data.
Supported types of control charts:

• mrMoving Range

Value

A plot with the control chart, and a list with the following elements:

Note

We have created this function since the qAnalyst package has been removed from CRAN, and it was used in the "Six Sigma with R" book to plot moving average control charts.

Author(s)

EL Cano

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

See Also

ss.cc.constants

Examples

ss.cc("mr", ss.data.pb1, CTQ = "pb.humidity")
testout <- ss.data.pb1
testout[31,] <- list(31,17)
ss.cc("mr", testout, CTQ = "pb.humidity")

Functions to find out constants of the relative range distribution.

Description

These functions compute the constants d2, d3 and c4 to get estimators of the standard deviation to set control limits.

Usage

ss.cc.getd2(n = NA)

ss.cc.getd3(n = NA)

ss.cc.getc4(n = NA)

Arguments

Value

A numeric value for the constant.

Author(s)

EL Cano

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

See Also

ss.cc

Examples

ss.cc.getd2(20)
ss.cc.getd3(20)
ss.cc.getc4(20)

Cause and Effect Diagram

Description

Represents a Cause and Effect Diagram by cause group.

Usage

ss.ceDiag(
  effect,
  causes.gr,
  causes,
  main = "Six Sigma Cause-and-effect Diagram",
  sub,
  ss.col = c("#666666", "#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE", "#FFFFFF", "#000000",
    "#000000")
)

Arguments

Details

The default value for ss.col is c("#666666", "#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE", "#FFFFFF", "#000000", "#000000"), a grayscale style. You can pass any accepted colour string.

Value

A drawing of the causes and effect with "fish-bone" shape

Note

The cause and effect diagram is also known as "Ishikawa diagram", and has been widely used in Quality Management. It is one of the Seven Basic Tools of Quality.

Author(s)

EL Cano

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Wikipedia, https://en.wikipedia.org/wiki/Ishikawa_diagram

See Also

ss.pMap

Examples

effect <- "Flight Time"
causes.gr <- c("Operator", "Environment", "Tools", "Design", 
  "Raw.Material", "Measure.Tool")
causes <- vector(mode = "list", length = length(causes.gr))
causes[1] <- list(c("operator #1", "operator #2", "operator #3"))
causes[2] <- list(c("height", "cleaning"))
causes[3] <- list(c("scissors", "tape"))
causes[4] <- list(c("rotor.length", "rotor.width2", "paperclip"))
causes[5] <- list(c("thickness", "marks"))
causes[6] <- list(c("calibrate", "model"))
ss.ceDiag(effect, causes.gr, causes, sub = "Paper Helicopter Project")

Confidence Interval for the mean

Description

Computes a confidence interval for the mean of the variable (parameter or feature of the process), and prints the data, a histogram with a density line, the result of the Shapiro-Wilks normality test and a quantile-quantile plot.

Usage

ss.ci(
  x,
  sigma2 = NA,
  alpha = 0.05,
  data = NA,
  xname = "x",
  approx.z = FALSE,
  main = "Confidence Interval for the Mean",
  digits = 3,
  sub = "",
  ss.col = c("#666666", "#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE", "#FFFFFF", "#000000",
    "#000000")
)

Arguments

Details

When the population variance is known, or the size is greater than 30, it uses z statistic. Otherwise, it is uses t statistic.
If the sample size is lower than 30, a warning is displayed so as to verify normality.

Value

The confidence Interval.
A graph with the figures, the Shapiro-Wilks test, and a histogram.

Note

Thanks to the kind comments and suggestions from the anonymous reviewer of a tentative article.

Author(s)

EL Cano

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

See Also

ss.data.rr

Examples

ss.ci(len, data=ss.data.strings, alpha = 0.05,
  sub = "Guitar Strings Test | String Length", 
  xname = "Length")

Data for the batteries example

Description

This is a simulated data set of 18 measurements of the voltage of batteries using different voltmeters.

Usage

data(ss.data.batteries)

Format

A data frame with 18 observations on the following 4 variables.

voltmeter

a factor with levels 1 2

battery

a factor with levels 1 2 3

run

a factor with levels 1 2 3

voltage

a numeric vector

Note

This data set is used in chapter 5 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

See Also

ss.rr

Examples

data(ss.data.batteries)
summary(ss.data.batteries)
plot(voltage~voltmeter, data = ss.data.batteries)

Errors in bills data set

Description

This data set contains the number of errors detected in a set of bills and the name of the person in charge of the bill.

Usage

data("ss.data.bills")

Format

A data frame with 32 observations on the following 3 variables.

nbill

a numeric vector identifying a given bill

clerk

a character vector for the clerk responsible for the bill

errors

a character vector with the number of errors in the bill

Details

This data set illustrates concepts in the book “Quality Control with R”.

Source

Table 6.1 in the reference below.

References

Cano, E.L. and Moguerza, J.M. and Prieto Corcoba, M. (2015) Quality Control with R. An ISO Standards Approach. Springer.

Examples

data(ss.data.bills)
str(ss.data.bills) 
barplot(table(ss.data.bills$clerk), 
    main = "number of invoices")
aggregate(errors ~ clerk, ss.data.bills, sum)

Data for the bolts example

Description

A data frame with 50 observations of the diameter of the bolts manufactured in a production line.

Usage

data(ss.data.bolts)

Format

A data frame with 50 observations on the following variable.

diameter

a numeric vector with the diameter of the bolts

Note

This data set is used in chapter 4 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

See Also

ss.lfa

Examples

data(ss.data.bolts)
summary(ss.data.bolts)
hist(ss.data.bolts$diameter)

Data for a filling process in a winery

Description

The only field of the data is the volume measured in 20 bottles.

Usage

data(ss.data.ca)

Format

A data frame with 20 observations on the following variable.

Volume

a numeric vector (volume in cl

Note

This data set is used in chapter 7 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

See Also

ss.study.ca

Examples

data(ss.data.ca)
summary(ss.data.ca)
hist(ss.data.ca$Volume)

Pellets density

Description

This data set contains the density for 24 pellets.

Usage

data("ss.data.density")

Format

A vector with 24 items for the density of a set of pellets (gr/cm$^3$).

Details

This data set illustrates concepts in the book “Quality Control with R”. Note that, in the book, the vector named pdensity is directly created and then used in the examples.

Source

Table 1.2 in the reference below.

References

Cano, E.L. and Moguerza, J.M. and Prieto Corcoba, M. (2015) Quality Control with R. An ISO Standards Approach. Springer.

Examples

data(ss.data.density)
str(ss.data.density) 
summary(ss.data.density) 

Pizza dough example data

Description

Experimental data for the scores given to a set of pizza doughs.

Usage

data(ss.data.doe1)

Format

A data frame with 16 observations on the following 6 variables.

repl

Replication id

flour

Level of flour in the recipe (- +)

salt

Level of salt in the recipe (- +)

bakPow

Level of Baking Powder in the recipe (- +)

score

Scored assigned to the recipe

ord

Randomized order

Note

This data set is used in chapter 11 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

data(ss.data.doe1)
summary(ss.data.doe1)
lattice::bwplot(score ~ flour | salt + bakPow , 
 data = ss.data.doe1, 
 xlab = "Flour", 
 strip = function(..., style) lattice::strip.default(..., strip.names=c(TRUE,TRUE)))

Data for the pizza dough example (robust design)

Description

Experimental data for the scores given to a set of pizza doughs. Noise factors added for robust design.

Usage

data(ss.data.doe2)

Format

A data frame with 64 observations on the following 7 variables.

repl

Replication id

flour

Level of flour in the recipe (- +)

salt

Level of salt in the recipe (- +)

bakPow

Level of Baking Powder in the recipe (- +)

temp

Level of temperature in preparation (- +)

time

Level of time in preparation (- +)

score

Scored assigned to the recipe

Note

This data set is used in chapter 11 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

data(ss.data.doe2)
summary(ss.data.doe2)
lattice::bwplot(score ~ temp | time, data = ss.data.doe2)

Pastries data

Description

A data frame with 18 observations of the amount of the CTQ compound in some pastries from a bakery. There are two runs for each combination of two factors (laboratory and batch).

Usage

data(ss.data.pastries)

Format

A data frame with 18 observations on the following 4 variables.

lab

laboratory: a factor with levels 1 2 3

batch

batch: a factor with levels 1 2 3

run

identifies the run: a factor with levels 1 2

comp

proportion of the compound in the pastry: a numeric vector

Note

This data set is used in chapter 5 exercises of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

data(ss.data.pastries)
summary(ss.data.pastries)
lattice::xyplot(comp ~ lab | batch, data = ss.data.pastries)

Particle Boards Example - Individual Data

Description

Humidity of 30 raw material used to make particle boards for individual control chart.

Usage

data(ss.data.pb1)

Format

A data frame with 30 observations on the following 2 variables.

pb.group

Group id (distinct for each observation)

pb.humidity

Humidity of the particle board

Note

This data set is used in chapter 12 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

data(ss.data.pb1)
summary(ss.data.pb1)

Particle Boards Example - by Groups

Description

Humidity of 20 groups of size 5 of raw materials to make particle boards. For the mean and range control chart.

Usage

data(ss.data.pb2)

Format

A data frame with 100 observations on the following 2 variables.

pb.group

a numeric vector

pb.humidity

a numeric vector

Note

This data set is used in chapter 12 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

data(ss.data.pb2)
summary(ss.data.pb2)

Particle Boards Example - Attribute data

Description

Counts of raw materials stockouts during 22 weekdays in a month.

Usage

data(ss.data.pb3)

Format

A data frame with 22 observations on the following 3 variables.

day

Day id

stockouts

Number of stockouts

orders

Number of orders

Note

This data set is used in chapter 12 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

data(ss.data.pb3)
summary(ss.data.pb3)

Data for Practicle Boards Example - number of defects

Description

Number of defects detected in an order of particle boards.

Usage

data(ss.data.pb4)

Format

A data frame with 80 observations on the following 2 variables.

order

Order id

defects

Number of defects

Note

This data set is used in chapter 12 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

data(ss.data.pb4)
summary(ss.data.pb4)

Data set for the printer cartridge example

Description

This data set contains data from a simulated process of printer cartridge filling.

Usage

data(ss.data.pc)

Format

A data frame with 24 observations on the following 6 variables.

pc.col

a factor with levels C B for the colour

pc.filler

a factor with levels 1 2 3

pc.volume

a numeric vector

pc.density

a numeric vector

pc.batch

a numeric vector

pc.op

a factor with levels A B C D for the operator

Note

This data set is used in chapter 8 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

data(ss.data.pc)
summary(ss.data.pc)

Larger data set for the printer cartridges example

Description

This data set contains data from a simulated process of printer cartridges filling with complete replications.

Usage

data(ss.data.pc.big)

Format

A data frame with 72 observations on the following 5 variables,

filler

a factor with levels 1 2 3

batch

a factor with levels 1 2 3 4

col

a factor with levels B C

operator

a factor with levels 1 2 3

volume

a numeric vector

Note

This data set is used in chapter 8 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

data(ss.data.pc.big)
summary(ss.data.pc.big)

Data set for the printer cartridge example, by region

Description

This data set contains data from a simulated process of printer cartridge filling. The dataframe contains defects by region of each type of cartridge.

Usage

data(ss.data.pc.r)

Format

A data frame with 5 observations on the following 4 variables.

pc.regions

a factor with levels region.1 region.2 region.3 region.4 region.5

pc.def.a

a numeric vector for defects type A

pc.def.b

a numeric vector for defects type B

pc.def

a numeric vector for total defects

Note

This data set is used in chapter 8 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

data(ss.data.pc.r)
summary(ss.data.pc.r)

Gage R&R data

Description

Example data for Measure phase of the Six Sigma methodology.

Usage

data(ss.data.rr)

Format

A data frame with 27 observations on the following 5 variables.

prototype

a factor with levels prot #1 prot #2 prot #3

operator

a factor with levels op #1 op #2 op #3

run

a factor with levels run #1 run #2 run #3

time1

a numeric vector

time2

a numeric vector

Note

This data set is used in chapter 5 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

data(ss.data.rr)
summary(ss.data.rr)

Data set for the Guitar Strings example

Description

This data set contains data from a simulated process of guitar strings production.

Usage

data(ss.data.strings)

Format

A data frame with 120 observations on the following 6 variables.

id

a numeric vector

type

a factor with levels A5 B2 D4 E1 E6 G3

res

a numeric vector for resistance

len

a numeric vector for length

sound

a numeric vector for

power

a numeric vector

Note

This data set is used in chapter 10 of the book “Six Sigma with R” (see References).

Source

See references.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andrés. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

data(ss.data.strings)
summary(ss.data.strings)

Metal Plates Thickness

Description

This data set contains the thickness and additional data for 24 metal plates.

Usage

data("ss.data.thickness")

Format

A data frame with 24 observations on the following 5 variables.

thickness

a numeric vector with the thickness (in)

day

a factor with the day (two days)

shift

a factor with the shift (two shifts)

dayshift

a factor with the day-shift combination

position

a factor with the position of the thickness with respect to the nominal value of 0.75 in

Details

This data set illustrates concepts in the book “Quality Control with R”. Note that, in the book, the data set is named plates and it is created sequentially throughout the examples.

Source

Table 5.1 in the reference below.

References

Cano, E.L. and Moguerza, J.M. and Prieto Corcoba, M. (2015) Quality Control with R. An ISO Standards Approach. Springer.

Examples

data(ss.data.thickness)
str(ss.data.thickness) 
lattice::bwplot(thickness ~ shift | day,
    data = ss.data.thickness)

Metal Plates thickness (extended)

Description

This data set contains the thickness and additional data for 84 metal plates.

Usage

data("ss.data.thickness2")

Format

A data frame with 84 observations on the following 5 variables.

day

a factor with the day (seven days)

shift

a factor with the shift (two shifts)

thickness

a numeric vector with the thickness (in)

ushift

a factor with the day-shift combination

flaws

an integer vector with the number of flaws on the surface of sampled plates

Details

This data set illustrates concepts in the book “Quality Control with R”.

Source

Examples 8.1 and 9.9 in the reference below.

References

Cano, E.L. and Moguerza, J.M. and Prieto Corcoba, M. (2015) Quality Control with R. An ISO Standards Approach. Springer.

Examples

data(ss.data.thickness2)
str(ss.data.thickness2) 
lattice::dotplot(thickness ~ shift | day,
    data = ss.data.thickness2,
    layout = c(7, 1))

Woodboard location for profiles

Description

This data set contains the 500 locations at which the density of a 0.5in-thick engineered woodboard is measured, i.e., 0.001 in apart

Usage

data("ss.data.wbx")

Format

A vector with 500 items for the locations (in).

Details

This data set illustrates concepts in the book “Quality Control with R”. This data set should be used along with the ss.data.wby data set.

Source

Example 10.1 in the reference below. It is a variation of the one introduced by Walker (2002).

References

Cano, E.L. and Moguerza, J.M. and Prieto Corcoba, M. (2015) Quality Control with R. An ISO Standards Approach. Springer.

Walker, E. amd Wright, W (2002) Comparing curves with additive models. J. Qual. Technol. 34(1), 118–129

See Also

ss.data.wby

Examples

data(ss.data.wbx)
data(ss.data.wby)
plotProfiles(profiles = ss.data.wby,
    x = ss.data.wbx)

Woodboard profiles

Description

This data set contains 50 profiles corresponding to the density measurements of 50 0.5in-thick engineered woodboard, measured in 500 locations.

Usage

data("ss.data.wby")

Format

A matrix with 500 rows (locations) and 50 columns (woodboard).

Details

This data set illustrates concepts in the book “Quality Control with R”. This data set should be used along with the ss.data.wbx data set.

Source

Example 10.1 in the reference below. It is a variation of the one introduced by Walker (2002).

References

Cano, E.L. and Moguerza, J.M. and Prieto Corcoba, M. (2015) Quality Control with R. An ISO Standards Approach. Springer.

Walker, E. amd Wright, W (2002) Comparing curves with additive models. J. Qual. Technol. 34(1), 118–129

See Also

ss.data.wbx

Examples

data(ss.data.wbx)
data(ss.data.wby)
plotProfiles(profiles = ss.data.wby,
    x = ss.data.wbx)

Creates a pdf file with the design of the Paper Helicopter

Description

The pdf file contains a template with lines and indications to build the paper helicopter described in many SixSigma publications.

Usage

ss.heli()

Details

The pdf file must be printed in A4 paper, without adjusting size to paper.

Value

No value is returned. A pdf file is saved in the working directory

Note

See the vignette("HelicopterInstructions") to see assembling instructions.

Author(s)

EL Cano

References

George Box. Teaching engineers experimental design with a paper helicopter. Quality Engineering, 4(3):453–459, 1992.

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Examples

## Not run: 
## ss.heli()
vignette("HelicopterInstructions")

## End(Not run)

Evaluates the Loss Function for a process.

Description

The quality loss function is one of the tools of the Six Sigma methodology. The function assigns a cost to an observed value, that is larger as far as it is from the target.

Usage

ss.lf(lfa.Y1, lfa.Delta, lfa.Y0, lfa.L0)

Arguments

Value

Author(s)

EL Cano

References

Taguchi G, Chowdhury S,Wu Y (2005) Taguchi's quality engineering handbook. John Wiley

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

See Also

ss.lfa

Examples

#Example bolts: evaluate LF at 10.5 if Target=10, Tolerance=0.5, L_0=0.001
ss.lf(10.5, 0.5, 10, 0.001)

Loss Function Analysis

Description

This function performs a Quality Loss Function Analysis, based in the Taguchi Loss Function for "Nominal-the-Best" characteristics.

Usage

ss.lfa(
  lfa.data,
  lfa.ctq,
  lfa.Delta,
  lfa.Y0,
  lfa.L0,
  lfa.size = NA,
  lfa.output = "both",
  lfa.sub = "Six Sigma Project"
)

Arguments

Details

lfa.output can take the values "text", "plot" or "both".

Value

Note

For smaller-the-better characteristics, the target should be zero (lfa.Y0 = 0). For larger-the-better characteristics, the target should be infinity (lfa.Y0 = Inf).

Author(s)

EL Cano

References

Taguchi G, Chowdhury S,Wu Y (2005) Taguchi's quality engineering handbook. John Wiley

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

See Also

ss.lf, ss.data.bolts.

Examples

ss.lfa(ss.data.bolts, "diameter", 0.5, 10, 0.001, 
		lfa.sub = "10 mm. Bolts Project", 
		lfa.size = 100000, lfa.output = "both")

Process Map

Description

This function takes information about the process we want to represent and draw the Process Map, with its X's, x's, Y's and y's in each step of the process

Usage

ss.pMap(
  steps,
  inputs.overall,
  outputs.overall,
  input.output,
  x.parameters,
  y.features,
  main = "Six Sigma Process Map",
  sub,
  ss.col = c("#666666", "#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE", "#FFFFFF", "#000000",
    "#000000")
)

Arguments

Details

The type of the x parameters and y features can be: C(controllable), N(noise), Cr(Critical), P(Procedure). The default value for ss.col is c("#666666", "#BBBBBB", "#CCCCCC", "#DDDDDD", "#EEEEEE", "#FFFFFF", "#000000", "#000000") a grayscale style.You can pass any accepted color string.

Value

A graphic representation of the Map Process.

Note

The process map is the starting point for a Six Sigma Project, and it is very important to find out who the x's and y'x are.

Author(s)

EL Cano

References

https://en.wikipedia.org/wiki/Business_Process_Mapping

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

See Also

ss.ceDiag

Examples

inputs.overall<-c("operators", "tools", "raw material", "facilities")
outputs.overall<-c("helicopter")
steps<-c("INSPECTION", "ASSEMBLY", "TEST", "LABELING")
#Inputs of process "i" are inputs of process "i+1"
input.output<-vector(mode="list",length=length(steps))
input.output[1]<-list(c("sheets", "..."))
input.output[2]<-list(c("sheets"))
input.output[3]<-list(c("helicopter"))
input.output[4]<-list(c("helicopter"))

#Parameters of each process
x.parameters<-vector(mode="list",length=length(steps))
x.parameters[1]<-list(c(list(c("width", "NC")),list(c("operator", "C")),
list(c("Measure pattern", "P")), list(c("discard", "P"))))
x.parameters[2]<-list(c(list(c("operator", "C")),list(c("cut", "P")),
list(c("fix", "P")), list(c("rotor.width", "C")),list(c("rotor.length",
"C")), list(c("paperclip", "C")), list(c("tape", "C"))))
x.parameters[3]<-list(c(list(c("operator", "C")),list(c("throw", "P")),
list(c("discard", "P")), list(c("environment", "N"))))
x.parameters[4]<-list(c(list(c("operator", "C")),list(c("label", "P"))))
x.parameters

#Features of each process
y.features<-vector(mode="list",length=length(steps))
y.features[1]<-list(c(list(c("ok", "Cr"))))
y.features[2]<-list(c(list(c("weight", "Cr"))))
y.features[3]<-list(c(list(c("time", "Cr"))))
y.features[4]<-list(c(list(c("label", "Cr"))))
y.features

ss.pMap(steps, inputs.overall, outputs.overall,
        input.output, x.parameters, y.features, 
        sub="Paper Helicopter Project")

Gage R & R (Measurement System Assessment)

Description

Performs Gage R&R analysis for the assessment of the measurement system of a process. Related to the Measure phase of the DMAIC strategy of Six Sigma.

Usage

ss.rr(
  var,
  part,
  appr,
  lsl = NA,
  usl = NA,
  sigma = 6,
  tolerance = usl - lsl,
  data,
  main = "Six Sigma Gage R&R Study",
  sub = "",
  alphaLim = 0.05,
  errorTerm = "interaction",
  digits = 4,
  method = "crossed",
  print_plot = TRUE,
  signifstars = FALSE
)

Arguments

Details

Performs an R&R study for the measured variable, taking into account part and appraiser factors. It outputs the sources of Variability, and six graphs: bar chart with the sources of Variability, plots by appraiser, part and interaction and x-bar and R control charts.

Value

Analysis of Variance Table/s. Variance composition and %Study Var. Graphics.

Note

The F test for the main effects in the ANOVA table is usually made taken the operator/appraisal interaction as the error term (repeated measures model), thereby computing F as $MS_factor/MS_interaction$, e.g. in appendix A of AIAG MSA manual, in Montgomery (2009) and by statistical software such as Minitab. However, in the example provided in page 127 of the AIAG MSA Manual, the F test is performed as $MS_factor/MS_equipment$, i.e., repeatability. Thus, since version 0.9-3 of the SixSigma package, a new argument errorTerm controls which term should be used as error Term, one of "interaction", "repeatability".

Argument alphaLim is used as upper limit to use the full model, i.e., with interaction. Above this value for the interaction effect, the ANOVA table without the interaction effect is also obtained, and the variance components are computed pooling the interaction term with the repeatibility.

Tolerance can be calculaten from usl and lsl values or specified by hand.

The type of analysis to perform can be specified with the parameter method, "crossed" or "nested". Be sure to select the correct one and to have the data prepare for such type of analysis. If you don't know wich one is for you check it before. It is really important to perform the correct one. Otherwise results have no sense.

Author(s)

EL Cano with contributions by Kevin C Limburg

References

Automotive Industry Action Group. (2010). Measurement Systems Analysis (Fourth Edition). AIAG.

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Montgomery, D. C. (2009). Introduction to Statistical Quality Control (Sixth Edition ed.). New York: Wiley & Sons, Inc.

See Also

ss.data.rr

Examples

ss.rr(time1, prototype, operator, data = ss.data.rr, 
	sub = "Six Sigma Paper Helicopter Project", 
	alphaLim = 0.05,
	errorTerm = "interaction",
	lsl = 0.7,
	usl = 1.8,
	method = "crossed")

Graphs and figures for a Capability Study

Description

Plots a Histogram with density lines about the data of a process. Check normality with qqplot and normality tests. Shows the Specification Limits and the Capability Indices.

Usage

ss.study.ca(
  xST,
  xLT = NA,
  LSL = NA,
  USL = NA,
  Target = NA,
  alpha = 0.05,
  f.na.rm = TRUE,
  f.main = "Six Sigma Capability Analysis Study",
  f.sub = "",
  f.colours = c("#4682B4", "#d1d1e0", "#000000", "#A2CD5A", "#D1EEEE", "#FFFFFF",
    "#000000", "#000000")
)

Arguments

Value

Figures and plot for Capability Analysis

Note

The argument f.colours takes a vector of colours for the graphical outputs. The order of the elements are, first the colour for histogram bars, then Density ST lines, Density LT lines, Target, and Specification limits. It can be partially specified.

Author(s)

Main author: Emilio L. Cano. Contributions by Manu Alfaro.

References

Cano, Emilio L., Moguerza, Javier M. and Redchuk, Andres. 2012. Six Sigma with R. Statistical Engineering for Process Improvement, Use R!, vol. 36. Springer, New York. https://link.springer.com/book/10.1007/978-1-4614-3652-2.

Montgomery, DC (2008) Introduction to Statistical Quality Control (Sixth Edition). New York: Wiley&Sons

See Also

ss.ca.cp

Examples

 ss.study.ca(ss.data.ca$Volume, rnorm(40, 753, 3), 
		LSL = 740, USL = 760, T = 750, alpha = 0.05, 
 			f.sub = "Winery Project")
 			
 ss.study.ca(ss.data.ca$Volume, rnorm(40, 753, 3), 
		LSL = 740, USL = 760, T = 750, alpha = 0.05, 
 			f.sub = "Winery Project", 
 			f.colours = c("#990000", "#007700", "#002299"))