adas.utils: Design of Experiments and Factorial Plans Utilities

Description

A number of functions to create and analyze factorial plans according to the Design of Experiments (DoE) approach, with the addition of some utility function to perform some statistical analyses. DoE approach follows the approach in "Design and Analysis of Experiments" by Douglas C. Montgomery (2019, ISBN:978-1-119-49244-3). The package also provides utilities used in the course "Analysis of Data and Statistics" at the University of Trento, Italy.

Author(s)

Maintainer: Paolo Bosetti paolo.bosetti@unitn.it

Pipe operator

Description

See magrittr::%>% for details.

Usage

lhs %>% rhs

Arguments

Value

The result of calling rhs(lhs).

Convert an alias matrix to a tibble

Description

Given an alias matrix, this function returns a tidy tibble of the alias structures, with the added generator column containing the generator (i.e. right-hand side) of the defining relationship that generates each alias.

Usage

## S3 method for class 'alias.matrix'
as_tibble(x, ..., compact = TRUE)

Arguments

Value

a tibble representation of the alias matrix

Examples

tibble::as_tibble(fp_alias_matrix(~A*B*C, ~B*C*D))

Battery experiment data

Description

Battery life in hour of a factorial experiment with 2 factors and 3 levels each. Factors are:

Usage

battery

Format

A data frame with 36 rows and 6 columns

Details

• Temperature: of the battery during the discharge experiment

• Material: Plate material for the battery

Other columns are:

• StandardOrder: Yate's standard order

• RunOrder: randomized order, in which tests have been executed

• Repeat: repeat number

• Response: battery life in hours

References

Douglas C. Montgomery, "Design and Analysis of Experiments", 8th edition, Wiley, 2019

Central Composite Design Experiment Yields

Description

Yield data for a two factor CCD experiment

Usage

ccd_experiment_yield

Format

A list with three vectors:

• base: the yield for a 2^2 factorial design, replicated 3 times

• center: the yield for the center points, replicated 4 times

• axial: the yield for the axial points, replicated 2 times

Chauvenet's criterion

Description

Applies the Chauvenet's criterion to a sample, identifying a possible outlier.

Usage

chauvenet(x, threshold = 0.5)

Arguments

Value

an object of class chauvenet with the following components:

sample

the name of the sample

s0

the maximum difference

index

the index of the suspect outlier

value

the value of the suspect outlier

expected

the expected frequency of the suspect outlier

reject

a logical value indicating whether the suspect outlier should be rejected

Examples

x <- rnorm(100)
chauvenet(x)
chauvenet(x, threshold=0.1)

Cotton yarn experiment data

Description

Yarn tensile strength in a completely randomized experiment with 5 different levels of cotton fiber.

Usage

cotton

Format

A data frame with 25 rows and 3 columns. Columns represent:

• Run: run order

• Cotton: cotton content in mass percentage

• Strength: yarn tensile strength in N

References

Douglas C. Montgomery, "Design and Analysis of Experiments", 8th edition, Wiley, 2019

Daniel's plot (half-normal)

Description

Given a non-replicated model of a factorial plan, this function provides a half-normal plot of the effects of the model, labeling the main n effects.

Usage

daniel_plot_hn(model, ...)

Arguments

Value

a half-normal plot (GGPlot2 object) with the effects of the model

See Also

gghalfnorm::gghalfnorm()

Examples

daniel_plot_hn(lm(Y~A*B*C*D, data=filtration))

Daniel's plot (quantile-quantile)

Description

Given a non-replicated model of a factorial plan, this function provides a QQ plot of the effects of the model, labeling all the effects.

Usage

daniel_plot_qq(model, alpha = 0.5, xlim = c(-3, 3))

Arguments

Value

a QQ plot (GGPlot2 object) with the effects of the model

Examples

daniel_plot_qq(lm(Y~A*B*C*D, data=filtration))

Examples URL

Description

Provides the URL for the desired example data, so that it can be more easily downloaded.

Usage

examples_url(example)

Arguments

Value

the full URL for the desired example

Examples

examples_url("battery.dat") |> read.table(header=TRUE)

Expand a formula

Description

Expand a formula

Usage

expand_formula(f)

Arguments

Value

a formula after expansion, e.g. Y ~ A + B becomes Y ~ A + B + A:B

Examples

expand_formula(Y ~ (A + B)^3)

Filtration data

Description

Non-replicated factorial plan for a slurry filtration process.

Usage

filtration

Format

Factors are:

• A: Temperature

• B: Pressure

• C: Concentration of solid phase

• D: Agitation speed

The yield is in column Y and represents the filtration speed

Add factor names to a design matrix

Description

Store factor names in the factorial.plan object, as a list within the factor.names attribute.

Usage

fp_add_names(dm, ...)

Arguments

Value

the design matrix with the named factors.

Examples

fp_design_matrix(3, rep=2) %>%
  fp_add_names(A="Temperature", B="Pressure")

Scale factors levels

Description

This function allows to add columns to a design matrix with scaled factor, i.e. factors reported in real units rather in coded units (e.g. -1, 1).

Usage

fp_add_scale(dm, ..., suffix = "_s")

Arguments

Value

the design matrix with the scaled factors.

Examples

fp_design_matrix(3, rep=2) %>%
  fp_add_scale(A=c(10, 30), B=c(0, 1), suffix=".scaled")

Build the alias matrix

Description

Given a list of formulas (defining relationships), this function returns a matrix of all possible aliases.

Usage

fp_alias_matrix(...)

Arguments

Details

It is also possible to pass a fractional factorial plan, in which case the defining relationships will be extracted from it.

Value

a square matrix: each cell is 0 if there is no alias, or an integer representing the index of the generator that produced that alias in the list of generators.

See Also

fp_fraction()

Examples

# with formulas:
fp_alias_matrix(~A*B*C, ~B*C*D)

# with a fractional factorial plan:
fp_design_matrix(5) %>%
  fp_fraction(~A*B*C*D) %>%
  fp_fraction(~B*C*D*E) %>%
  fp_alias_matrix() %>%
  plot()

Return a list of all defining relationships

Description

Given two or more independent refining relationships, represented as one side formulas,, this function returns a list of all possible defining relationships, including the dependent ones.

Usage

fp_all_drs(...)

Arguments

Details

Defining relationships are represented as one side formulas, e.g. $I=ABC$ becomes ~A*B*C.

Value

a list of formulas.

Examples

fp_all_drs(~A*B*C, ~B*C*D)

Augment to a central composite design

Description

Adds the axial points to a $2^n$ centered factorial plan.

Usage

fp_augment_axial(dm, rep = 1)

Arguments

Value

A central composite design (a factorial.plan object).

Examples

fp_design_matrix(3) %>%
  fp_augment_center(rep=4) %>%
  fp_augment_axial()

Augment to a centered design

Description

Add the central points to an existing $2^n$ factorial plan.

Usage

fp_augment_center(dm, rep = 5)

Arguments

Value

A central composite design (a factorial.plan object).

Examples

fp_design_matrix(3) %>%
  fp_augment_center()

Factorial Plan Design Matrix

Description

Builds a design matrix from a one side formula or a number of factors.

Usage

fp_design_matrix(arg, rep = 1, levels = c(-1, 1))

Arguments

Details

Defining relationships are represented as one side formulas, e.g. $I=ABC$ becomes ~A*B*C.

Value

A design matrix: a subclass of a tibble of class factorial.plan. The class has the following attributes:

def.rel

The defining relationship (a formula).

generators

The list of generators (formulas) if the factorial plan is fractional.

fraction

The list of fractions (character vectors) if the factorial plan is fractional.

levels

The levels of the factors (all equal), in coded units.

scales

A list: for each factor, a vector of two values corresponding to the extreme values in coded units.

Examples

fp_design_matrix(3, rep=2, levels=c("-", "+"))

Factorial Plan effect names from a formula

Description

Returns the effect names from a formula, according to Yates' convention.

Usage

fp_effect_names(arg)

Arguments

Details

Defining relationships are represented as one side formulas, e.g. $I=ABC$ becomes ~A*B*C.

Value

An ordered factor with the effect names.

Examples

fp_effect_names(~A*B*C)

Reduce a Factorial Plan by 1/2 Fraction

Description

Reduce a Factorial Plan by 1/2 Fraction

Usage

fp_fraction(dm, formula, remove = TRUE)

Arguments

Value

A reduced factorial plan table (a factorial.plan object).

See Also

fp_design_matrix()

Examples

# build a 2^5-2 fractional factorial plan with defining relationships
#   I=ABCD and I=BCDE
fp_design_matrix(5) %>%
  fp_fraction(~A*B*C*D) %>%
  fp_fraction(~B*C*D*E)

Given a generator, find the alias

Description

Given a generator and an effect, this function returns the alias.

Usage

fp_gen2alias(generator, effect)

Arguments

Details

Generators and aliases are strings of capital letters.

Value

An effect (string).

Examples

fp_gen2alias("ABCD", "BD")

Factorial plan info

Description

Print information about the factorial plan.

Usage

fp_info(x, file = "", comment = "")

Arguments

Value

No return value, just prints the fp information.

Examples

fp_design_matrix(3, rep=2) %>%
  fp_info()

Return a merged defining relationship

Description

This function, given one or more independent refining relationships, returns the most complete relationship, i.e. that which includes all the factors.

Usage

fp_merge_drs(f1, ...)

Arguments

Details

Defining relationships are represented as one side formulas, e.g. $I=ABC$ becomes ~A*B*C.

Value

a formula.

Examples

fp_merge_drs(~A*B*C, ~B*C*D)

Load a design matrix from a CSV file

Description

Load from a CSV file the design matrix that has previously been saved with fp_write_csv(). It is an error if the loaded data frame has different dimensions or column names than the original design matrix.

Usage

fp_read_csv(dm, file, type = c(1, 2), yield = "Y", comment = "#")

Arguments

Details

Note that the design matrix is sorted by the StdOrder column after loading.

Value

the design matrix with the new values.

See Also

fp_write_csv()

Factorial Plan List of Treatments

Description

Builds a list of treatments from a formula, or from a number of factors.

Usage

fp_treatments(arg)

Arguments

Details

Defining relationships are represented as one side formulas, e.g. $I=ABC$ becomes ~A*B*C.

Value

A list of treatments (character vector).

Examples

fp_treatments(3)

Save a design matrix to a CSV file

Description

Writes the design matrix to a CSV file, with a timestamp and comment lines.

Usage

fp_write_csv(dm, file, comment = "# ", timestamp = TRUE, type = c(1, 2), ...)

Arguments

Details

Note that the design matrix is saved in the same order of the RunOrder column, i.e. random.

Value

Invisibly return the design matrix, unchanged, for further piping.

ggTukey

Description

This is a generic function for plotting Tukey's HSD test via GGplot2.

Usage

ggTukey(obj, ...)

Arguments

Value

a GGPlot2 object

ggTukey for TukeyHSD

Description

Plot Tukey's HSD test via GGplot2.

Usage

## S3 method for class 'TukeyHSD'
ggTukey(obj, which = 1, ...)

Arguments

Value

a GGPlot2 object

See Also

TukeyHSD() ggTukey.data.frame() ggTukey.TukeyHSD()]]

Examples

library(tidyverse)
cotton %>%
  aov(Strength~Cotton, data=.) %>%
  TukeyHSD() %>%
  ggTukey()

ggTukey for data.frame

Description

ggTukey for data.frame

Usage

## S3 method for class 'data.frame'
ggTukey(obj, formula, which = 1, splt = NULL, ...)

Arguments

Value

a GGPlot2 object

Examples

library(tidyverse)
battery %>%
  ggTukey(Response~Material, splt=~Temperature, conf.level=0.99)

Normal probability plot

Description

Normal probability plot

Usage

normplot(data, var, breaks = seq(0.1, 0.9, 0.1), linecolor = "red")

Arguments

Value

a normal probability plot (GGPlot2 object)

Examples

library(tibble)
df <- tibble(
  xn = rnorm(100, mean=20, sd=5),
  xu = runif(100, min=0, max=40)
)

df %>% normplot(xn)
df %>% normplot(xu)

Pareto's chart

Description

This is a generic function for Pareto's chart.

Usage

pareto_chart(obj, ...)

Arguments

Value

a Pareto chart of the effects of the model

See Also

pareto_chart.data.frame() pareto_chart.lm()

Examples

# For a data frame:
library(tibble)
set.seed(1)
tibble(
  val=rnorm(10, sd=5),
  cat=LETTERS[1:length(val)]
  ) %>%
  pareto_chart(labels=cat, values=val)

# For a linear model:
pareto_chart(lm(Y~A*B*C*D, data=filtration))

Pareto's chart

Description

Create a Pareto chart for a data frame.

Usage

## S3 method for class 'data.frame'
pareto_chart(obj, labels, values, ...)

Arguments

Value

a Pareto chart (GGPlot2 object) of the data frame

Invisibly returns a data frame with the absolute values of the data frame, their sign, and the cumulative value.

Examples

library(tibble)
set.seed(1)
tibble(
  val=rnorm(10, sd=5),
  cat=LETTERS[1:length(val)]
  ) %>%
  pareto_chart(labels=cat, values=val)

Pareto's chart

Description

Creates a Pareto chart for the effects of a linear model.

Usage

## S3 method for class 'lm'
pareto_chart(obj, ...)

Arguments

Value

a Pareto chart (GGPlot2 object) of the effects of the model

Invisibly returns a data frame with the absolute effects of the model, their sign, and the cumulative effect.

Examples

pareto_chart(lm(Y~A*B*C*D, data=filtration))

Plot the alias matrix

Description

Produces a tile plot of the alias matrix.

Usage

## S3 method for class 'alias.matrix'
plot(x, ..., compact = TRUE)

Arguments

Value

a ggplot object.

Examples

fp_alias_matrix(~A*B*C, ~B*C*D) %>%
  plot()