paper.md
In ComtekAdvancedStructures/cmstatr: Statistical Methods for Composite Material Data
affiliations:
- index: 1
name: 'Comtek Advanced Structures, Ltd.'
authors:
- affiliation: 1
name: Stefan Kloppenborg
orcid: '0000-0002-1908-5214'
bibliography: 'paper.bib'
date: '6/24/2020'
output:
md_document:
pandoc_args: '--atx-headers'
preserve_yaml: True
variant: markdown
pdf_document: default
tags:
- R
- statistics
- composite materials
- material science
title: |
cmstatr: An R Package for Statistical Analysis of Composite Material
Data
Summary
Strength data for composite materials used in aerospace applications,
such as carbon fiber and fiberglass reinforced composites, are normally
analyzed using statistical methods because of the inherent variability
in the constituent materials and in the processing. The design standards
for civil aviation requires that the probability of structural failure
due to this variability must be minimized, and to do so, the designer
must use what are called "Design Values" for each material in stress
analyses and ensure they exceed the actual stresses experienced by those
materials in service. Design Values are set based on the one-sided lower
confidence bound of the material strength. For some types of structure,
the content of this lower confidence bound is $99\%$ with a confidence
level of $95\%$; in this case, the confidence bound is referred to as
A-Basis. For some other types of structure, the content of the lower
confidence bound is instead $90\%$ with a confidence level of $95\%$; in
this case, the confidence bound is referred to as B-Basis. The
statistical methods for calculating these basis values are outlined in
Composite Materials Handbook, Volume 1, Revision G, or CMH-17-1G in
short [@CMH171G]. The use of these methods is widely accepted by
industry and civil aviation regulators.
Design Values are often adjusted to account for anticipated in-service
damage and other factors, however those adjustments are outside the
scope of the present software package.
For a detailed discussion of the theory and applications of tolerance
bounds, the reader is referred to @Meeker_Hahn_Escobar_2017 or
@Krishnamoorthy_Mathew_2008.
Currently, many users use MS Excel spreadsheets to perform these
analyses. The MS Excel spreadsheets typically used, such as STAT-17
[@STAT-17], ASAP [@Raju_Tomblin_2008] and CMH17-STATS
[@CMH17-STATS], use password-protected VBA macros to perform the
computations. As such, the code cannot be audited by the user. cmstatr
is an R package that addresses this issue by implementing the same
statistical analysis techniques found in CMH-17-1G in an open-source
environment.
Statement of Need
The purpose of cmstatr is to:
- Provide a consistent user interface for computing A- and B-Basis
values and performing the related diagnostic tests in the
R
programming environment
- Allow auditing of the code used to compute A- and B-Basis values,
and performing the related diagnostic tests
- Enable users to automate computation workflows or to perform
simulation studies
Implementation Goals
cmstatr aims give a consistent interface for the user. Most functions
are written to work with the tidyverse [@tidyverse] and most functions
have similar argument lists. The intent is to make the package easy to
learn and use.
The implementation of cmstatr also aims to avoid the use of lookup
tables that are prevalent in calculation spreadsheets and minimize the
use of approximations. While this decision leads to increased
computation time, the typically small data sets (tens to hundreds of
observations) associated with composite material test data and the speed
of modern computers make this practical for interactive programming.
Example Usage
Normally, to use cmstatr the user will load cmstatr itself as well
as the tidyverse package.
library(cmstatr)
library(tidyverse)
cmstatr contains some example data sets, which can be used to
demonstrate the features of the package. One of those data sets ---
carbon.fabric.2 --- will be used in the following example. This data
set contains results from several mechanical tests of a typical
composite material, and contains the typical measurements obtained from
a test lab. In the following examples, results from tension testing in
the warp fiber direction (WT) will be used. Part of this data set is
shown below.
carbon.fabric.2 %>%
filter(test == "WT") %>%
head(10)
## test condition batch thickness nplies strength modulus failure_mode
## 1 WT CTD A 0.112 14 142.817 9.285 LAT
## 2 WT CTD A 0.113 14 135.901 9.133 LAT
## 3 WT CTD A 0.113 14 132.511 9.253 LAT
## 4 WT CTD A 0.112 14 135.586 9.150 LAB
## 5 WT CTD A 0.113 14 125.145 9.270 LAB
## 6 WT CTD A 0.113 14 135.203 9.189 LGM
## 7 WT CTD A 0.113 14 128.547 9.088 LAB
## 8 WT CTD B 0.113 14 127.709 9.199 LGM
## 9 WT CTD B 0.113 14 127.074 9.058 LGM
## 10 WT CTD B 0.114 14 126.879 9.306 LGM
One common task is to calculate B-Basis values. There are several
statistical methods for doing so, depending on the distribution of the
data. The single-point basis functions automatically perform the
following diagnostic tests:
- the maximum normed residual test for outliers within a batch
[@CMH171G],
- the Anderson--Darling k-Sample test to check if batches are drawn
from the same (unspecified) distribution [@Scholz_Stephens_1987],
- the maximum normed residual test for outliers within the data, and
- the Anderson--Darling test for a particular probability distribution
[@Lawless_1982].
Assuming that the data from the warp tension (WT) tested at
elevated-temperature/wet condition (ETW) follows a normal distribution,
then this can be done using the function. Note that all of the functions
in cmstatr that compute basis values default to computing tolerance
bounds with a content of $p=0.9$ and a confidence of $conf=0.95$, or
B-Basis.
carbon.fabric.2 %>%
filter(test == "WT") %>%
filter(condition == "ETW") %>%
basis_normal(strength, batch)
## Warning: `anderson_darling_normal` failed: Anderson-Darling test rejects
## hypothesis that data is drawn from a normal distribution
##
## Call:
## basis_normal(data = ., x = strength, batch = batch)
##
## Distribution: Normal ( n = 18 )
## The following diagnostic tests failed:
## `anderson_darling_normal`
## B-Basis: ( p = 0.9 , conf = 0.95 )
## 122.9315
All of the various basis functions perform diagnostic tests for each of
the statistical tests mentioned above. If any of the diagnostic tests
failed, a warning is shown and the test failure is also recorded in the
returned object (and shown in that object's print method). In the
example above, the output shows that the Anderson--Darling test for
normality [@Lawless_1982] rejects the hypothesis that the data is drawn
from a normal distribution.
Two non-parametric basis calculations, based on @Guenther_1970 and
@Vangel_1994 are also implemented in cmstatr. These functions perform
the same diagnostic tests, but omit the Anderson--Darling test for a
particular distribution.
The diagnostic test can be run directly using cmstatr as well. For
example, the failed diagnostic test above can be run as follows:
carbon.fabric.2 %>%
filter(test == "WT") %>%
filter(condition == "ETW") %>%
anderson_darling_normal(strength)
##
## Call:
## anderson_darling_normal(data = ., x = strength)
##
## Distribution: Normal ( n = 18 )
## Test statistic: A = 0.9381665
## OSL (p-value): 0.01103075 (assuming unknown parameters)
## Conclusion: Sample is not drawn from a Normal distribution ( alpha = 0.05 )
If the failure of a diagnostic test is decided to be acceptable, the
test result can be overridden to hide the warning in the basis function
output:
carbon.fabric.2 %>%
filter(test == "WT") %>%
filter(condition == "ETW") %>%
basis_normal(strength, batch, override = c("anderson_darling_normal"))
##
## Call:
## basis_normal(data = ., x = strength, batch = batch, override = c("anderson_darling_normal"))
##
## Distribution: Normal ( n = 18 )
## The following diagnostic tests were overridden:
## `anderson_darling_normal`
## B-Basis: ( p = 0.9 , conf = 0.95 )
## 122.9315
cmstatr also provides functions for calculating basis values from data
pooled across multiple testing environments, as recommended by
[@CMH171G]. There are two methods of pooling: both calculate a measure
of global variation from the data in all tested environmental
conditions, then they calculate a basis value for each condition using
the measure of the global variation and the individual mean values of
each condition. The two methods of pooling have different underlying
assumptions and hence the data must pass a different set diagnostic
tests for each of the two functions.
Validation and Comparison With Existing Tools
Where possible, cmstatr has been verified against the examples given
in the articles in which the statistical methods were published. Unit
tests have been written so that this verification is re-checked
routinely to prevent unintended regressions. Agreement between cmstatr
and the examples in the original articles is within the expected numeric
accuracy.
cmstatr has also been verified against existing software, such as
STAT-17 [@STAT-17], ASAP [@Raju_Tomblin_2008] and CMH17-STATS
[@CMH17-STATS] using several example data sets. Agreement between
cmstatr and the other software is generally good, but some results
differ slightly, likely due to various approximations used in the
software. Comparison between cmstatr and the other software is
performed within various unit tests to guard against future regressions.
The tests are automatically run each time a change is made to the code
of cmstatr using a continuous integration service.
Reproducibility
It is envisioned that many users of cmstatr will use it within an R
Notebook or a Jupyter Notebook. It is further envisioned that this
notebook will be directly converted into the statistical analysis
report. If this is done, the reader of the statistical report will be
able to verify all of the detailed steps used in the statistical
analysis.
Acknowledgement
The author would like to thank Mr. Billy Cheng for his contributions to
cmstatr and this paper. The author would also like to thank Comtek
Advanced Structures Ltd. for its support in developing and releasing the
cmstatr package.
References {#references .unnumbered}
ComtekAdvancedStructures/cmstatr documentation built on Nov. 20, 2024, 6:39 p.m.
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affiliations: - index: 1 name: 'Comtek Advanced Structures, Ltd.' authors: - affiliation: 1 name: Stefan Kloppenborg orcid: '0000-0002-1908-5214' bibliography: 'paper.bib' date: '6/24/2020' output: md_document: pandoc_args: '--atx-headers' preserve_yaml: True variant: markdown pdf_document: default tags: - R - statistics - composite materials - material science title: | cmstatr: An R Package for Statistical Analysis of Composite Material Data
Summary
Strength data for composite materials used in aerospace applications, such as carbon fiber and fiberglass reinforced composites, are normally analyzed using statistical methods because of the inherent variability in the constituent materials and in the processing. The design standards for civil aviation requires that the probability of structural failure due to this variability must be minimized, and to do so, the designer must use what are called "Design Values" for each material in stress analyses and ensure they exceed the actual stresses experienced by those materials in service. Design Values are set based on the one-sided lower confidence bound of the material strength. For some types of structure, the content of this lower confidence bound is $99\%$ with a confidence level of $95\%$; in this case, the confidence bound is referred to as A-Basis. For some other types of structure, the content of the lower confidence bound is instead $90\%$ with a confidence level of $95\%$; in this case, the confidence bound is referred to as B-Basis. The statistical methods for calculating these basis values are outlined in Composite Materials Handbook, Volume 1, Revision G, or CMH-17-1G in short [@CMH171G]. The use of these methods is widely accepted by industry and civil aviation regulators.
Design Values are often adjusted to account for anticipated in-service damage and other factors, however those adjustments are outside the scope of the present software package.
For a detailed discussion of the theory and applications of tolerance bounds, the reader is referred to @Meeker_Hahn_Escobar_2017 or @Krishnamoorthy_Mathew_2008.
Currently, many users use MS Excel spreadsheets to perform these
analyses. The MS Excel spreadsheets typically used, such as STAT-17
[@STAT-17], ASAP [@Raju_Tomblin_2008] and CMH17-STATS
[@CMH17-STATS], use password-protected VBA macros to perform the
computations. As such, the code cannot be audited by the user. cmstatr
is an R package that addresses this issue by implementing the same
statistical analysis techniques found in CMH-17-1G in an open-source
environment.
Statement of Need
The purpose of cmstatr is to:
- Provide a consistent user interface for computing A- and B-Basis
values and performing the related diagnostic tests in the
Rprogramming environment - Allow auditing of the code used to compute A- and B-Basis values, and performing the related diagnostic tests
- Enable users to automate computation workflows or to perform simulation studies
Implementation Goals
cmstatr aims give a consistent interface for the user. Most functions
are written to work with the tidyverse [@tidyverse] and most functions
have similar argument lists. The intent is to make the package easy to
learn and use.
The implementation of cmstatr also aims to avoid the use of lookup
tables that are prevalent in calculation spreadsheets and minimize the
use of approximations. While this decision leads to increased
computation time, the typically small data sets (tens to hundreds of
observations) associated with composite material test data and the speed
of modern computers make this practical for interactive programming.
Example Usage
Normally, to use cmstatr the user will load cmstatr itself as well
as the tidyverse package.
library(cmstatr)
library(tidyverse)
cmstatr contains some example data sets, which can be used to
demonstrate the features of the package. One of those data sets ---
carbon.fabric.2 --- will be used in the following example. This data
set contains results from several mechanical tests of a typical
composite material, and contains the typical measurements obtained from
a test lab. In the following examples, results from tension testing in
the warp fiber direction (WT) will be used. Part of this data set is
shown below.
carbon.fabric.2 %>%
filter(test == "WT") %>%
head(10)
## test condition batch thickness nplies strength modulus failure_mode
## 1 WT CTD A 0.112 14 142.817 9.285 LAT
## 2 WT CTD A 0.113 14 135.901 9.133 LAT
## 3 WT CTD A 0.113 14 132.511 9.253 LAT
## 4 WT CTD A 0.112 14 135.586 9.150 LAB
## 5 WT CTD A 0.113 14 125.145 9.270 LAB
## 6 WT CTD A 0.113 14 135.203 9.189 LGM
## 7 WT CTD A 0.113 14 128.547 9.088 LAB
## 8 WT CTD B 0.113 14 127.709 9.199 LGM
## 9 WT CTD B 0.113 14 127.074 9.058 LGM
## 10 WT CTD B 0.114 14 126.879 9.306 LGM
One common task is to calculate B-Basis values. There are several statistical methods for doing so, depending on the distribution of the data. The single-point basis functions automatically perform the following diagnostic tests:
- the maximum normed residual test for outliers within a batch [@CMH171G],
- the Anderson--Darling k-Sample test to check if batches are drawn from the same (unspecified) distribution [@Scholz_Stephens_1987],
- the maximum normed residual test for outliers within the data, and
- the Anderson--Darling test for a particular probability distribution [@Lawless_1982].
Assuming that the data from the warp tension (WT) tested at
elevated-temperature/wet condition (ETW) follows a normal distribution,
then this can be done using the function. Note that all of the functions
in cmstatr that compute basis values default to computing tolerance
bounds with a content of $p=0.9$ and a confidence of $conf=0.95$, or
B-Basis.
carbon.fabric.2 %>%
filter(test == "WT") %>%
filter(condition == "ETW") %>%
basis_normal(strength, batch)
## Warning: `anderson_darling_normal` failed: Anderson-Darling test rejects
## hypothesis that data is drawn from a normal distribution
##
## Call:
## basis_normal(data = ., x = strength, batch = batch)
##
## Distribution: Normal ( n = 18 )
## The following diagnostic tests failed:
## `anderson_darling_normal`
## B-Basis: ( p = 0.9 , conf = 0.95 )
## 122.9315
All of the various basis functions perform diagnostic tests for each of
the statistical tests mentioned above. If any of the diagnostic tests
failed, a warning is shown and the test failure is also recorded in the
returned object (and shown in that object's print method). In the
example above, the output shows that the Anderson--Darling test for
normality [@Lawless_1982] rejects the hypothesis that the data is drawn
from a normal distribution.
Two non-parametric basis calculations, based on @Guenther_1970 and
@Vangel_1994 are also implemented in cmstatr. These functions perform
the same diagnostic tests, but omit the Anderson--Darling test for a
particular distribution.
The diagnostic test can be run directly using cmstatr as well. For
example, the failed diagnostic test above can be run as follows:
carbon.fabric.2 %>%
filter(test == "WT") %>%
filter(condition == "ETW") %>%
anderson_darling_normal(strength)
##
## Call:
## anderson_darling_normal(data = ., x = strength)
##
## Distribution: Normal ( n = 18 )
## Test statistic: A = 0.9381665
## OSL (p-value): 0.01103075 (assuming unknown parameters)
## Conclusion: Sample is not drawn from a Normal distribution ( alpha = 0.05 )
If the failure of a diagnostic test is decided to be acceptable, the test result can be overridden to hide the warning in the basis function output:
carbon.fabric.2 %>%
filter(test == "WT") %>%
filter(condition == "ETW") %>%
basis_normal(strength, batch, override = c("anderson_darling_normal"))
##
## Call:
## basis_normal(data = ., x = strength, batch = batch, override = c("anderson_darling_normal"))
##
## Distribution: Normal ( n = 18 )
## The following diagnostic tests were overridden:
## `anderson_darling_normal`
## B-Basis: ( p = 0.9 , conf = 0.95 )
## 122.9315
cmstatr also provides functions for calculating basis values from data
pooled across multiple testing environments, as recommended by
[@CMH171G]. There are two methods of pooling: both calculate a measure
of global variation from the data in all tested environmental
conditions, then they calculate a basis value for each condition using
the measure of the global variation and the individual mean values of
each condition. The two methods of pooling have different underlying
assumptions and hence the data must pass a different set diagnostic
tests for each of the two functions.
Validation and Comparison With Existing Tools
Where possible, cmstatr has been verified against the examples given
in the articles in which the statistical methods were published. Unit
tests have been written so that this verification is re-checked
routinely to prevent unintended regressions. Agreement between cmstatr
and the examples in the original articles is within the expected numeric
accuracy.
cmstatr has also been verified against existing software, such as
STAT-17 [@STAT-17], ASAP [@Raju_Tomblin_2008] and CMH17-STATS
[@CMH17-STATS] using several example data sets. Agreement between
cmstatr and the other software is generally good, but some results
differ slightly, likely due to various approximations used in the
software. Comparison between cmstatr and the other software is
performed within various unit tests to guard against future regressions.
The tests are automatically run each time a change is made to the code
of cmstatr using a continuous integration service.
Reproducibility
It is envisioned that many users of cmstatr will use it within an R
Notebook or a Jupyter Notebook. It is further envisioned that this
notebook will be directly converted into the statistical analysis
report. If this is done, the reader of the statistical report will be
able to verify all of the detailed steps used in the statistical
analysis.
Acknowledgement
The author would like to thank Mr. Billy Cheng for his contributions to
cmstatr and this paper. The author would also like to thank Comtek
Advanced Structures Ltd. for its support in developing and releasing the
cmstatr package.
References {#references .unnumbered}
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