Rula Coroneos, Shantaram S. Pai, and Pappu Murthy

Glenn Research Center, Cleveland, Ohio

Statistical Analyses of Raw Material Data for

MTM45-1/CF7442A-36% RW: CMH Cure Cycle

NASA/TM—2013-216572

December 2013
NASA STI Program . . . in Pro¿ le

Since its founding, NASA has been dedicated to the

advancement of aeronautics and space science. The

NASA Scienti¿ c and Technical Information (STI)

program plays a key part in helping NASA maintain

this important role.

The NASA STI Program operates under the auspices

of the Agency Chief Information Of¿ cer. It collects,

organizes, provides for archiving, and disseminates

NASA’s STI. The NASA STI program provides access

to the NASA Aeronautics and Space Database and

its public interface, the NASA Technical Reports

Server, thus providing one of the largest collections

of aeronautical and space science STI in the world.

Results are published in both non-NASA channels

and by NASA in the NASA STI Report Series, which

includes the following report types:

• TECHNICAL PUBLICATION. Reports of

completed research or a major signi¿ cant phase

of research that present the results of NASA

programs and include extensive data or theoretical

analysis. Includes compilations of signi¿ cant

scienti¿ c and technical data and information

deemed to be of continuing reference value.

NASA counterpart of peer-reviewed formal

professional papers but has less stringent

limitations on manuscript length and extent of

graphic presentations.

• TECHNICAL MEMORANDUM. Scienti¿ c

and technical ¿ ndings that are preliminary or

of specialized interest, e.g., quick release

reports, working papers, and bibliographies that

contain minimal annotation. Does not contain

extensive analysis.

• CONTRACTOR REPORT. Scienti¿ c and

technical ¿ ndings by NASA-sponsored

contractors and grantees.

• CONFERENCE PUBLICATION. Collected

papers from scienti¿ c and technical

conferences, symposia, seminars, or other

meetings sponsored or cosponsored by NASA.

• SPECIAL PUBLICATION. Scienti¿ c,

technical, or historical information from

NASA programs, projects, and missions, often

concerned with subjects having substantial

public interest.

• TECHNICAL TRANSLATION. Englishlanguage translations of foreign scienti¿ c and

technical material pertinent to NASA’s mission.

Specialized services also include creating custom

thesauri, building customized databases, organizing

and publishing research results.

For more information about the NASA STI

program, see the following:

• Access the NASA STI program home page at

http://www.sti.nasa.gov

• E-mail your question to help@sti.nasa.gov

• Fax your question to the NASA STI

Information Desk at 443–757–5803

• Phone the NASA STI Information Desk at

 443–757–5802

• Write to:

 STI Information Desk

NASA Center for AeroSpace Information

 7115 Standard Drive

 Hanover, MD 21076–1320
Rula Coroneos, Shantaram S. Pai, and Pappu Murthy

Glenn Research Center, Cleveland, Ohio

Statistical Analyses of Raw Material Data for

MTM45-1/CF7442A-36% RW: CMH Cure Cycle

NASA/TM—2013-216572

December 2013

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

This work is supported by Advanced Exploration Systems under NASA’s Exploration Program.

Available from

NASA Center for Aerospace Information

7115 Standard Drive

Hanover, MD 21076–1320

National Technical Information Service

5301 Shawnee Road

Alexandria, VA 22312

Available electronically at http://www.sti.nasa.gov

Trade names and trademarks are used in this report for identi¿ cation

only. Their usage does not constitute an of¿ cial endorsement,

either expressed or implied, by the National Aeronautics and

Space Administration.

Level of Review: This material has been technically reviewed by technical management.

This report contains preliminary ¿ ndings,

subject to revision as analysis proceeds.

Supplementary Notes

Prepared for MMSEV (Multi Mission Space Exploration Vehicle) Task January 2013.
NASA/TM22013-216572 iii

Contents

Summary ....................................................................................................................................................... 1

Introduction ................................................................................................................................................... 1

Statistical Details for Distribution Analysis .................................................................................................. 2

Overview of Distribution Types ................................................................................................................... 3

Gaussian or Normal Distribution ............................................................................................................ 3

Lognormal Distribution .......................................................................................................................... 3

Weibull Distribution ............................................................................................................................... 4

Exponential Distribution ........................................................................................................................ 4

Normal Mixtures Distribution ................................................................................................................ 4

Johnson Su, Johnson Sb, and Johnson SI Distributions ......................................................................... 4

Data Analysis Details .................................................................................................................................... 4

Test Methods and Test Types ................................................................................................................. 6

Summary of Distributions by Test ................................................................................................................ 7

Concluding Remarks ................................................................................................................................... 19

Forward Work ............................................................................................................................................. 19

Appendix A ................................................................................................................................................. 21

A.1 Fill Compression (FC) ................................................................................................................... 21

A.2 Quasi Filled Hole Compression (FHC1) ....................................................................................... 32

A.3 Soft Filled Hole Compression (FHC2) .......................................................................................... 34

A.4 Hard Filled Hole Compression (FHC3) ......................................................................................... 36

A.5 Quasi Isotropic Filled Hole Tension (FHT1) ................................................................................. 38

A.6 Soft Filled Hole Tension (FHT2) .................................................................................................. 40

A.7 Hard Filled Hole Tension (FHT3) ................................................................................................. 43

A.8 Warp Flexure Strength and Modulus (FSM) ................................................................................. 44

A.9 Fill Tension (FT) ........................................................................................................................... 47

A.10 In-Plane Shear (IPS1) .................................................................................................................. 58

A.11 Quasi Isotropic Open Hole Compression (OHC1) ...................................................................... 69

A.12 Soft Open Hole Compression (OHC2) ........................................................................................ 73

A.13 Hard Open Hole Compression (OHC3) ....................................................................................... 75

A.14 Quasi Isotropic Open Hole Tension (OHT1) ............................................................................... 77

A.15 Soft Open Hole Tension (OHT2) ................................................................................................ 82

A.16 Hard Open Hole Tension (OHT3) ............................................................................................... 84

A.17 Quasi Isotropic Pin Bearing (PB1) .............................................................................................. 87

A.18 Soft Pin Bearing (PB2) ................................................................................................................ 91

A.19 Hard Pin Bearing (PB3) ............................................................................................................... 95

A.20 Short Beam Strength (SBS) ......................................................................................................... 99

A.21 Quasi Isotropic Short Beam Strength (SBS1) ........................................................................... 102

A.22 Quasi Isotropic Compression (UNC1)....................................................................................... 104

A.23 Soft Compression (UNC2) ........................................................................................................ 108

A.24 Hard Compression (UNC3) ....................................................................................................... 111

A.25 Quasi Isotropic Tension (UNT1) ............................................................................................... 114

A.26 Soft Tension (UNT2) ................................................................................................................. 118

A.27 Hard Tension (UNT3) ............................................................................................................... 122

A.28 Warp Compression (WC) .......................................................................................................... 126

A.29 Warp Tension (WT)................................................................................................................... 132

References ................................................................................................................................................. 138

NASA/TM22013-216572 1

Statistical Analyses of Raw Material Data for

MTM45-1/CF7442A-36% RW: CMH Cure Cycle

Rula Coroneos, Shantaram S. Pai, and Pappu Murthy

National Aeronautics and Space Administration

Glenn Research Center

Cleveland, Ohio 44135

Summary

This report describes statistical characterization of physical properties of the composite material

system MTM45-1/CF7442A, which has been tested and is currently being considered for use on

spacecraft structures. This composite system is made of 6K plain weave graphite fibers in a highly

toughened resin system. This report summarizes the distribution types and statistical details of the tests

and the conditions for the experimental data generated. These distributions will be used in multivariate

regression analyses to help determine material and design allowables for similar material systems and to

establish a procedure for other material systems. Additionally, these distributions will be used in future

probabilistic analyses of spacecraft structures. The specific properties that are characterized are the

ultimate strength, modulus, and Poisson¶s ratio by using a commercially available statistical package.

Results are displayed using graphical and semigraphical methods and are included in the accompanying

appendixes.

Introduction

The work described in this report is based on the database entitled 3NPN100101 AITR1615-IMPW

MTM45-1 IM7 6K PW RAW DATA REPORT ́ (Ref. 1, internal database). Material MTM45-1 is a

composite with 6K plain weave IM7 (Hexcel Corporation) graphite fibers, in a highly toughened resin

system 36 percent by weight and is currently being considered for spacecraft structures. The primary

objective is to determine the underlying statistical distributions for the various properties that were

experimentally determined and reported. These distributions will be used in multivariate regression

analyses to help determine material and design allowables for similar material systems and to establish a

procedure for other material systems. Additionally, these distributions will be used in future probabilistic

analyses of spacecraft structures. This document summarizes the distribution types as well as the details

of the tests and conditions for the experimental data generated for the material characterized as MTM45-

1/CF7442A-36% RW: CMH Cure Cycle. The material form and CMH (condensed medium-temperature

cure/high-temperature postcure) cure cycle are described in Reference 2. The document summarizes the

distribution types and details of the tests and conditions for the experimental data generated for the

material characterized as provided in the database. The distribution types for material physical properties

such as ultimate strength, modulus, and Poisson¶s ratio are determined using the commercially available

statistical discovery software JMP Pro (Ref. 3). The distributions are displayed using graphical and

semigraphical methods and are included in Appendix A of this report. For stiffness-critical applications,

the measured modulus variability becomes important, and tailoring of sections with appropriate

orientations becomes a design consideration in order to quantify and minimize the uncertainty. However,

for those structural components where failures due to inadequate strength becomes critical, one needs to

address various types of failure modes and the appropriate strengths initiating those failure modes. Here

the uncertainty in strength could decrease the reliability, and therefore one must execute extra caution and

factor of safety. Furthermore, an a priori knowledge of these issues can be utilized to tailor manufacturing

and testing of the material with the goal of reducing the uncertainty as much as possible. Discussion of

such optimization is beyond the scope of the current project.
NASA/TM22013-216572 2

Statistical Details for Distribution Analysis

The Excel spreadsheet 3NPN100101 AITR1615-IMPW MTM45-1 IM7 6K PW RAW DATA

REPORT, ́ containing the test data was imported into JMP Pro software. Variables such as 3Ultimate

Strength Measured in ksi, ́3Elastic Modulus Measured in Msi, ́3Poisson¶s ratio, ́3Strength Initial

Peak, ́3Ultimate Strength, ́3Strength at 2% Offset, ́ and 3Strength at 4% Offset, ́ were declared

3Continuous variables. ́ For analyzing the distributions, the 3Continuous Fit ALL ́ option was used for

each test temperature. In the 3Compare Distributions ́ report, the 3Show Distribution ́ list is sorted by the

3Corrected Akaike¶s Information Criterion (AICc ́ (Ref. 3) in ascending order. Distributions with the

smaller AICc values indicate the best fit. They are computed as

2log( ) 2

1

n

AICc likelihood k

n k

 (1)

where likelihood is the value of the likelihood function at best fit parameters, k is the number of estimated

parameters in the model, and n is the number of observations in the data set.

Appendix A presents the results of each distribution analysis performed using graphical and

semigraphical methods. The graphical methods depict the 3Normal Quantile Plot ́ to assist in visualizing

the extent to which a variable is normally distributed. The normal quantile plot also shows Lilliefors

confidence bounds and Probability Normal Quantile Scales (Ref. 3). The 3Outlier Box Plot ́ identifies

possible outliers. The vertical line within the box represents the median sample value. The confidence

diamond represents the upper and lower 95 percent of the mean. A line through the middle of the

diamond represents the mean. The ends of the box represent the 25th and 75th quantiles, and the bracket

outside of the box identifies the shortest half, which is the most dense 50 percent of the observations.

The data are displayed using histograms, which show a bar for grouped values of the continuous

variable and a line graph depicting the best distribution fit. Summary statistics for each distribution are

given in terms of the mean, standard deviation, the standard error of the mean. The upper 95 percent mean

and lower 95 percent mean confidence limits about the mean define the interval that is likely to contain

the true sample mean.

A comparison of the distribution is depicted next in the appendix including the AICc as given in

Equation (1). This value may be compared with those from other models to determine the best-fitting

model for the data. The model having the smallest AICc value, as discussed in Reference 3, is usually the

preferred model.

The best-fitting distribution report includes a 3Diagnostic Plot ́ with 3Goodness-of-Fit ́ statistics

displayed. The diagnostic plot creates a quantile or probability plot. Depending on the fitted distribution,

the plot is in one of the formats listed in Table 1.

The 3Parameter Estimates ́ table shows the estimates of the parameters in the model and a test for the

hypothesis that each parameter is zero. Confidence limits are also displayed.

TABLE 1.2DISTRIBUTION PLOT FORMATS

Plot format Distribution

Fitted probability versus data Normal

Exponential

Fitted probability versus data on log scale

Weibull

Lognormal

Extreme value

Fitted quantiles versus data Gamma

Poisson
NASA/TM22013-216572 3

The 3Goodness-of-Fit ́ test is also shown in the appendix. Analogous to lack-of-fit tests, they test for

adequacy of the model by computing the goodness-of-fit for the fitted distribution. In the JMP software,

the goodness-of-fit tests are not chi-square tests, but are empirical distribution function (EDF) tests. EDF

tests offer advantages over the chi-square tests, including improved power and invariance with respect to

histogram midpoints (Ref. 3).

Analysis of the distribution was performed using the JMP software of each variable, and comparison

was performed using the option 3Continuous Fit All. ́ The best-fit distribution is selected and plotted as

shown in the charts in the appendix. However, in the cases where the best distribution fit was of the type

Normal 2 Mixture or Normal 3 Mixture or any of the Johnson options such as Johnson Su, Johnson Sb,

and Johnson Sl, the next-best fit was chosen instead. This choice was made in anticipation for future use

of NASA/NESSUS 6.2c code (Ref. 4) for further sensitivity analysis because these types of distributions

are not available in NESSUS 6.2c. NASA/NESSUS 6.2c is a general-purpose, probabilistic analysis

program that accounts for variations and uncertainties in loads, geometry, material behavior, and other

user-defined inputs, and it computes probability of failure and probabilistic sensitivity measures of

engineered systems. A brief description of the different statistical distribution types that are also available

in the NASA/NESSUS 6.2c version follows.

Overview of Distribution Types

The following sections give descriptions of the distribution types in the JMP software that are used in

the analyses in this report.

Gaussian or Normal Distribution

The normal distribution is a continuous probability distribution defined on the entire real line often

used to model measures that are symmetric with most of the values falling in the middle of the curve. It

has a bell-shaped probability density function, given as

2

1 1 ( ) exp , for

2 2

x

fx x (2)

The parameter μ is the mean and is the standard deviation. The standard normal distribution is with μ =

0 and variance 2

 = 1 in a general normal distribution.

Lognormal Distribution

The lognormal distribution is a continuous probability distribution of a random variable whose

logarithm is normally distributed. A variable Y is lognormal if and only if X = ln(Y) is normal. Lognormal

is often used to model values that can only take positive values and if negative values are inadmissible.

The lognormal distribution can be obtained by substituting 3ln(x ́ for 3x ́ in the above equation for the

normal distribution. The lognormal fitting option estimates the parameters μ (scale) and (shape).

2

2

1 (ln ) ( ; , ) exp , for 0

2 2

x

fx x

x

 (3)
NASA/TM22013-216572 4

Weibull Distribution

The Weibull distribution is a continuous probability distribution that often provides a good model for

estimating the length of life. The probability density function of a Weibull random variable x is

1

exp 0 (; ,)

0 0

x x

x

f x

x

 (4)

where 0 is the scale parameter and 0 is the shape parameter of the distribution.

Exponential Distribution

The exponential distribution is useful for describing events that randomly occur over time. The

probability density function of an exponential distribution f is

exp 0

f( ; )

0 0

x x

x

x

 (5)

where 0 is the scale parameter of the distribution.

Normal Mixtures Distribution

The normal mixtures distribution fits a mixture of normal distributions. This flexible distribution is

capable of fitting multimodal data. The probability density function generated from a mixture of two

normal distributions for a random variable x is given by

2 2

2 2 1 2

121 2 2 2 2 2 1 2 1 2

() ( ) 1

f( ; , , , , ) exp exp

2 2 2 2

p p x x

x p (6)

where parameters μ1 and μ2 are the two means, 1 and 2 are two standard deviations, and p is the

probability.

Johnson Su, Johnson Sb, and Johnson SI Distributions

The Johnson system of distributions contains three distributions that are all based on a transformed

normal distribution: Johnson Su, which is unbounded for Y; the Johnson Sb, which is bounded on both

tails (0 Y 1); and the Johnson SI distribution leading to the lognormal family of distributions. All three

Johnson system distributions are useful for their data-fitting capabilities because they support every

possible combination of skewness and kurtosis. More details on the Johnson system can be found in

Reference 3.

Data Analysis Details

The actual experimental data for the MTM45-1/CF7442A-36% RW, 6K plain weave IM7 fabric,

196 g/m2, 36% RW (resin weight) material was analyzed. The elastic modulus and ultimate strength of

the material were obtained for the test conditions and test types as defined in Tables 2 and 3.
NASA/TM22013-216572 5

TABLE 2.2TEST CONDITIONS

CTD ±65 5 F (18 3 C), ambient moisture cold temperature dry

RTD Room temperature, ambient dry

RTW Room temperature, wet (equilibrium moisture content)

ETD1 220 5 F (104 3 C), elevated temperature dry

ETD2 350 5 F (177 3 C), elevated temperature dry

ETW 180 5 F (82 3 C), elevated temperature wet (equilibrium moisture)

ETW2 250 5 F (121 3 C), elevated temperature wet (equilibrium moisture)

TABLE 3.2TESTS RUN ON

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

WITH CORRESPONDING CODES FOR

JMP PRO SOFTWARE ANALYSIS

Test code Test

FC Fill compression

FHC1 Quasi filled hole compression

FHC2 Soft filled hole compression

FHC3 Hard filled hole compression

FHT1 Quasi isotropic filled hole tension

FHT2 Soft filled hole tension

FHT3 Hard filled hole tension

FSM Warp flexure strength and modulus

FT Fill tension

ILT1 Quasi isotropic interlaminar tension

IPS1 In plane shear (11.5 inches length)

OHC1 Quasi isotropic open hole compression

OHC2 Soft open hole compression

OHC3 Hard open hole compression

OHT1 Quasi isotropic open hole tension

OHT2 Soft open hole tension

OHT3 Hard open hole tension

PB1 Quasi isotropic pin bearing

PB2 Soft pin bearing

PB3 Hard pin bearing

SBS Short beam strength

SBS1 Quasi isotropic short beam strength

UNC0 0/90 compression

UNC1 Quasi isotropic compression

UNC2 Soft compression

UNC3 Hard compression

UNT0 0/90 tension

UNT1 Quasi isotropic tension

UNT2 Soft tension

UNT3 Hard tension

WC Warp compression

WT Warp tension
NASA/TM22013-216572 6

Test Methods and Test Types

All testing was executed in accordance with nationally recognized standard methods and procedures.

Details of the specific test methods used are defined in Reference 2, together with relevant specimen nominal

geometry and configurations. Table 4 presents the 10 ASTM Standard Test Methods used for this data.

Distribution analyses and comparisons were performed for variables such as 3Ultimate Strength

Measured in ksi, ́3Elastic Modulus Measured in Msi, ́3Poisson¶s ratio, ́3Strength Initial Peak, ́

3Ultimate Strength, ́3Strength at 2% Offset, ́ and 3Strength at 4% Offset. ́ Importing the data in JMP

involved combining and concatenating data across batches and test conditions for each property type.

The distribution type for each of these variables at each available test temperature was analyzed

separately. Ninety-four tests of the MTM45-1/CF7442A-36% RW material were performed, as described

and summarized in Reference 2. Results of the distribution types by property and test temperature are

summarized in the next section and in Appendix A. The tables depict the distribution types along with the

parameter types and estimates for each distribution type as given in Table 5. Appendix A provides the

TABLE 4.2ASTM STANDARD TEST METHODS USED FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE MATERIAL TESTS

Test

code

ASTM test

method

ASTM test description

SBS

SBS1

ASTMD2344 Standard test method for short-beam strength of polymer-matrix-composite materials and their

laminates

WT

FT

UNT1

UNT2

UNT3

ASTMD3039 Standard test method for tensile properties of polymer-matrix-composite materials

IPS1 ASTMD3518 Standard test method for in-plane shear response of polymer-matrix-composite materials by

tensile test of a 45 laminate

OHT1

OHT2

OHT3

ASTMD5766 Standard test method for open-hole tensile strength of polymer-matrix-composite laminates

PB1

PB2

PB3

ASTMD5961 Standard test method for bearing response of polymer-matrix-composite laminates

ILT1 ASTMD6415 Standard test method for measuring the curved-beam strength of a fiber-reinforced polymermatrix composite

OHC1

OHC2

OHC3

ASTMD6484 Standard test method for open-hole compressive strength of polymer-matrix-composite

laminates

WC

FC

UNC1

UNC2

UNC3

ASTMD6641 Standard test method for determining the compressive properties of polymer-matrix-composite

laminates using a combined loading compression test fixture

FHT1

FHT2

FHT3

FHC1

FHC2

FHC3

ASTMD6742 Standard test method for filled-hole tension and compression testing of polymer-matrixcomposite laminates

FSM ASTMD790 Standard test method for flexural properties of unreinforced and reinforced plastics and

electrical insulating materials
NASA/TM22013-216572 7

TABLE 5.2DISTRIBUTION PARAMETER TYPES

Distribution Parameter type

Normal (Location μ, dispersion )

Lognormal (Scale μ, shape )

Weibull (Scale , shape )

Exponential Scale

3Summary Statistics, ́ such as the mean and standard deviation, the standard error mean, and upper

95 percent of the mean, and lower 95 percent of the mean for each test type and variable, as well as a

comparison table of all the distribution types ranging from the smallest value of AICc to the biggest value.

The 3Fitted Parameter Estimate ́ for the best fit distribution, the 3Goodness-of-Fit Test, ́ and the

3Diagnostic Plot ́ are also displayed in the appendix.

Summary of Distributions by Test

The best fit distribution type for the data was compared with the normal distribution to determine how

significantly they differ from one another. The comparison was done by calculating the percent change of

the Akaike¶s Information Criterion value (AICc) with respect to the AICc of the normal distribution. As

mentioned in the previous section, AICc is a measure of the relative goodness-of-fit for a specific

statistical distribution and provides a rationale for the distribution type selection. The AICc values for all

properties and tests are provided in Appendix A. In the subsequent discussions for each specific property

we make note on the tables that normal distribution can be assumed if the percent change of the best fit

distribution is less than 2 percent, based on the AICc criteria.

Fill Compression (FC): The distribution types for the Fill Compression (FC) tests are shown in

Table 6 and Appendix A.1. For cold temperature dry (CTD) conditions the best fit distribution type for

ultimate strength, modulus, and Poisson¶s ratio is Weibull. For all other temperature conditions the

distribution types vary. Comparing the percent change of the AICc value for the best-fit distribution type

with respect to normal distribution is less than 2 percent for both ultimate strength and Poisson¶s ratio.

Quasi Filled Hole Compression (FHC1): The distribution types for the Quasi Filled Hole

Compression (FHC1) properties are shown in Table 7 and Appendix A.2. For room temperature dry

(RTD) conditions the distribution for ultimate strength is lognormal, and for 250 5 F elevated

temperature wet (ETW2) conditions it is normal. However, in comparing the AICc value for these

distributions, the strength at RTD = 37. 772 ksi (260.43 MPa) for lognormal and 38.157 ksi (263.08 MPa)

for normal, the percent difference is 1.02 percent; therefore, normal distribution can be considered for the

RTD condition. Modulus data were not available. For the FHC1 properties, the percent change of the

AICc value with respect to normal for ultimate strength at the RTD condition is 1.02 percent.

Soft Filled Hole Compression (FHC2): The distribution types for the Soft Filled Hole Compression

(FHC2) properties are shown in Table 8 and Appendix A.3. For RTD conditions the distribution for

ultimate strength is lognormal and for the ETW2 condition it is Weibull. The scale and shape parameters

for these distributions are given in the table. Modulus test data were not available. The maximum percent

change of the AICc value with respect to normal for ultimate strength at both temperature conditions is

1.21 percent.

Hard Filled Hole Compression (FHC3): The distribution types for the Hard Filled Hole

Compression (FHC3) properties are shown in Table 9 and Appendix A.4. For RTD conditions the

distribution for ultimate strength is lognormal, and for the ETW2 condition it is normal. The scale and

shape parameters for these distributions are given in Table 9. For RTD, the percent difference of the AICc

value between lognormal (43.971 ksi, 303.17 MPa) and normal (44.160 ksi, 304.47 MPa) is small at 0.43

percent; thus normal can be considered as the distribution for ultimate strength for both test temperature

conditions. Modulus test data were not available. For the FHC3 properties, the percent change of the AICc

value with respect to normal for ultimate strength at the RTD condition is less than 0.5 percent.
NASA/TM22013-216572 8

TABLE 6.2BEST-FIT DISTRIBUTION TYPES FOR FILL COMPRESSION (FC) TEST PROPERTIES

FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.1.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

Modulus (Msi) Poisson¶s ratio

CTD Weibull (106.301, 17.198)

 or normal Weibull (9.441, 18.381) Weibull (0.058, 9.746) or normal

RTD Weibull (83.806, 22.070)

 or normal

Lognormal (2.146, 0.080)

 or normal

Lognormal (±2.964, 0.060)

 or normal

RTW Normal (70.028, 6.523) Weibull (9.161, 71.045) Lognormal (±3.309, 0.098)

 or normal

ETD1 Weibull (69.341, 16.841)

 or normal Weibull (9.299, 14.094) Lognormal (±3.137, 0.117) or normal

ETD2 Lognormal (3.981, 0.121)

 or normal Lognormal (2.129, 0.099) Weibull (0.036, 7.699) or normal

ETW Weibull (62.210, 8.994)

 or normal

Lognormal (2.253, 0.046)

 or normal Normal (0.039, 0.006)

ETW2 Lognormal (3.981, 0.121)

 or normal Weibull (9.493, 17.059) Weibull (0.044, 8.077) or normal

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in the Section 3Overview of Distribution

Types. ́

TABLE 7.2BEST-FIT DISTRIBUTION TYPES FOR QUASI FILLED

HOLE COMPRESSION (FHC1) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.2.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi) Modulus (Msi)

RTD Lognormal (4.018, 0.031)

 or normal Excluded or not tested

ETW2 Normal (38.870, 3.303) Excluded or not tested

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

TABLE 8.2BEST-FIT DISTRIBUTION TYPES FOR SOFT FILLED

HOLE COMPRESSION (FHC2) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.3.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi) Modulus (Msi)

RTD Lognormal (3.841, 0.019)

 or normal Excluded or not tested

ETW2 Weibull (33.837, 23.123)

 or normal Excluded or not tested

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́
NASA/TM22013-216572 9

TABLE 9.2BEST-FIT DISTRIBUTION TYPES FOR HARD FILLED

HOLE COMPRESSION (FHC3) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.4.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi) Modulus (Msi)

RTD Lognormal (4.067, 0.043)

 or normal

Excluded or not tested

ETW2 Normal (42.977, 3.826) Excluded or not tested

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

TABLE 10.2BEST-FIT DISTRIBUTION TYPES FOR QUASI ISOTROPIC

FILLED HOLE TENSION (FHT1) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.5.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi) Modulus (Msi)

CTD Lognormal (4.135, 0.037)

 or normal

Excluded or not tested

RTD Lognormal (4.102, 0.019)

 or normal

Excluded or not tested

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

Quasi Isotropic Filled Hole Tension (FHT1): The distribution types for the Quasi Filled Hole

Tension (FHT1) properties are shown in Table 10 and Appendix A.5. Both temperature conditions, RTD

and ETW2 give a lognormal distribution with minor differences in the scale and shape parameters. For

the FHT1 properties, the percent change of AICc value with respect to normal for ultimate strength at the

CTD temperature condition is 0.08 percent, and for RTD it is 0.76 percent.

Soft Filled Hole Tension (FHT2): The distribution types for the Soft Filled Hole Tension (FHT2)

properties are shown in Table 11 and Appendix A.6. Temperature conditions CTD and RTD give a

Weibull distribution with minor differences in the scale and shape parameters, whereas ETW2 is

lognormal. For the FHT2 properties, the percent change of the AICc value with respect to normal for

ultimate strength at CTD and RTD temperature conditions is significantly different at 11 percent.

However, for ETW2 the AICc value change is 0.32 percent between lognormal and normal distributions.

Hard Filled Hole Tension (FHT3): The distribution types for the Hard Filled Hole Tension (FHT3)

properties are shown in Table 12 and Appendix A.7. Both temperature conditions, CTD and RTD, give a

lognormal distribution with minor differences in the scale and shape parameters. Test data for modulus

are not available. The percent change of the AICc value with respect to normal for ultimate strength at the

CTD and RTD conditions is 0.34 and 0.15 percent, respectively.

Warp Flexure Strength and Modulus (FSM): The distribution types for the Warp Flexure Strength

and Modulus (FSM) properties are shown in Table 13 and Appendix A.8. The RTD condition gives a

Weibull distribution for ultimate strength and normal for modulus. The difference of the AICc for Weibull

(151.529 ksi, 1044.76 MPa) and normal (151.643 ksi, 1045.54 MPa) is minor at 0.08 percent; thus,

normal distribution can be considered for ultimate strength, for RTD. The percent change of the AICc

value with respect to normal for ultimate strength at the 180 5 F elevated temperature wet (ETW)

condition is 0.7. The modulus for ETW is different at 2.33 percent with respect to normal distribution.
NASA/TM22013-216572 10

TABLE 11.2BEST-FIT DISTRIBUTION TYPES FOR SOFT FILLED

HOLE TENSION (FHT2) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.6.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi) Modulus (Msi)

CTD Weibull (50.952, 71.599) Excluded or not tested

RTD Weibull (45.116, 69.277) Excluded or not tested

ETW2 Lognormal (3.556, 0.032)

 or normal Excluded or not tested

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

TABLE 12.2BEST-FIT DISTRIBUTION TYPES FOR HARD FILLED

HOLE TENSION (FHT3) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.7.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi) Modulus (Msi)

CTD Lognormal (4.310, 0.029)

 or normal Excluded or not tested

RTD Lognormal (4.361, 0.038)

 or normal Excluded or not tested

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

TABLE 13.2BEST-FIT DISTRIBUTION TYPES FOR WARP FLEXURE

STRENGTH AND MODULUS (FSM) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.8.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

Modulus (Msi),

measured

Poisson¶s

ratio

RTD Weibull (117.573, 8.949)

 or normal Excluded or not tested Not tested

ETW Lognormal (4.489, 0.077)

 or normal Excluded or not tested Not tested

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́
NASA/TM22013-216572 11

Fill Tension (FT): The distribution types for the Fill Tension (FT) properties are shown in Table 14

and Appendix A.9. There is variation in the distribution types for the different test temperatures and

response variables. However, when comparing the AICc values for each of these distributions with those

for normal distribution, the differences are small2less than 2 percent difference2thus normal

distribution can be considered. However, the difference in the variations for ETW condition for ultimate

strength is 2.45 percent, and for modulus it is 4.51 percent. The percent difference of the modulus for the

350 5 F elevated temperature dry (ETD2) condition is 2.58 percent.

In-Plane Shear (11.5 Inches Length) (IPS1): The distribution types for the In-Plane Shear (IPS1)

properties are shown in Table 15 and Appendix A.10. The response variables are shear strength measured

at 2 percent offset, 5 percent offset, and maximum shear, as well as modulus. There is variation in the

distribution types between the test temperatures and the response variables. Normal distribution can be

assumed for a few of the test temperatures and properties as noted in the table.

Quasi Isotropic Open Hole Compression (OHC1): The distribution types for the Quasi Isotropic

Open Hole Compression (OHC1) properties are shown in Table 16 and Appendix A.11. The response

variables are ultimate strength and modulus. Normal distribution can be assumed for ultimate strength and

modulus for the different test temperature conditions, as noted in the table.

Soft Open Hole Compression (OHC2): The distribution types for the Soft Open Hole Compression

(OHC2) properties are shown in Table 17 and Appendix A.12. The distribution type for ultimate strength

is Weibull. Data were not available for modulus. Normal distribution cannot be assumed for these

properties since the percent variation of the AICc value is 6.86 percent for RTD and 5.14 percent for

ETW2.

TABLE 14.2BEST-FIT DISTRIBUTION TYPES FOR FILL TENSION (FT) TEST PROPERTIES

FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.9.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

Modulus (Msi),

measured

Poisson¶s

ratio

CTD Weibull (141.923, 25.610)

 or normal

Weibull (10.615, 25.841)

 or normal

Normal (0.0690, 0.012)

RTD Lognormal (4.878, 0.057)

 or normal

Normal (9.628, 0.678) Lognormal (±2.899, 0.189)

RTW Lognormal (4.814, 0.062)

 or normal

Lognormal (2.295, 0.033)

 or normal

Lognormal (±2.959, 0.0981)

 or normal

ETD1 Weibull (120.861, 11.814)

 or normal

Lognormal (2.170, 0.032)

 or normal

Weibull (0.0459, 5.993)

 or normal

ETD2 Weibull (110.091, 10.944)

 or normal

Lognormal (2.0915, 0.046) N 4

ETW Weibull (115.277, 21.907) Weibull (10.585, 32.659)

 or normal

Lognormal (±3.091, 0.220)

 or normal

ETW2 Lognormal (4.689, 0.057)

 or normal

Lognormal (2.347, 0.055) Weibull (0.0618, 6.685)

 or normal

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́
NASA/TM22013-216572 12

TABLE 15.2BEST-FIT DISTRIBUTION TYPES FOR IN PLANE SHEAR (11.5 INCHES LENGTH) (IPS1)

TEST PROPERTIES FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.10.]

Test

temperature

conditiona

Propertyb

Shear strength (ksi),

at 0.2% offset

Shear strength (ksi),

at 5% offset

Shear strength (ksi),

maximum

Modulus (Msi),

measured

CTD Normal (8.903,0.892) Lognormal (2.646, 0.058)

 or normal

Lognormal (2.908, 0.079)

 or normal

Normal (0.683, 0.032)

RTD Lognormal (1.737, 0.051)

 or normal

Lognormal (2.373, 0.066)

 or normal

Lognormal (2.673, 0.062)

 or normal

Weibull (0.598, 16.574)

ETD1 Lognormal (1.436,0.060) Lognormal (1.955, 0.037)

 or normal

Lognormal (2.272, 0.020) Lognormal (±0.841, 0.081)

 or normal

ETD2 Gage error Gage error Weibull (7.207, 48.6) Gage error

ETW Lognormal (1.426, 0.08) Weibull (6.912, 86.099) Lognormal (2.221, 0.036)

 or normal

Lognormal (±0.824, 0.083)

 or normal

ETW2 Lognormal (1.187, 0.081) N 2 Lognormal (2.077, 0.028) Lognormal (±1.086, 0.109)

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

TABLE 16.2BEST-FIT DISTRIBUTION TYPES FOR QUASI ISOTROPIC

OPEN HOLE COMPRESSION (OHC1) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.11.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi) Modulus (Msi)

RTD Lognormal (3.727, 0.032)

 or normal

Normal (5.136, 0.240)

ETD2 Weibull (31.380, 19.852) Lognormal (1.685, 0.112)

 or normal

ETW Lognormal (3.504, 0.029)

 or normal

Gage error

ETW2 Lognormal (3.441, 0.034)

 or normal

Lognormal (1.926, 0.093)

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

TABLE 17.2BEST-FIT DISTRIBUTION TYPES FOR SOFT OPEN

HOLE COMPRESSION (OHC2) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.12.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi) Modulus (Msi)

RTD Weibull (36.831, 69.938) Excluded or not tested

ETW2 Weibull (26.489, 27.357) Excluded or not tested

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́
NASA/TM22013-216572 13

Hard Open Hole Compression (OHC3): The distribution types for the Hard Open Hole

Compression (OHC3) properties are shown in Table 18 and Appendix A.13. The distribution type for

ultimate strength is lognormal; however, normal can also be assumed. Data were not available for

modulus.

Quasi Isotropic Open Hole Tension (OHT1): The distribution types for the Quasi Isotropic Open

Hole Tension (OHT1) properties are shown in Table 19 and Appendix A.14. The distribution types vary

for ultimate strength and test temperatures. For the modulus, the distribution types are lognormal for all

test temperatures. Normal distribution can also be assumed as noted in the table.

Soft Open Hole Tension (OHT2): The distribution types for the Soft Open Hole Tension (OHT2)

properties are shown in Table 20 and Appendix A.15. The distribution types for ultimate strength are

evaluated as lognormal or normal for CTD, Weibull or normal for RTD, and Weibull for ETW2, with

their respective shape and scale parameters, as given in Table 20. Data for modulus were not available.

Hard Open Hole Tension (OHT3): The distribution types for the Hard Open Hole Tension (OHT3)

properties are shown in Table 21 and Appendix A.16. The distribution types for ultimate strength are

evaluated as lognormal for RTD and ETW2 and Weibull for CTD. However, normal can also be assumed.

Data for modulus were not available.

TABLE 18.2BEST-FIT DISTRIBUTION TYPES FOR HARD OPEN

HOLE COMPRESSION (OHC3) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.13.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi) Modulus (Msi)

RTD Lognormal (3.771, 0.039)

 or normal

Excluded or not tested

ETW2 Lognormal (3.408, 0.050)

 or normal

Excluded or not tested

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

TABLE 19.2BEST-FIT DISTRIBUTION TYPES FOR QUASI ISOTROPIC

OPEN HOLE TENSION (OHT1) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.14.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi) Modulus (Msi)

CTD Normal (60.356, 1.997) Lognormal (2.046, 0.061)

 or normal

RTD Lognormal (4.114, 0.040)

 or normal

Lognormal (2.016, 0.021)

ETD2 Lognormal (3.820, 0.033)

 or normal

Lognormal (1.892, 0.046)

 or normal

ETW Weibull (59.233, 54.230) Lognormal (2.046, 0.026)

ETW2 Normal (57.725, 3.290) Lognormal (2.054, 0.023)

 or normal

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́
NASA/TM22013-216572 14

TABLE 20.2BEST-FIT DISTRIBUTION TYPES FOR SOFT

OPEN HOLE TENSION (OHT2) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.15.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi) Modulus (Msi)

CTD Normal (60.356, 1.997) Lognormal (2.046, 0.061)

 or normal

RTD Lognormal (4.114, 0.040)

 or normal

Lognormal (2.016, 0.021)

ETW2 Lognormal (3.820, 0.033)

 or normal

Lognormal (1.892, 0.046)

 or normal

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

TABLE 21.2BEST-FIT DISTRIBUTION TYPES FOR HARD

OPEN HOLE TENSION (OHT3) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.16.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi) Modulus (Msi)

CTD Weibull (76.321, 15.912)

 or normal

Not tested

RTD Lognormal (4.359, 0.044)

 or normal

Not tested

ETW2 Lognormal (4.311, 0.032)

 or normal

Not tested

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

Quasi Isotropic Pin Bearing (PB1): The distribution types for the Quasi Isotropic Pin Bearing (PB1)

properties are shown in Table 22 and Appendix A.17. For RTD, the distribution type for ultimate

strength, strength at 2 percent offset, and strength at 4 percent offset is Weibull with the scale and shape

parameters given in the table. For the ETW2 condition, the distribution types are evaluated as lognormal

for the strength at initial peak and Weibull for the ultimate, 2 percent offset, and 4 percent offset. Normal

distribution can be assumed as noted in the table.

Soft Pin Bearing (PB2): The distribution types for the Soft Pin Bearing (PB2) properties are shown

in Table 23 and Appendix A.18. The response variables are strength initial peak, ultimate strength,

strength at 2 percent offset, and strength at 4 percent offset. The distribution types vary for RTD and

ETW2. However, normal distribution can be assumed for these property conditions.

Hard Pin Bearing (PB3): The distribution types for the Hard Pin Bearing (PB3) properties are

shown in Table 24 and Appendix A.19. The response variables are strength initial peak, ultimate strength,

strength at 2 percent offset, and strength at 4 percent offset. The distribution types are lognormal for RTD

and ETW2 test temperatures and Weibull for the 4-percent-offset strength. The percent change between

the best fit distributions with respect to normal is less than 2 percent; therefore, normal can also be

assumed for these properties.

Short Beam Strength (SBS): The distribution types for the Short Beam Strength (SBS) properties

are shown in Table 25 and Appendix A.20. For ultimate strength, the distribution varies between

lognormal and Weibull as shown in the table. Normal can be assumed for CTD only.
NASA/TM22013-216572 15

TABLE 22.2BEST-FIT DISTRIBUTION TYPES FOR QUASI ISOTROPIC PIN BEARING (PB1) TEST PROPERTIES

FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.17.]

Test

temperature

conditiona

Propertyb

Initial peak strength (ksi) Ultimate strength (ksi) 2% offset strength (ksi) 4% offset strength (ksi)

RTD No result Weibull (128.987, 27.58)

 or normal

Weibull (83.138, 10.013)

 or normal

Weibull (97.352, 16.242)

ETW2 Lognormal (4.423, 0.084)

 or normal

Weibull (105.228, 25.917) Weibull (81.878, 12.259) Weibull (87.516, 17.625)

 or normal

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

TABLE 23.2BEST-FIT DISTRIBUTION TYPES FOR SOFT PIN BEARING (PB2) TEST PROPERTIES

FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.18.]

Test

temperature

conditiona

Propertyb

Initial peak strength

(ksi)

Ultimate strength

(ksi)

2% Offset strength

(ksi)

4% Offset strength

(ksi)

RTD No result Weibull (121.662, 40.553)

 or normal

Lognormal (4.447, 0.049)

 or normal

Lognormal (4.541, 0.051)

 or Normal

ETW2 Normal (81.442, 7.203) Lognormal (4.516, 0.037)

 or normal

Weibull (68.039, 12.645)

 or normal

Normal (74.470, 3.60)

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

TABLE 24.2BEST-FIT DISTRIBUTION TYPES FOR HARD PIN BEARING (PB3) TEST PROPERTIES

FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.19.]

Test

temperature

conditiona

Propertyb

Initial peak strength

(ksi)

Ultimate strength

(ksi)

2% Offset strength

(ksi)

4% Offset strength

(ksi)

RTD Lognormal (4.671, 0.069)

 or normal

Lognormal (4.810, 0.054)

 or normal

Lognormal (4.320, 0.154)

 or normal

Weibull (97.163, 9.308)

 or normal

ETW2 Lognormal (4.246, 0.100)

 or normal

Lognormal (4.533, 0.060)

 or normal

Lognormal (3.997, 0.203)

 or normal

Weibull (68.510, 10.652)

 or normal

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in the Section 3Overview of Distribution Types. ́

TABLE 25.2BEST-FIT DISTRIBUTION TYPES FOR SHORT

BEAM STRENGTH (SBS) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.20.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

CTD Lognormal (2.433, 0.046)

 or normal

RTD Weibull (9.564, 38.118)

ETD1 Lognormal (1.962, 0.032)

ETW Weibull (6.506, 25.324)

ETW2 Lognormal (1.600, 0.049)

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type

 are described in the Section 3Overview of

 Distribution Types. ́
NASA/TM22013-216572 16

Quasi Isotropic Short Beam Strength (SBS1): The distribution types for the Quasi Isotropic Short

Beam Strength (SBS1) properties are shown in Table 26 and Appendix A.21. For ultimate strength, the

distribution is Weibull for all three test temperature conditions. Normal distribution cannot be assumed

for any of these properties, since the difference in the AICc value is in the range 4.45 to 26.13 percent.

Quasi Isotropic Compression (UNC1): The distribution types for the Quasi Isotropic Compression

(UNC1) properties are shown in Table 27 and Appendix A.22. For ultimate strength and modulus, the

distribution is Weibull for ETW2 and lognormal for ETW test conditions. RTD has a normal distribution

for ultimate strength and lognormal for modulus; however, normal distribution is acceptable. Poisson¶s

ratio data are not available.

Soft Compression (UNC2): The distribution types for the Soft Compression (UNC2) properties are

shown in Table 28 and Appendix A.23. For ultimate strength, the distribution is lognormal or normal for

RTD and Weibull for ETW2. For modulus the distribution type is Weibull for RTD and lognormal for

ETW2. Poisson¶s ratio data are not available.

Hard Compression (UNC3): The distribution types for the Hard Compression (UNC3) properties

are shown in Table 29 and Appendix 24. For RTD ultimate strength the distribution is Weibull for RTD

and lognormal for ETW2. For ETW2 the distribution type is lognormal or normal for ultimate strength

and Weibull for modulus. Poisson¶s ratio data are not available.

Quasi Isotropic Tension (UNT1): The distribution types for the Quasi Isotropic Tension (UNT1)

properties are shown in Table 30 and Appendix A.25. For ultimate strength the distribution varies

between the three test temperatures and for modulus the distribution is lognormal for CTD and ETW2 and

Weibull for RTD. Poisson¶s ratio data are not available.

Soft Tension (UNT2): The distribution types for the Soft Tension (UNT2) properties are shown in

Table 31 and Appendix A.26. For ultimate strength and modulus response variables, the distributions are

lognormal with the exception of RTD ultimate strength with a Weibull distribution. Poisson¶s ratio data

are not available. Normal distribution can be assumed for ultimate strength and modulus, as noted in the

table.

TABLE 26.2BEST-FIT DISTRIBUTION TYPES FOR QUASI ISOTROPIC

SHORT BEAM STRENGTH (SBS1) TEST PROPERTIES FOR

MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.21.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

RTD Weibull (8.606, 34.978)

ETW Weibull (6.114, 17.023)

ETW2 Weibull (4.70, 22.380)

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described

 in the Section 3Overview of Distribution Types. ́

TABLE 27.2BEST-FIT DISTRIBUTION TYPES FOR QUASI ISOTROPIC COMPRESSION

(UNC1) TEST PROPERTIES FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.22.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

Modulus (Msi),

measured

RTD Normal (67.523, 3.823) Lognormal (1.847, 0.032)

ETW Lognormal (3.957, 0.036)

 or normal Lognormal (1.911, 0.034)

ETW2 Weibull (46.421, 20.814)

 or normal Weibull (6.946, 27.106)

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in the Section

 3Overview of Distribution Types. ́
NASA/TM22013-216572 17

TABLE 28.2BEST-FIT DISTRIBUTION TYPES FOR SOFT COMPRESSION (UNC2)

TEST PROPERTIES FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.23.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

Modulus (Msi),

measured

RTD Lognormal (3.891, 0.030)

 or normal

Weibull (4.372, 103.167)

ETW2 Weibull (35.332, 37.019) Lognormal (1.405, 0.041)

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in the Section

 3Overview of Distribution Types. ́

TABLE 29.2BEST-FIT DISTRIBUTION TYPES FOR HARD COMPRESSION (UNC3)

TEST PROPERTIES FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.24.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

Modulus (Msi),

measured

RTD Weibull (81.148, 50.142) Lognormal (2.143, 0.033)

ETW2 Lognormal (4.068, 0.072)

 or normal

Weibull (8.785, 95.155)

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in the Section

 3Overview of Distribution Types. ́

TABLE 30.2BEST-FIT DISTRIBUTION TYPES FOR QUASI ISOTROPIC TENSION

(UNT1) TEST PROPERTIES FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.25.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

Modulus (Msi),

measured

CTD Normal (105.729, 5.941) Lognormal (2.092, 0.039)

RTD Lognormal (4.618, 0.048)

 or normal

Weibull (7.271, 58.429)

ETW2 Weibull (73.847, 39.746) Lognormal (2.00, 0.023)

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in

 the Section 3Overview of Distribution Types. ́

TABLE 31.2BEST-FIT DISTRIBUTION TYPES FOR SOFT TENSION (UNT2)

TEST PROPERTIES FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.26.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

Modulus (Msi),

measured

CTD Lognormal (4.176, 0.015)

 or normal

Lognormal (1.420, 0.034)

RTD Weibull (59.029, 42.698)

 or normal

Lognormal (1.522, 0.017)

 or normal

ETW2 Lognormal (3.703, 0.025)

 or normal

Lognormal (1.422, 0.033)

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in the Section

 3Overview of Distribution Types. ́

Hard Tension (UNT3): The distribution types for the Hard Tension (UNT3) properties are shown in

Table 32 and Appendix A.27. For ultimate strength the distributions are Weibull and lognormal and for

modulus the distributions are lognormal. Poisson¶s ratio data are not available. Normal distribution can be

assumed for RTD and ETW2 for ultimate strength.
NASA/TM22013-216572 18

Warp Compression (WC): The distribution types for the Warp Compression (WC) properties are

shown in Table 33 and Appendix A.28. For the ETW temperature condition the distribution is Weibull for

all three response variables. For test temperature ETW2, the distributions are lognormal for all three

response variables. For CTD and RTD the distributions vary as shown in the table. For both ultimate

strength and Poisson¶s ratio, normal distribution can be assumed for all temperature conditions.

Warp Tension (WT): The distribution types for the Warp Tension (WT) properties are shown in

Table 34 and Appendix A.29. For ETW2 the distribution is lognormal for both ultimate strength and

modulus response variables. Comparing the AICc values for CTD, RTD, and ETW the difference is less

than 1 percent; therefore, either distribution can be assumed, as noted in the table. Data for Poisson¶s ratio

are not available.

TABLE 32.2BEST-FIT DISTRIBUTION TYPES FOR HARD TENSION (UNT3)

TEST PROPERTIES FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.27.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

Modulus (Msi),

measured

CTD Weibull (139.818, 26.967) Lognormal (2.113, 0.025)

RTD Lognormal (4.877, 0.042)

 or normal Lognormal (2.232, 0.022)

ETW2 Weibull (106.552, 31.986)

 or normal Lognormal (2.246, 0.012)

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in the Section

 3Overview of Distribution Types. ́

TABLE 33.2BEST-FIT DISTRIBUTION TYPES FOR WARP COMPRESSION (WC)

TEST PROPERTIES FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.28.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

Modulus (Msi),

measured

Poisson¶s

ratio

CTD Lognormal (4.731, 0.066)

 or normal

Weibull (9.517, 26.959) Lognormal (±2.951, 0.164)

 or normal

RTD Lognormal (4.399, 0.066)

 or normal

Normal (8.611, 0.384) Lognormal (±3.177, 0.167)

 or normal

ETW Weibull (65.778, 11.128)

 or normal

Weibull (10.051, 26.983) Weibull (0.046, 6.353)

 or normal

ETW2 Lognormal (4.051, 0.087)

 or normal

Lognormal (2.279, 0.057)

 or normal

Lognormal (±3.247, 0.148)

 or normal

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in the Section 3Overview of Distribution Types. ́

TABLE 34.2BEST-FIT DISTRIBUTION TYPES FOR WARP TENSION (WT)

TEST PROPERTIES FOR MTM45-1/CF7442A-36% RW: CMH CURE CYCLE

[Graphical results in Appendix A.29.]

Test

temperature

conditiona

Propertyb

Ultimate strength (ksi),

measured

Modulus (Msi),

measured

CTD Lognormal (4.984, 0.069)

 or normal

Normal (10.286, 0.557)

RTD Normal (141.518, 8.840) Lognormal (2.326, 0.029)

ETW Normal (124.661, 8.533) Lognormal (2.345, 0.017)

 or normal

ETW2 Lognormal (4.803, 0.075)

 or normal

Lognormal (2.362, 0.033)

aConditions are defined in Table 2.

b

Parameters displayed with each distribution type are described in the Section

 3Overview of Distribution Types. ́
NASA/TM22013-216572 19

Concluding Remarks

Statistical distributions were investigated for the material reported in 3NPN100101 AITR1615-IMPW

MTM45-1 IM7 6K PW RAW DATA REPORT. ́ The best-fitted distributions that are obtained using the

JPM software will be utilized in future probabilistic analyses of spacecraft structures. A comparison table

for all distributions was generated and the Akaike¶s Information Criterion (AICc) value is depicted for

each type in ascending order, along with the Summary Distributions for each fitted distribution type,

Diagnostic Plots, and Goodness-of-Fit Tests. Distribution types with the smaller AICc values indicate the

best fit. In many cases, as noted in the tables, the difference of the AICc values compared with the normal

distribution was very small, namely less than 2 percent, indicating that various test temperature conditions

and properties can fit a normal distribution. For these cases there is no need to choose only one particular

distribution, which eliminates the problems of making incorrect assumptions of the chosen distribution.

Forward Work

We recommend a building block analysis approach to study material combinations and their effects

on the performance of structural components accounting for the scatter in stiffness and strength of the

composite material. To this end we can start with simple beams and plates and consider their stability,

vibrations, and strength. We can explore how the performance is affected because of the measured

variability in the properties and arrive at recommendations regarding the extent of material uncertainties

that can be endured without adversely affecting the performance and reliability.

NASA/TM22013-216572 21

Appendix A

The distribution types for material physical properties such as ultimate strength, modulus, and

Poisson¶s ratio are determined using the commercially available statistical discovery software JMP Pro

(Ref. 3). This appendix presents the best-fit distributions for each test type described in the report, using

JMP¶s graphical and semigraphical methods. The 3Distribution Condition ́ is shown on the top bar

followed by the material property, such as 3Ultimate Strength, ksi, Measured, ́ and the corresponding

results. The graphical methods depict the 3Normal Quantile Plot ́ to assist in visualizing the extent to

which a variable is normally distributed. The normal quantile plot also shows confidence bounds and

Probability Normal Quantile Scales. The 3Outlier Box Plot ́ identifies possible outliers. The vertical line

within the box represents the median sample value. The confidence diamond represents the upper and

lower 95 percent of the mean. A line through the middle of the diamond represents the mean. The ends of

the box represent the 25th and 75th quantiles, and the bracket outside of the box identifies the shortest

half, which is the most dense 50 percent of the observations. The data are displayed using histograms that

show a bar for grouped values of the continuous variable and a line graph depicting the best distribution

fit. 3Summary Statistics ́ for each distribution are given in terms of the mean, standard deviation, and the

standard error of the mean. The upper and lower 95 percent mean confidence limits about the mean define

the interval that is likely to contain the true sample mean. Next to Summary Statistics, a 3Compare

Distributions ́ table including the AICc value is provided. The fitted 3Parameter Estimates ́ along with the

3Goodness-of-Fit ́ test statistics and a 3Diagnostic Plot ́ is displayed for the best fit distribution.

A.1 Fill Compression (FC)

The determination of statistical distribution types for the Fill Compression (FC) test results is

presented here.

-1.28

-0.67

0.0

0.67

1.28

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal QuantilePlot

90 95 100 105 110 115

 Weibull(106.301,17.1983)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

102.9642

7.7544773

2.5848258

108.92482

97.003585

9

Summary Statistics

Show

Weibull

Extreme Value

Normal

Gamma

LogNormal

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Exponential

Distribution

66.8326862

66.8326862

67.4097608

67.4602919

67.5271419

71.3928688

72.1497155

79.3499817

87.6848505

103.990294

AICc

Compare Distributions

Scale

Shape

Type

?

?

Parameter

106.30099

17.198346

Estimate

101.40241

9.4154868

Lower 95%

111.07772

27.923539

Upper 95%

-2log(Likelihood) = 60.8326861986863

Parameter Estimates

 Cramer-von Mises W Test

0.065192

W-Square

 > 0.2500

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test Weibull 2 parameterProbabili yt

0.10

0.15

0.20

0.25

0.30

0.40

0.50

0.60

0.70

0.80

0.90

100 114.21850996

Ultimate Strength, ksi, Measured

Diagnostic Plot

Fitted 2 parameter Weibull

Ultimate Strength, ksi, Measured

Distributions Condition=CTD
NASA/TM22013-216572 22 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Normal Probability
NASA/TM22013-216572 23 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 24 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability

Gamma Quantile
NASA/TM22013-216572 25 Normal Quantile Plot

Weibull 2 parameter Probability

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

7.5 8 8.5 9 9.5 10 10.5

LogNormal(2.14612,0.08034)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

8.5793889

0.7142993

0.1683619

8.9346016

8.2241762

18

Summary Statistics

Show

LogNormal

Gamma

Normal

Johnson Sl

Weibull

Extreme Value

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

42.3703752

42.4653374

42.7694692

45.0075529

45.2211344

45.2211344

45.2846609

48.3701903

51.1199646

67.010997

115.627057

AICc

Compare Distributions

Scale

Shape

Type Parameter

2.1461215

0.0803439

Estimate

2.106934

0.05984

Lower 95%

2.1853091

0.1159046

Upper 95%

-2log(Likelihood) = 37.5703751997931

Parameter Estimates

Kolmogorov's D

0.143169

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

7 8 9 10

Modulus, Msi, Measured

Diagnostic Plot

Fitted LogNormal

Modulus, Msi, Measured

Distributions Condition=RTD
NASA/TM22013-216572 26 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 27 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 28

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

7.5 8 8.5 9 9.5 10 10.5

Weibull(9.49353,17.0587)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

9.1860476

0.7221574

0.1575877

9.5147697

8.8573255

21

Summary Statistics

Show

Weibull

Extreme Value

Johnson Sl

Normal

Gamma

LogNormal

GLog

Normal 2 Mixture

Johnson Su

Normal 3 Mixture

Exponential

Distribution

46.3296897

46.3296897

48.036456

49.5905759

50.3409609

50.7696594

52.3110807

53.6132781

55.3994399

68.692667

137.353329

AICc

Compare Distributions

Scale

Shape

Type Parameter

9.4935349

17.058671

Estimate

9.225184

11.64229

Lower 95%

9.753752

23.694769

Upper 95%

-2log(Likelihood) = 41.6630230713182

Parameter Estimates

Cramer-von Mises W Test

0.047108

W-Square

> 0.2500

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test Weibull 2 parameter Probability

0.05

0.10

0.15

0.20

0.30

0.40

0.50

0.60

0.75

0.85

0.95

10 8 9

Modulus, Msi, Measured

Diagnostic Plot

Fitted 2 parameter Weibull

Modulus, Msi, Measured

Distributions Condition=ETW2

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 29 Normal Quantile Plot

Log Normal Probability

-1.28

-0.67

0.0

0.67

1.28

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

0.032 0.036 0.040.042 0.046

LogNormal(-3.3096,0.09792)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

0.0367143

0.0041115

0.001554

0.0405168

0.0329117

7

Summary Statistics

Show

LogNormal

Gamma

Normal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Exponential

Normal 2 Mixture

Distribution

-51.999195

-51.72261

-51.050267

-49.16161

-49.16161

-49.101622

-44.999195

-35.101622

-29.464251

8.48464204

AICc

Compare Distributions

Scale

Shape

Type Parameter

-3.309569

0.0979206

Estimate

-3.393297

0.0626703

Lower 95%

-3.22584

0.1845148

Upper 95%

-2log(Likelihood) = -58.9991945533725

Parameter Estimates

Kolmogorov's D

0.273822

D

0.1106

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.03 0.04 0.05

Poisson¶s Ratio

Diagnostic Plot

Fitted LogNormal

Poisson¶s Ratio

Distributions Condition=RTW
NASA/TM22013-216572 30

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

0.035 0.04 0.045 0.05

LogNormal(-3.1375,0.11697)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

0.0436923

0.0053756

0.0014909

0.0469408

0.0404438

13

Summary Statistics

Show

LogNormal

Gamma

Normal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Exponential

Normal 3 Mixture

Distribution

-95.273264

-95.156169

-94.780448

-93.740999

-93.740999

-92.28621

-91.354337

-87.021028

-84.911139

-53.031527

-48.896992

AICc

Compare Distributions

Scale

Shape

Type Parameter

-3.13747

0.1169716

Estimate

-3.206056

0.0831878

Lower 95%

-3.068885

0.1817334

Upper 95%

-2log(Likelihood) = -100.473264159044

Parameter Estimates

Kolmogorov's D

0.148274

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.04 0.05

Poisson¶s Ratio

Diagnostic Plot

Fitted LogNormal

Poisson¶s Ratio

Distributions Condition=ETD1

-1.28

-0.67

0.0

0.67

1.28

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

0.025 0.03 0.035 0.04

Weibull(0.03608,7.69979)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

0.0338333

0.0057764

0.0023582

0.0398953

0.0277714

6

Summary Statistics

Show

Weibull

Extreme Value

Normal

Gamma

LogNormal

Johnson Sl

GLog

Exponential

Johnson Su

Distribution

-38.177132

-38.177132

-37.820457

-37.79147

-37.692452

-28.176897

-27.914386

-25.635705

2.0856179

AICc

Compare Distributions

Scale

Shape

Type Parameter

0.0360779

7.6997903

Estimate

0.0314521

3.5991169

Lower 95%

0.0410474

13.7165

Upper 95%

-2log(Likelihood) = -46.1771316330355

Parameter Estimates

Cramer-von Mises W Test

0.041610

W-Square

> 0.2500

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test Weibull 2 parameter Probability

0.15

0.20

0.25

0.30

0.35

0.40

0.50

0.60

0.70

0.80

0.03 0.04

Poisson¶s Ratio

Diagnostic Plot

Fitted 2 parameter Weibull

Poisson¶s Ratio

Distributions Condition=ETD2
NASA/TM22013-216572 31 Normal Quantile Plot

Normal Probability

Normal Quantile Plot
NASA/TM22013-216572 32

A.2 Quasi Filled Hole Compression (FHC1)

The determination of statistical distribution types for the Quasi Filled Hole Compression (FHC1) test

results is presented here.

Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Normal Probability
NASA/TM22013-216572 33

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=RTD
NASA/TM22013-216572 34

A.3 Soft Filled Hole Compression (FHC2)

The determination of statistical distribution types for the Soft Filled Hole Compression (FHC2) test

results is presented here.

Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 35

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=RTD
NASA/TM22013-216572 36

A.4 Hard Filled Hole Compression (FHC3)

The determination of statistical distribution types for the Hard Filled Hole Compression (FHC3) test

results is presented here.

-1.28

-0.67

0.0

0.67

1.28

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

54 56 58 60 62 64

LogNormal(4.06781,0.04334)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

58.484104

2.7279254

0.9644673

60.764707

56.203502

8

Summary Statistics

Show

LogNormal

Gamma

Normal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Exponential

Distribution

43.9709324

44.0074584

44.159679

45.4806583

45.4806583

49.2750652

49.5709324

58.6083985

77.5733752

83.7667466

AICc

Compare Distributions

Scale

Shape

Type Parameter

4.0678116

0.0433449

Estimate

4.0337819

0.0284385

Lower 95%

4.1018413

0.0777932

Upper 95%

-2log(Likelihood) = 37.5709324304758

Parameter Estimates

Kolmogorov's D

0.176648

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.2

0.3

0.4

0.5

0.6

0.7

0.8

50 60

Ultimate Strength, ksi

Diagnostic Plot

Fitted LogNormal

Ultimate Strength, ksi

Distributions Condition=RTD

Normal Quantile Plot

Normal Probability
NASA/TM22013-216572 37

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=RTD
NASA/TM22013-216572 38

A.5 Quasi Isotropic Filled Hole Tension (FHT1)

The determination of statistical distribution types for the Quasi Isotropic Filled Hole Tension (FHT1)

test results is presented here.

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

58 59 60 61 62 63 64 65 66 67

LogNormal(4.13524,0.03736)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

62.548319

2.4051565

0.5669008

63.744375

61.352262

18

Summary Statistics

Show

LogNormal

Gamma

Normal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

86.4081176

86.415913

86.4759257

87.7317183

87.7317183

89.3062298

89.361359

92.7241154

94.0879304

111.554562

187.143817

AICc

Compare Distributions

Scale

Shape

Type Parameter

4.1352415

0.037355

Estimate

4.1170217

0.0278219

Lower 95%

4.1534613

0.0538886

Upper 95%

-2log(Likelihood) = 81.6081176434759

Parameter Estimates

Kolmogorov's D

0.099544

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

60 70

Ultimate Strength, ksi

Diagnostic Plot

Fitted LogNormal

Ultimate Strength, ksi

Distributions Condition=CTD

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 39

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=CTD

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=RTD
NASA/TM22013-216572 40

A.6 Soft Filled Hole Tension (FHT2)

The determination of statistical distribution types for the Soft Filled Hole Tension (FHT2) test results

is presented here.

-1.28

-0.67

0.0

0.67

1.28

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

48 48.5 49 49.5 50 50.5 51 51.5 52

Weibull(50.9516,71.5996)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

50.477759

1.1868514

0.4196153

51.469991

49.485526

8

Summary Statistics

Show

Weibull

Extreme Value

Johnson Sl

Normal

Gamma

LogNormal

GLog

Johnson Su

Normal 2 Mixture

Exponential

Distribution

27.7877282

27.7877282

29.2622874

30.8438796

30.8978393

30.9597717

36.3756293

45.709018

49.7705931

81.4111918

AICc

Compare Distributions

Scale

Shape

Type Parameter

50.951575

71.599572

Estimate

50.324056

35.689153

Lower 95%

51.552706

125.1388

Upper 95%

-2log(Likelihood) = 21.3877281668755

Parameter Estimates

Cramer-von Mises W Test

0.113412

W-Square

0.0558

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test Weibull 2 parameter Probability

0.15

0.20

0.25

0.30

0.35

0.45

0.55

0.65

0.75

0.85

48.2119469 50

Ultimate Strength, ksi

Diagnostic Plot

Fitted 2 parameter Weibull

Ultimate Strength, ksi

Distributions Condition=CTD

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 41

-1.28

-0.67

0.0

0.67

1.28

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

33.5 34 34.5 35 35.5 36 36.5 37

LogNormal(3.5566,0.03171)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

35.061472

1.1900886

0.4207598

36.056411

34.066533

8

Summary Statistics

Show

LogNormal

Gamma

Normal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Exponential

Distribution

30.79006

30.7986522

30.8874602

31.1738178

31.1738178

35.0375688

36.4192087

45.7526009

53.5310544

75.5803127

AICc

Compare Distributions

Scale

Shape

Type Parameter

3.5565997

0.0317088

Estimate

3.5317053

0.0208041

Lower 95%

3.5814941

0.0569095

Upper 95%

-2log(Likelihood) = 24.3900600490189

Parameter Estimates

Kolmogorov's D

0.256788

D

0.1206

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.2

0.3

0.4

0.5

0.6

0.7

0.8

30 40

Ultimate Strength, ksi

Diagnostic Plot

Fitted LogNormal

Ultimate Strength, ksi

Distributions Condition=ETW2
NASA/TM22013-216572 42

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=CTD

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=RTD
NASA/TM22013-216572 43

A.7 Hard Filled Hole Tension (FHT3)

The determination of statistical distribution types for the Hard Filled Hole Tension (FHT3) test results

is presented here.

Normal Quantile Plot

Log Normal Probability

-2e+307-1e+307 05e+306 1.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=CTD

-2e+307-1e+307 05e+306 1.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=RTD
NASA/TM22013-216572 44

A.8 Warp Flexure Strength and Modulus (FSM)

The determination of statistical distribution types for the Warp Flexure Strength and Modulus (FSM)

test results is presented here.

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

80 90 100 110 120 130 140

Weibull(117.573,8.94927)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

111.34611

14.699668

3.4647449

118.65608

104.03614

18

Summary Statistics

Show

Weibull

Extreme Value

Normal

Gamma

LogNormal

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

151.528874

151.528874

151.643483

151.991675

152.29554

154.338806

154.528919

157.891978

161.658225

178.344284

207.905165

AICc

Compare Distributions

Scale

Shape

Type Parameter

117.57276

8.949266

Estimate

110.7889

6.0321449

Lower 95%

124.3428

12.439583

Upper 95%

-2log(Likelihood) = 146.728873689672

Parameter Estimates

Cramer-von Mises W Test

0.044464

W-Square

> 0.2500

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test Weibull 2 parameter Probability

0.10

0.15

0.20

0.25

0.35

0.45

0.55

0.65

0.75

0.85

100 80 90 200

Ultimate Strength, ksi, Measured

Diagnostic Plot

Fitted 2 parameter Weibull

Ultimate Strength, ksi, Measured

Distributions Condition=RTD

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

75 80 85 90 95 100 105 110

LogNormal(4.4888,0.07705)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

89.282934

7.225399

1.7030429

92.87604

85.689827

18

Summary Statistics

Show

LogNormal

Gamma

Normal

Johnson Sl

GLog

Weibull

Extreme Value

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

125.201605

125.456327

126.075476

126.610239

128.11589

129.801143

129.801143

129.972876

132.709953

149.588529

199.955173

AICc

Compare Distributions

Scale

Shape

Type Parameter

4.4888024

0.0770538

Estimate

4.4512197

0.0573895

Lower 95%

4.5263852

0.1111582

Upper 95%

-2log(Likelihood) = 120.401604678275

Parameter Estimates

Kolmogorov's D

0.136784

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

80 90 100

Ultimate Strength, ksi, Measured

Diagnostic Plot

Fitted LogNormal

Ultimate Strength, ksi, Measured

Distributions Condition=ETW
NASA/TM22013-216572 45 Normal Quantile Plot

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

8.5 8.75 9 9.25 9.5 9.75 10

LogNormal(2.22033,0.03846)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

9.2172222

0.3685872

0.0868768

9.4005163

9.0339281

18

Summary Statistics

Show

LogNormal

Gamma

Normal

Johnson Sl

Johnson Su

GLog

Normal 2 Mixture

Weibull

Extreme Value

Normal 3 Mixture

Exponential

Distribution

18.5197326

18.6452833

18.9509822

20.7046183

21.2930624

21.4340183

23.3876238

23.6105094

23.6105094

39.4772122

118.208654

AICc

Compare Distributions

Scale

Shape

Type Parameter

2.2203292

0.0384589

Estimate

2.2015709

0.0286441

Lower 95%

2.2390874

0.0554811

Upper 95%

-2log(Likelihood) = 13.719732573022

Parameter Estimates

Kolmogorov's D

0.189612

D

0.0858

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

8 9 10

Modulus, Msi, Measured

Diagnostic Plot

Fitted LogNormal

Modulus, Msi, Measured

Distributions Condition=ETW
NASA/TM22013-216572 46

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=ETW

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=RTD
NASA/TM22013-216572 47

A.9 Fill Tension (FT)

The determination of statistical distribution types for the Fill Tension (FT) test results is presented

here.

Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 48 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 49 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 50 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 51 Normal Quantile Plot

Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 52 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 53 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 54 Normal Quantile Plot

Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 55 Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 56

All fits require at least 4 pointsNormal Quantile Plot Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 57 Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 58

A.10 In-Plane Shear (IPS1)

The determination of statistical distribution types for the In-Plane Shear (IPS1) test results is

presented here.

Normal Quantile Plot

Normal Probability

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

5.2 5.4 5.6 5.8 6 6.2

LogNormal(1.7374,0.05071)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

5.6898539

0.2980002

0.0702393

5.8380459

5.5416619

18

Summary Statistics

Show

LogNormal

Gamma

Normal

Johnson Sl

Weibull

Extreme Value

GLog

Normal 2 Mixture

Johnson Su

Normal 3 Mixture

Exponential

Distribution

11.090344

11.1404797

11.2979824

11.2992656

13.102419

13.102419

14.0046297

16.6475373

17.0829402

26.9856244

100.842644

AICc

Compare Distributions

Scale

Shape

Type Parameter

1.7373957

0.0507115

Estimate

1.7126613

0.0377698

Lower 95%

1.7621301

0.0731567

Upper 95%

-2log(Likelihood) = 6.29034397406901

Parameter Estimates

Kolmogorov's D

0.142427

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

5 6

Shear Strength, ksi 0.2% Offset

Diagnostic Plot

Fitted LogNormal

Shear Strength, ksi 0.2% Offset

Distributions Condition=RTD
NASA/TM22013-216572 59 Normal Quantile Plot Normal Quantile Plot
NASA/TM22013-216572 60 Normal Quantile Plot Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 61 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 62 Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 63

Normal Quantile Plot

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 64 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 65 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 66 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Normal Probability
NASA/TM22013-216572 67 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 68 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 69

A.11 Quasi Isotropic Open Hole Compression (OHC1)

The determination of statistical distribution types for the Quasi Isotropic Open Hole Compression

(OHC1) test results is presented here. Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 70

-1.28

-0.67

0.0

0.67

1.28

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

32 32.5 33 33.5 34 34.5 35 35.5 36

LogNormal(3.50401,0.02933)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

33.26303

1.0617758

0.3753944

34.150697

32.375363

8

Summary Statistics

Show

LogNormal

Gamma

Normal

Johnson Sl

Weibull

Extreme Value

GLog

Johnson Su

Normal 2 Mixture

Exponential

Distribution

28.7006695

28.7966404

29.0621012

31.2265986

32.2003241

32.2003241

34.3006695

40.7666132

63.9388546

74.7378118

AICc

Compare Distributions

Scale

Shape

Type Parameter

3.5040113

0.0293296

Estimate

3.4809849

0.0192431

Lower 95%

3.5270378

0.0526393

Upper 95%

-2log(Likelihood) = 22.3006694642085

Parameter Estimates

Kolmogorov's D

0.281746

D

0.0607

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.2

0.3

0.4

0.5

0.6

0.7

0.8

30 40

Ultimate Strength, ksi

Diagnostic Plot

Fitted LogNormal

Ultimate Strength, ksi

Distributions Condition=ETW

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

29 30 31 32 33 34

LogNormal(3.44148,0.03367)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

31.250989

1.0943175

0.2579331

31.79518

30.706798

18

Summary Statistics

Show

LogNormal

Gamma

Normal

Johnson Su

Normal 2 Mixture

Johnson Sl

GLog

Weibull

Extreme Value

Normal 3 Mixture

Exponential

Distribution

57.6990457

57.8243251

58.1264986

58.5312456

59.5067793

59.7754848

60.6133314

63.6705162

63.6705162

69.6229151

162.163837

AICc

Compare Distributions

Scale

Shape

Type Parameter

3.4414802

0.033675

Estimate

3.4250553

0.025081

Lower 95%

3.457905

0.0485797

Upper 95%

-2log(Likelihood) = 52.8990457023508

Parameter Estimates

Kolmogorov's D

0.186236

D

0.0957

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

30 34.035596923

Ultimate Strength, ksi

Diagnostic Plot

Fitted LogNormal

Ultimate Strength, ksi

Distributions Condition=ETW2
NASA/TM22013-216572 71

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

4.6 4.8 5 5.2 5.4 5.6

Normal(5.13639,0.23984)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

5.1363889

0.2398439

0.0565317

5.2556604

5.0171173

18

Summary Statistics

Show

Normal

Gamma

LogNormal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

3.48216914

3.5888807

3.67267649

4.11273534

4.11273534

6.18115242

6.36760327

9.09757148

11.2856766

27.5012415

97.1586101

AICc

Compare Distributions

Location

Dispersion

Type Parameter

5.1363889

0.2398439

Estimate

5.0171173

0.1799759

Lower 95%

5.2556604

0.3595605

Upper 95%

-2log(Likelihood) = -1.31783086055385

Parameter Estimates

Shapiro-Wilk W Test

0.982085

W

0.9689

Prob<W

Note: Ho = The data is from the Normal distribution. Small p-values

reject Ho.

Goodness-of-Fit Test Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

4.6 4.8 5 5.2 5.4 5.6

Modulus, Msi

Diagnostic Plot

Fitted Normal

Modulus, Msi

Distributions Condition=RTD

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 72

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

5.5 6 6.5 7 7.5 8 8.5 9

LogNormal(1.92635,0.09329)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

6.8952222

0.6939245

0.1635596

7.2403028

6.5501417

18

Summary Statistics

Show

LogNormal

Gamma

Johnson Sl

Normal

GLog

Johnson Su

Weibull

Extreme Value

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

39.8384022

40.4003525

40.5372028

41.7276722

42.7526879

43.6604407

47.531398

47.531398

52.6400561

67.9275567

107.759835

AICc

Compare Distributions

Scale

Shape

Type Parameter

1.9263455

0.0932944

Estimate

1.8808414

0.0694855

Lower 95%

1.9718496

0.134587

Upper 95%

-2log(Likelihood) = 35.038402226102

Parameter Estimates

Kolmogorov's D

0.124212

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

6 7 89

Modulus, Msi

Diagnostic Plot

Fitted LogNormal

Modulus, Msi

Distributions Condition=ETW2
NASA/TM22013-216572 73

A.12 Soft Open Hole Compression (OHC2)

The determination of statistical distribution types for the Soft Open Hole Compression (OHC2) test

results is presented here.

Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 74

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=RTD
NASA/TM22013-216572 75

A.13 Hard Open Hole Compression (OHC3)

The determination of statistical distribution types for the Hard Open Hole Compression (OHC3) test

results is presented here.

Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 76

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=RTD
NASA/TM22013-216572 77

A.14 Quasi Isotropic Open Hole Tension (OHT1)

The determination of statistical distribution types for the Quasi Isotropic Open Hole Tension (OHT1)

test results is presented here.Normal Quantile Plot

Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 78 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 79 Normal Quantile Plot

Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 80 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 81 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 82

A.15 Soft Open Hole Tension (OHT2)

The determination of statistical distribution types for the Soft Open Hole Tension (OHT2) test results

is presented here.

Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 83 Normal Quantile Plot

Weibull 2 parameter Probability

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=CTD

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=RTD
NASA/TM22013-216572 84

A.16 Hard Open Hole Tension (OHT3)

The determination of statistical distribution types for the Hard Open Hole Tension (OHT3) test results

is presented here.

Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 85 Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 86

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=CTD

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Modulus, Msi

Distributions Condition=RTD
NASA/TM22013-216572 87

A.17 Quasi Isotropic Pin Bearing (PB1)

The determination of statistical distribution types for the Quasi Isotropic Pin Bearing (PB1) test

results is presented here.

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 88 Normal Quantile Plot

Weibull 2 parameter Probability

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

90 95 100 105 110

Weibull(105.228,25.9168)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

102.93165

5.2551515

1.1750876

105.39113

100.47216

20

Summary Statistics

Show

Weibull

Extreme Value

Johnson Sl

Normal

Gamma

LogNormal

GLog

Normal 2 Mixture

Johnson Su

Normal 3 Mixture

Exponential

Distribution

124.010989

124.010989

126.169611

126.831777

127.232743

127.462395

129.60003

132.410274

132.767009

137.640437

227.584828

AICc

Compare Distributions

Scale

Shape

Type Parameter

105.22814

25.91675

Estimate

103.20519

17.561829

Lower 95%

107.16885

36.172378

Upper 95%

-2log(Likelihood) = 119.30510688805

Parameter Estimates

Cramer-von Mises W Test

0.055909

W-Square

> 0.2500

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test Weibull 2 parameter Probability

0.05

0.10

0.15

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

100 111.54264927

Strength, ksi, Ultimate

Diagnostic Plot

Fitted 2 parameter Weibull

Strength, ksi, Ultimate

Distributions Condition=ETW2
NASA/TM22013-216572 89

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

55 60 65 70 75 80 85 90 95 100

Weibull(83.1379,10.0129)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

79.138667

9.3987053

2.2152961

83.812533

74.4648

18

Summary Statistics

Show

Weibull

Extreme Value

Normal

Gamma

LogNormal

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

135.243107

135.243107

135.542377

136.020108

136.376512

138.056533

139.290798

141.412084

147.952757

161.216487

195.613257

AICc

Compare Distributions

Scale

Shape

Type Parameter

83.137943

10.012917

Estimate

78.842744

6.7554852

Lower 95%

87.403746

13.894341

Upper 95%

-2log(Likelihood) = 130.443106892178

Parameter Estimates

Cramer-von Mises W Test

0.031126

W-Square

> 0.2500

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test Weibull 2 parameter Probability

0.10

0.15

0.20

0.25

0.35

0.45

0.55

0.65

0.75

0.85

60 70 80 90

Strength, ksi, 2% Offset

Diagnostic Plot

Fitted 2 parameter Weibull

Strength, ksi, 2% Offset

Distributions Condition=RTD

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 90 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 91

A.18 Soft Pin Bearing (PB2)

The determination of statistical distribution types for the Soft Pin Bearing (PB2) test results is

presented here.

Normal Quantile Plot

Normal Probability
NASA/TM22013-216572 92 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 93 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 94

-1.28

-0.67

0.0

0.67

1.28

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

85 90 95 100 105

LogNormal(4.54092,0.05092)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

93.900375

5.206868

1.8409058

98.253426

89.547324

8

Summary Statistics

Show

LogNormal

Gamma

Normal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Exponential

Distribution

54.118501

54.2192225

54.5026729

56.4508678

56.4508678

58.3837708

59.718501

65.6200218

84.986588

91.3424167

AICc

Compare Distributions

Scale

Shape

Type Parameter

4.540922

0.0509223

Estimate

4.5009433

0.03341

Lower 95%

4.5809007

0.0913928

Upper 95%

-2log(Likelihood) = 47.7185009648236

Parameter Estimates

Kolmogorov's D

0.259561

D

0.1107

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.2

0.3

0.4

0.5

0.6

0.7

0.8

90 100

Strength, ksi, 4% Offset

Diagnostic Plot

Fitted LogNormal

Strength, ksi, 4% Offset

Distributions Condition=RTD

Normal Quantile Plot

Normal Probability
NASA/TM22013-216572 95

A.19 Hard Pin Bearing (PB3)

The determination of statistical distribution types for the Hard Pin Bearing (PB3) test results is

presented here.

Normal Quantile Plot

Log Normal Probability

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

55 60 65 70 75 80 85 90

LogNormal(4.24574,0.10038)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

70.162333

7.293121

1.4887021

73.241948

67.082718

24

Summary Statistics

Show

LogNormal

Gamma

Normal

Johnson Sl

GLog

Johnson Su

Weibull

Extreme Value

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

166.132602

166.347842

167.053194

168.568387

168.761174

171.473651

171.770028

171.770028

176.377651

184.797184

254.220775

AICc

Compare Distributions

Scale

Shape

Type Parameter

4.245737

0.1003774

Estimate

4.2039165

0.0775083

Lower 95%

4.2875574

0.1371701

Upper 95%

-2log(Likelihood) = 161.561173518896

Parameter Estimates

Kolmogorov's D

0.115984

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

60 70 80 90

Strength, ksi, Initial Peak

Diagnostic Plot

Fitted LogNormal

Strength, ksi, Initial Peak

Distributions Condition=ETW2
NASA/TM22013-216572 96 Normal Quantile Plot

Log Normal Probability

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

80 85 90 95 100 105 110

LogNormal(4.53336,0.06026)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

93.240806

5.8127094

1.1865143

95.695297

90.786314

24

Summary Statistics

Show

LogNormal

Gamma

Normal

Johnson Sl

GLog

Johnson Su

Weibull

Extreme Value

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

155.448097

155.643274

156.162725

157.743697

158.076668

159.221725

162.615268

162.615268

165.487182

176.96016

267.87072

AICc

Compare Distributions

Scale

Shape

Type Parameter

4.5333559

0.0602634

Estimate

4.5082482

0.0465335

Lower 95%

4.5584636

0.0823525

Upper 95%

-2log(Likelihood) = 150.876668203408

Parameter Estimates

Kolmogorov's D

0.116687

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

80 90 100

Strength, ksi, Ultimate

Diagnostic Plot

Fitted LogNormal

Strength, ksi, Ultimate

Distributions Condition=ETW2
NASA/TM22013-216572 97

Log Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 98

-1.28

-0.67

0.0

0.67

1.28

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

70 75 80 85 90 95 100 105 110

Weibull(97.1626,9.30792)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

92.07375

12.299935

4.3486836

102.35675

81.790747

8

Summary Statistics

Show

Weibull

Extreme Value

Gamma

Normal

LogNormal

Johnson Sl

GLog

Johnson Su

Exponential

Normal 2 Mixture

Distribution

68.1382857

68.1382857

68.2437048

68.2565195

68.3083558

73.7443359

73.7882714

83.1218246

91.0281048

100.068356

AICc

Compare Distributions

Scale

Shape

Type Parameter

97.162615

9.3079175

Estimate

88.488672

4.9380084

Lower 95%

106.02002

15.367119

Upper 95%

-2log(Likelihood) = 61.738285737615

Parameter Estimates

Cramer-von Mises W Test

0.037526

W-Square

> 0.2500

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test Weibull 2 parameter Probability

0.15

0.20

0.25

0.30

0.35

0.45

0.55

0.65

0.75

0.85

100 70 80 90

Strength, ksi, 4% Offset

Diagnostic Plot

Fitted 2 parameter Weibull

Strength, ksi, 4% Offset

Distributions Condition=RTD

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

50 55 60 65 70 75 80

Weibull(68.5096,10.6522)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

65.270292

7.5753936

1.5463208

68.4691

62.071483

24

Summary Statistics

Show

Weibull

Extreme Value

Normal

Gamma

Johnson Sl

LogNormal

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

167.472605

167.472605

168.875933

169.617813

169.965627

170.114126

172.742697

172.870876

172.959384

187.751228

250.751593

AICc

Compare Distributions

Scale

Shape

Type Parameter

68.509631

10.652223

Estimate

65.648423

7.5276395

Lower 95%

71.322796

14.408265

Upper 95%

-2log(Likelihood) = 162.901176094753

Parameter Estimates

Cramer-von Mises W Test

0.039524

W-Square

> 0.2500

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test Weibull 2 parameter Probability

0.05

0.10

0.15

0.20

0.30

0.40

0.50

0.65

0.80

0.90

50 60 70 80

Strength, ksi, 4% Offset

Diagnostic Plot

Fitted 2 parameter Weibull

Strength, ksi, 4% Offset

Distributions Condition=ETW2
NASA/TM22013-216572 99

 A.20 Short Beam Strength (SBS)

The determination of statistical distribution types for the Short Beam Strength (SBS) test results is

presented here.

Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 100 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 101

Log Normal Probability
NASA/TM22013-216572 102

A.21 Quasi Isotropic Short Beam Strength (SBS1)

The determination of statistical distribution types for the Quasi Istrotropic Short Beam Strength

(SBS1) test results is presented here. Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 103 Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 104

A.22 Quasi Isotropic Compression (UNC1)

The determination of statistical distribution types for the Quasi Isotropic Compression (UNC1) test

results is presented here.

Normal Quantile Plot

Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 105 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 106 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 107

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=ETW

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=RTD
NASA/TM22013-216572 108

A.23 Soft Compression (UNC2)

The determination of statistical distribution types for the Soft Compression (UNC2) test results is

presented here.

Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot
NASA/TM22013-216572 109 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 110

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=RTD
NASA/TM22013-216572 111

A.24 Hard Compression (UNC3)

The determination of statistical distribution types for the Hard Compression (UNC3) test results is

presented here.

Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 112 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 113

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=RTD
NASA/TM22013-216572 114

A.25 Quasi Isotropic Tension (UNT1)

The determination of statistical distribution types for the Quasi Isotropic Tension (UNT1) test results

is presented here.

Normal Quantile Plot

Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 115 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 116 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 117

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=CTD

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=RTD
NASA/TM22013-216572 118

A.26 Soft Tension (UNT2)

The determination of statistical distribution types for the Soft Tension (UNT2) test results is

presented here.

Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Weibull 2 parameter Probability
NASA/TM22013-216572 119 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 120

-1.28

-0.67

0.0

0.67

1.28

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

4.5 4.55 4.6 4.65 4.7

LogNormal(1.52204,0.01745)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

4.58225

0.0858067

0.0303372

4.6539862

4.5105138

8

Summary Statistics

Show

LogNormal

Gamma

Normal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Exponential

Distribution

-11.318561

-11.298065

-11.187519

-9.8413971

-9.8413971

-7.1231858

-5.6557701

3.67759132

19.3168362

43.021709

AICc

Compare Distributions

Scale

Shape

Type Parameter

1.5220375

0.0174505

Estimate

1.5083372

0.0114492

Lower 95%

1.5357378

0.0313193

Upper 95%

-2log(Likelihood) = -17.7185612005223

Parameter Estimates

Kolmogorov's D

0.241649

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test Log Normal Probability

0.2

0.3

0.4

0.5

0.6

0.7

0.8

4 5

Modulus, Msi, Measured

Diagnostic Plot

Fitted LogNormal

Modulus, Msi, Measured

Distributions Condition=RTD

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 121

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=CTD

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=RTD
NASA/TM22013-216572 122

A.27 Hard Tension (UNT3)

The determination of statistical distribution types for the Hard Tension (UNT3) test results is

presented here.

Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 123 Normal Quantile Plot

Weibull 2 parameter Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 124 Normal Quantile Plot

Log Normal Probability

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 125

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=CTD

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=ETW2

-2e+307-1e+307 05e+3061.5e+307

Quantiles

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=RTD
NASA/TM22013-216572 126

A.28 Warp Compression (WC)

The determination of statistical distribution types for the Warp Compression (WC) test results is

presented here.

Normal Quantile Plot

Log Normal Probability

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

70 75 80 85 90

LogNormal(4.39957,0.06612)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

81.5945

5.5753397

1.3141202

84.367051

78.821949

18

Summary Statistics

Show

LogNormal

Gamma

Normal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

116.478183

116.535199

116.742504

119.193591

119.193591

119.314196

119.392469

122.676834

123.902718

143.960108

196.713427

AICc

Compare Distributions

Scale

Shape

Type Parameter

4.3995708

0.0661165

Estimate

4.3673227

0.0492434

Lower 95%

4.431819

0.09538

Upper 95%

-2log(Likelihood) = 111.678183233328

Parameter Estimates Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

70 80 90

Ultimate Strength, ksi, Measured

Diagnostic Plot

Kolmogorov's D

0.115266

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test

Fitted LogNormal

Ultimate Strength, ksi, Measured

Distributions Condition=RTD
NASA/TM22013-216572 127

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

45 50 55 60 65 70 75

Weibull(65.7784,11.1278)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

62.798566

6.9537937

1.4194372

65.734895

59.862236

24

Summary Statistics

Show

Weibull

Extreme Value

Normal

Gamma

LogNormal

Johnson Sl

GLog

Normal 2 Mixture

Johnson Su

Normal 3 Mixture

Exponential

Distribution

163.371169

163.371169

164.766272

165.471274

165.933628

166.064578

167.373414

170.011375

170.279114

180.091138

248.898565

AICc

Compare Distributions

Scale

Shape

Type Parameter

65.778426

11.127807

Estimate

63.151268

7.882501

Lower 95%

68.361678

14.976333

Upper 95%

-2log(Likelihood) = 158.799740642437

Parameter Estimates Weibull 2 parameter Probability

0.05

0.10

0.15

0.20

0.30

0.40

0.50

0.65

0.80

0.90

50 60 70 80

Ultimate Strength, ksi, Measured

Diagnostic Plot

Cramer-von Mises W Test

0.043897

W-Square

> 0.2500

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test

Fitted 2 parameter Weibull

Ultimate Strength, ksi, Measured

Distributions Condition=ETW

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

50 55 60 65 70

LogNormal(4.05124,0.08731)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

57.688655

5.1970767

1.2249627

60.2731

55.10421

18

Summary Statistics

Show

LogNormal

Gamma

Normal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

113.946876

113.997401

114.213254

115.667179

115.667179

116.7403

117.098687

120.461646

123.733506

137.70519

184.232179

AICc

Compare Distributions

Scale

Shape

Type Parameter

4.0512434

0.087307

Estimate

4.0086596

0.0650261

Lower 95%

4.0938272

0.1259496

Upper 95%

-2log(Likelihood) = 109.146875873784

Parameter Estimates Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

50 60 70

Ultimate Strength, ksi, Measured

Diagnostic Plot

Kolmogorov's D

0.146777

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test

Fitted LogNormal

Ultimate Strength, ksi, Measured

Distributions Condition=ETW2
NASA/TM22013-216572 128

-1.28

-0.67

0.0

0.67

1.28

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

8 8.5 9 9.5 10

Weibull(9.5173,26.9595)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

9.3014444

0.5588741

0.1862914

9.7310331

8.8718558

9

Summary Statistics

Show

Weibull

Extreme Value

Johnson Sl

Normal

Gamma

LogNormal

GLog

Johnson Su

Normal 2 Mixture

Exponential

Distribution

16.7689771

16.7689771

19.8487198

20.0679351

20.4685008

20.7086011

25.5086011

27.0487194

38.6843608

60.7144833

AICc

Compare Distributions

Scale

Shape

Type Parameter

9.5172957

26.959492

Estimate

9.2358369

14.312231

Lower 95%

9.7928128

44.386224

Upper 95%

-2log(Likelihood) = 10.768977134893

Parameter Estimates Weibull 2 parameter Probability

0.10

0.15

0.20

0.25

0.30

0.40

0.50

0.60

0.70

0.80

0.90

8 9

Modulus, Msi, Measured

Diagnostic Plot

Cramer-von Mises W Test

0.070908

W-Square

0.2364

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test

Fitted 2 parameter Weibull

Modulus, Msi, Measured

Distributions Condition=CTD

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

8 8.5 9 9.5

Normal(8.61056,0.3838)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

8.6105556

0.3837964

0.0904617

8.801413

8.4196981

18

Summary Statistics

Show

Normal

Gamma

LogNormal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

20.4066361

20.4618702

20.5174549

21.4233448

21.4233448

23.2095762

23.2920705

26.6547603

29.5534211

44.0191378

115.757598

AICc

Compare Distributions

Location

Dispersion

Type Parameter

8.6105556

0.3837964

Estimate

8.4196981

0.2879961

Lower 95%

8.801413

0.5753661

Upper 95%

-2log(Likelihood) = 15.6066360615726

Parameter Estimates Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

8 8.5 9 9.5

Modulus, Msi, Measured

Diagnostic Plot

Shapiro-Wilk W Test

0.963114

W

0.6627

Prob<W

Note: Ho = The data is from the Normal distribution. Small p-values

reject Ho.

Goodness-of-Fit Test

Fitted Normal

Modulus, Msi, Measured

Distributions Condition=RTD
NASA/TM22013-216572 129

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

8.5 9 9.5 10 10.5

Weibull(10.051,26.9833)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

9.8546667

0.4387218

0.0895537

10.039923

9.6694107

24

Summary Statistics

Show

Weibull

Extreme Value

Normal

Gamma

LogNormal

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

30.9856534

30.9856534

32.1337716

32.6227978

32.9080286

33.2609699

35.5366

36.097228

40.1088066

45.185561

160.003184

AICc

Compare Distributions

Scale

Shape

Type Parameter

10.051008

26.983329

Estimate

9.8838519

19.30739

Lower 95%

10.21195

35.971483

Upper 95%

-2log(Likelihood) = 26.4142248445334

Parameter Estimates Weibull 2 parameter Probability

0.05

0.10

0.15

0.20

0.30

0.40

0.50

0.65

0.80

0.90

10 8 9

Modulus, Msi, Measured

Diagnostic Plot

Cramer-von Mises W Test

0.098828

W-Square

0.0980

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test

Fitted 2 parameter Weibull

Modulus, Msi, Measured

Distributions Condition=ETW

Normal Quantile Plot

Log Normal Probability
NASA/TM22013-216572 130

-1.28

-0.67

0.0

0.67

1.28

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

0.045 0.05 0.055 0.06 0.065

LogNormal(-2.9511,0.16366)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

0.053

0.01

0.0044721

0.0654166

0.0405834

5

Summary Statistics

Show

LogNormal

Gamma

Normal

Weibull

Extreme Value

Exponential

GLog

Distribution

-23.42196

-23.293356

-22.862317

-22.584921

-22.584921

-16.0413

-2.9780343

AICc

Compare Distributions

Scale

Shape

Type Parameter

-2.951141

0.1636553

Estimate

-3.127105

0.0978595

Lower 95%

-2.775177

0.3565927

Upper 95%

-2log(Likelihood) = -33.4219597631823

Parameter Estimates Log Normal Probability

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.04 0.05 0.06 0.07

Poisson¶s Ratio

Diagnostic Plot

Kolmogorov's D

0.299132

D

0.1448

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test

Fitted LogNormal

Poisson¶s Ratio

Distributions Condition=CTD

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

0.03 0.035 0.04 0.045 0.05 0.055 0.06

LogNormal(-3.1775,0.16662)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

0.0422857

0.0075898

0.0020284

0.0466679

0.0379035

14

Summary Statistics

Show

LogNormal

Gamma

Normal

Johnson Sl

Weibull

Extreme Value

GLog

Johnson Su

Normal 2 Mixture

Exponential

Normal 3 Mixture

Distribution

-94.326771

-93.938327

-92.845576

-92.423818

-91.148198

-91.148198

-91.01768

-88.379374

-84.728158

-58.239234

-57.874337

AICc

Compare Distributions

Scale

Shape

Type Parameter

-3.17751

0.1666166

Estimate

-3.271131

0.1198104

Lower 95%

-3.083889

0.2541814

Upper 95%

-2log(Likelihood) = -99.4176804223509

Parameter Estimates Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.03 0.04 0.05 0.06

Poisson¶s Ratio

Diagnostic Plot

Kolmogorov's D

0.158773

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test

Fitted LogNormal

Poisson¶s Ratio

Distributions Condition=RTD
NASA/TM22013-216572 131

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

0.03 0.035 0.04 0.045 0.05 0.055

Weibull(0.04564,6.35318)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

0.0424

0.0079565

0.0017791

0.0461237

0.0386763

20

Summary Statistics

Show

Weibull

Extreme Value

Normal

Gamma

LogNormal

Normal 2 Mixture

Johnson Sl

GLog

Johnson Su

Normal 3 Mixture

Exponential

Distribution

-133.23608

-133.23608

-132.88742

-132.66937

-132.33704

-131.75539

-130.22145

-129.54292

-127.05479

-118.88925

-84.202054

AICc

Compare Distributions

Scale

Shape

Type Parameter

0.0456391

6.3531777

Estimate

0.0421573

4.3401018

Lower 95%

0.0491676

8.8227653

Upper 95%

-2log(Likelihood) = -137.941961099895

Parameter Estimates Weibull 2 parameter Probability

0.05

0.10

0.15

0.20

0.30

0.40

0.50

0.60

0.70

0.80

0.90

0.03 0.04 0.05 0.06

Poisson¶s Ratio

Diagnostic Plot

Cramer-von Mises W Test

0.080276

W-Square

0.1938

Prob>W^2

Note: Ho = The data is from the Weibull distribution. Small p-values

reject Ho.

Goodness-of-Fit Test

Fitted 2 parameter Weibull

Poisson¶s Ratio

Distributions Condition=ETW

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

0.03 0.035 0.04 0.045 0.05

LogNormal(-3.2472,0.14763)

 Gamma(46.3575,0.00085,0)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

0.0393077

0.0059892

0.0016611

0.0429269

0.0356884

13

Summary Statistics

Show

Gamma

LogNormal

Normal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Exponential

Normal 3 Mixture

Distribution

-92.113257

-92.073239

-91.97024

-91.528633

-91.528633

-88.618823

-88.544128

-84.210791

-76.669368

-55.781075

-45.986853

AICc

Compare Distributions

Scale

Shape

Type Parameter

-3.24716

0.1476283

Estimate

-3.33372

0.1049903

Lower 95%

-3.160599

0.2293634

Upper 95%

-2log(Likelihood) = -97.2732385832574

Parameter Estimates Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

0.03 0.04 0.05

Poisson¶s Ratio

Diagnostic Plot

Kolmogorov's D

0.137475

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test

Fitted LogNormal

Poisson¶s Ratio

Distributions Condition=ETW2
NASA/TM22013-216572 132

A.29 Warp Tension (WT)

The determination of statistical distribution types for the Warp Tension (WT) test results is presented

here.

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

125130135140145150155160165170

LogNormal(4.98408,0.06916)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

146.41901

10.419922

2.4559992

151.60072

141.23731

18

Summary Statistics

Show

LogNormal

Gamma

Normal

Weibull

Extreme Value

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

139.142749

139.150124

139.255691

140.769716

140.769716

142.055245

142.057035

145.417883

149.611613

164.744792

217.763008

AICc

Compare Distributions

Scale

Shape

Type Parameter

4.9840816

0.0691638

Estimate

4.9503471

0.0515131

Lower 95%

5.017816

0.0997761

Upper 95%

-2log(Likelihood) = 134.342748931088

Parameter Estimates Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

100 200

Ultimate Strength, ksi, Measured

Diagnostic Plot

Kolmogorov's D

0.097146

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test

Fitted LogNormal

Ultimate Strength, ksi, Measured

Distributions Condition=CTD

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

125 130 135 140 145 150 155

Normal(141.518,8.8405)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

141.51829

8.8404957

2.0837248

145.91457

137.12202

18

Summary Statistics

Show

Normal

Weibull

Extreme Value

Gamma

LogNormal

Johnson Sl

GLog

Normal 2 Mixture

Johnson Su

Normal 3 Mixture

Exponential

Distribution

133.338133

133.369748

133.369748

133.37262

133.422673

136.087086

136.22357

138.288699

139.586413

152.906562

216.537443

AICc

Compare Distributions

Location

Dispersion

Type Parameter

141.51829

8.8404957

Estimate

137.12202

6.6337983

Lower 95%

145.91457

13.253176

Upper 95%

-2log(Likelihood) = 128.538133254744

Parameter Estimates Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

125 130 135 140 145 150 155

Ultimate Strength, ksi, Measured

Diagnostic Plot

Shapiro-Wilk W Test

0.933482

W

0.2235

Prob<W

Note: Ho = The data is from the Normal distribution. Small p-values

reject Ho.

Goodness-of-Fit Test

Fitted Normal

Ultimate Strength, ksi, Measured

Distributions Condition=RTD
NASA/TM22013-216572 133

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

105 110 115 120 125 130 135 140

Normal(124.661,8.53278)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

124.66089

8.532784

2.0111965

128.90414

120.41763

18

Summary Statistics

Show

Normal

Weibull

Extreme Value

Gamma

LogNormal

Johnson Sl

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

132.062752

132.14456

132.14456

132.207765

132.326403

134.740502

135.240689

137.404211

138.307975

156.184566

211.971497

AICc

Compare Distributions

Location

Dispersion

Type Parameter

124.66089

8.532784

Estimate

120.41763

6.4028952

Lower 95%

128.90414

12.791872

Upper 95%

-2log(Likelihood) = 127.262751744163

Parameter Estimates Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

105 110 115 120 125 130 135 140

Ultimate Strength, ksi, Measured

Diagnostic Plot

Shapiro-Wilk W Test

0.957124

W

0.5472

Prob<W

Note: Ho = The data is from the Normal distribution. Small p-values

reject Ho.

Goodness-of-Fit Test

Fitted Normal

Ultimate Strength, ksi, Measured

Distributions Condition=ETW

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

105 110 115 120 125 130 135 140

LogNormal(4.80276,0.07506)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

122.19208

9.5431794

2.249349

126.93779

117.44637

18

Summary Statistics

Show

LogNormal

Gamma

Normal

Johnson Sl

Weibull

Extreme Value

GLog

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

135.561308

135.707259

136.091548

137.598237

138.497169

138.497169

138.976981

142.340014

144.400914

155.611047

211.251393

AICc

Compare Distributions

Scale

Shape

Type Parameter

4.8027568

0.0750623

Estimate

4.7661454

0.0559062

Lower 95%

4.8393683

0.1082853

Upper 95%

-2log(Likelihood) = 130.76130798584

Parameter Estimates Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

100 140.75509775

Ultimate Strength, ksi, Measured

Diagnostic Plot

Kolmogorov's D

0.170986

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test

Fitted LogNormal

Ultimate Strength, ksi, Measured

Distributions Condition=ETW2
NASA/TM22013-216572 134

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

9 9.5 10 10.5 11 11.5

Normal(10.2857,0.55669)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

10.285667

0.5566855

0.131212

10.5625

10.008833

18

Summary Statistics

Show

Normal

Gamma

LogNormal

Weibull

Extreme Value

Johnson Sl

GLog

Normal 2 Mixture

Johnson Su

Normal 3 Mixture

Exponential

Distribution

33.794611

33.9633186

34.0888782

34.7643346

34.7643346

36.5099713

37.0031639

38.5924425

39.1988449

45.7082995

122.157048

AICc

Compare Distributions

Location

Dispersion

Type Parameter

10.285667

0.5566855

Estimate

10.008833

0.4177299

Lower 95%

10.5625

0.8345517

Upper 95%

-2log(Likelihood) = 28.9946109732572

Parameter Estimates Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

9 9.5 10 10.5 11 11.5

Modulus, Msi, Measured

Diagnostic Plot

Shapiro-Wilk W Test

0.935318

W

0.2406

Prob<W

Note: Ho = The data is from the Normal distribution. Small p-values

reject Ho.

Goodness-of-Fit Test

Fitted Normal

Modulus, Msi, Measured

Distributions Condition=CTD

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

9.6 9.8 10 10.2 10.4 10.6 10.8 11

LogNormal(2.32569,0.02935)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

10.238167

0.3112323

0.0733582

10.392939

10.083394

18

Summary Statistics

Show

LogNormal

Gamma

Normal

Johnson Sl

GLog

Weibull

Extreme Value

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

12.5809436

12.6609445

12.8620246

14.5683917

15.4952293

16.8531999

16.8531999

17.9310291

22.6267106

39.1696944

121.990412

AICc

Compare Distributions

Scale

Shape

Type Parameter

2.32569

0.0293492

Estimate

2.311375

0.0218592

Lower 95%

2.340005

0.0423393

Upper 95%

-2log(Likelihood) = 7.78094358749449

Parameter Estimates Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10 10.950564015

Modulus, Msi, Measured

Diagnostic Plot

Kolmogorov's D

0.166486

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test

Fitted LogNormal

Modulus, Msi, Measured

Distributions Condition=RTD
NASA/TM22013-216572 135 Normal Quantile Plot

Log Normal Probability

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

10 10.2 10.4 10.6 10.8 11 11.2 11.4

LogNormal(2.36206,0.03273)

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

10.6185

0.3607184

0.0850222

10.797881

10.439119

18

Summary Statistics

Show

LogNormal

Gamma

Normal

Johnson Sl

GLog

Weibull

Extreme Value

Johnson Su

Normal 2 Mixture

Normal 3 Mixture

Exponential

Distribution

17.8138818

17.9194187

18.1741149

19.1955403

20.7281676

22.4615367

22.4615367

22.5581777

23.2824751

40.4301139

123.303519

AICc

Compare Distributions

Scale

Shape

Type Parameter

2.3620591

0.0327288

Estimate

2.3460958

0.0243763

Lower 95%

2.3780225

0.0472147

Upper 95%

-2log(Likelihood) = 13.013881844361

Parameter Estimates Log Normal Probability

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

10 11.409833516

Modulus, Msi, Measured

Diagnostic Plot

Kolmogorov's D

0.156788

D

> 0.1500

Prob>D

Note: Ho = The data is from the LogNormal distribution. Small pvalues reject Ho.

Goodness-of-Fit Test

Fitted LogNormal

Modulus, Msi, Measured

Distributions Condition=ETW2
NASA/TM22013-216572 136

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

-2e+307-1e+307 05e+306 1.5e+307

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

-2e+307-1e+307 05e+306 1.5e+307

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=RTD
NASA/TM22013-216572 137

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

-2e+307-1e+307 05e+306 1.5e+307

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=ETW

-1.64

-1.28

-0.67

0.0

0.67

1.28

1.64

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

Normal Quantile Plot

-2e+307-1e+307 05e+306 1.5e+307

Mean

Std Dev

Std Err Mean

Upper 95% Mean

Lower 95% Mean

N

.

.

.

.

.

0

Summary Statistics

Poisson¶s Ratio

Distributions Condition=ETW2
NASA/TM22013-216572 138

References

1. Lowry David R.: NPN100101 AITR1615-IMPW MTM45-1 IM7 6K PW RAW DATA

REPORT_files. NASA internal database, 2012.

2. Advanced Composites Group: A Data Acquisition and Test Plan for MTM45 1 Prepregs.

AI/TR/1615 Initial Release, Feb. 2009.

3. JMP Pro Software: SAS Institute Inc. http://www.jmp.com Accessed Nov. 21, 2013.

4. Pai, Shantaram S., et al.: NASA/NESSUS 6.2c Probabilistic Structural Analysis Software. NASA

Tech Brief LEW 18229 1, 2012.