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NIST Technical Note 1444

International Comparison of Guarded

Hot Plate Apparatus Using National

and Regional Reference Materials

dtJapan Testing Center

for Construction Materials

LABORATOIRE (^-^ kN N A T I O N A L L<^v n °' EssAis

National NPLBPhysical Laboratory

1*1 National Research Conseil national Council Canada de recherches Canada

Arm

Institute formReference

Materials and Measurements

Robert R. Zarr

James J. Filliben

QC

UJ5153

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NIST Technical Note 1444

International Comparison of Guarded

Hot Plate Apparatus Using National

and Regional Reference Materials

Laboratory Participants

Masayoshi Uezono

Physical Testing Section Central Laboratory

Japan Testing Centerfor Construction Materials

5-21-20, Inari, Soka, Saitama, Japan 340

Gianni Venuti and Sylvie Quin

Departement Energie et Metrologie Thermique

Laboratoire National d'Essais

F-78190 Trappes, France

David Salmon and Ronald Tye

Thermophysical Properties Section

National Physical Laboratory

Queens Road, Teddington, Middlesex, UK TW11 OLW

M. Kumar Kumaran and Fitsum Tariku

Institute for Research in Construction

National Research Council Canada

Ottawa, Ontario K1A0R6 Canada

Jean Pauwels, Andree Lamberty, and Chris Ingelbrecht

European Commission - Joint Research Centre

Institute for Reference Materials and Measurements

Retieseweg, B-2440 GEEL, Belgium

Robert R. Zarr Building and Fire Research Laboratory

National Institute ofStandards and Technology

Gaithersburg, MD 20899-8632

James J. Filliben

Information Technology Laboratory

National Institute ofStandards and Technology

Gaithersburg, MD 20899-8980

May 2002

U.S. Department of Commerce

Donald L. Evans, Secretary

Technology Administration

Phillip J. Bond, Under Secretaryfor Technology

National Institute of Standards and Tcchnolog\

Ardent. Bemcnt. Jr., Director
Certain commercial entities, equipment, or materials may be identified in this document in order to describe an experimental procedure or concept adequately.

Such identification is not intended to imply recommendation or endorsement by the National Institute of Standards and Technology, nor is it intended to imply that the

entities, materials, or equipment are necessarily the best available for the purpose.

National Institute of Standards and Technology Technical Note 1444

Natl. Inst. Stand. Technol. Tech. Note 1444, 88 pages (May 2002)

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ABSTRACT

As part of an international comparison of guarded-hot-plate apparatus, thermal conductivity

measurements of four different thermal insulation materials are presented. The test program

evaluates one regional and three national reference materials using a two-part experimental plan:

1) five independent replicate measurements taken at. a fixed temperature (297.1 5 K); and, singlepoint measurements taken at multiple temperatures (280 K to 320 K). The analysis of the

replicate data provides rankings for the primary factors - laboratory and material. A major

finding of the replicate analysis is the existence of a laboratory-material interaction. In other

words, there are laboratory-to-laboratory changes in both location and variation, which change

from material to material. Further analyses attempt to determine the sources (i.e., underlying

causes) for the variation in the replicate data. Secondary laboratory factors are investigated both

individually following a cause-and-effect chart, and collectively using graphical analysis,

correlation analysis and analysis of variance. The major finding of the multi-temperature (280 K

to 320 K) analysis confirms and supports the laboratory-material interaction as found in the

fixed-temperature replicate data analysis. The multi-temperature analysis also reveals an

increasing difference between laboratories as the mean specimen temperature departs from

297.15 K.

KEY WORDS: comparison, density, certified reference material, expanded polystyrene, fibrous

glass, exploratory data analysis, graphical analysis, guarded hot plate, interlaboratory,

repeatability, SRM, thermal conductivity, thermal insulation

in

Table of Contents

Abstract ii

1 Introduction 1

1 .

Problem Definition 1

1 .2 Comparison Process 1

1 .3 Background 1

1 .4 Overview 2

2 Test Program 2

2.1 Purpose and Objectives 3 2.2 Laboratory Participants 3 2.3 Reference Materials 3

2.4 Certified Values for Reference Materials 4

2.5 Protocol 5

3 Test Method and Apparatus 5 3 .

Operating Principle

3 .2 Equipment 6

3.2.1 Uncertainty 6

3 .2.2 Components 7

3.2.3 Control Stability

4 Material Characterization 8

4.1 Bulk Density (Source Laboratories) 8

4.2 Thermal Conductivity (Source Laboratories) 12

5 Analysis of Fixed Temperature (297.15 K) Replicate Data 14

5.1 Presentation of Laboratory Data 14

5.2 Graphical Exploration of Laboratory Data 17

5.3 Engineering Significance of Laboratory Data 19

5.4 Detailed Investigation of Laboratory Location and Variation 19

5.5 Laboratory and Material Rankings 28

5.6 Comparison of Source and Recipient Laboratory Data 29

6 Assessment of Fixed Temperature (297.15 K) Replicate Data 31

6.Presentation of (Secondary) Laboratory Factors 31

6.2 Evaluation of Major Sources of Variation 34

6.2.Procedure 34

6.2. 1 .Steady-State Conditions 34

6.2. 1 .2 Specimen Conditioning 34

6.2. 1 .3 Surface Temperature Measurement Technique 34

6.2.2 Specimen 35

6.2.3 Equipment 39

6.2.4 Measurement 39

6.2.4.1 Check of Protocol Execution 39

6.2.4.2 Mean Temperature (Tm) 41

6.2.4.3 Temperature Difference (AT) 41

6.2.4.4 Thickness (L) 41
Table of Contents (continued)

6.3 Detailed Investigation of Laboratory Factors 45

6.3.1 Analysis of Variance 50

6.3.2 Correlation 51

6.4 Comparison with Certified Values 53

6.5 Comparison with Standard Test Method Precision Indices 56

7 Summary Findings for Replicate Date (297.15 K) 57

7.1 Descriptive Statistics 59

7.2 Assessment 59

Q 1 : For 2 of the 4 materials laboratory 1 is high, why? 59

Q2: For material 1, laboratory 5 is low, why? 60

Q3 : For material 2, laboratory 3 is low, why? 60

Q4: For material 3, laboratory 4 is low, why? 60

Q5 : For 3 of the 4 materials, laboratory 1 is noisy, why? 60

Q6: For material 2, laboratory 5 appears to have one outlying observation, why? .... 60

7.2.

1

Anomalous Data Points 60

7.2.2 Marginal Data Points 61

7.2.3 Laboratory Factors 61

7.2.4 Comparison of A. with Certified Values 61

7.2.5 Comparison with Standard Test Method Precision Indices 62

7.2.6 Procedural Recommendations for Future Comparisons 62

8 Analysis of Multi-Temperature (280 K to 320 K) Data 63

8.1 Presentation of Laboratory Data 63

8.2 Graphical Exploration of Laboratory Data 63

8.3 Check of Protocol Execution 68

8.4 Comparison with Certified Values 68

8.5 Comparison with Standard Test Method Precision Indices 71

9 Conclusions and Recommendations 73

9.

1

Results 73

9.2 Recommendations 74

1 Acknowledgements 75

1

1

References 75

Appendix A - Participants' Addresses 77

Appendix B - Test Protocols 78

Appendix C - Material Characterization Report Form 79

Appendix D -Test Report Form 80

Appendix E - Postscript - Update After Completion of Analysis of Data 81

VI
List of Tables

TABLE 1 Laboratory Participants 3 TABLE 2 Reference Materials 4

TABLE 3 Regression Coefficients (Eq 1) for SRM 1451, IRMM-440, and SRM 1453 ... 4

TABLE4 Guarded Hot Plate Apparatus 7

TABLE 5 Physical Characteristics of Reference Materials Determined By Source

Laboratories 8 TABLE 6 Summary Statistics for Bulk Density Determined by Source Laboratories 9

TABLE 7 Thermal Conductivity (297.15 K) of Reference Materials Determined by

Source Laboratories 12

TABLE 8 Fixed Temperature (297.15 K) Replicate Data 15

TABLE 9 Summary of the Interlaboratory Comparison 17

TABLE 10a Means for Replicate Data (297.15 K) 21

TABLE 10b Standard Deviations for Replicate Data (297.15 K) 21

TABLE 11a Relative Means for Replicate Data (297.15 K) 28

TABLE lib Relative Standard Deviations for Replicate Data (297.15 K) 28

TABLE 12a Laboratory Ranking by Location 28

TABLE 12b Laboratory Ranking by Variation 29

TABLE 12c Material Ranking by Location and Variation 29

TABLE 13 Laboratory Factors Affecting the Measurement Variability of A, 32

TABLE 14 Conditioning Environments for Specimens (Post-Comparison, except Lab 2) 34

TABLE 15a Mean, Standard Deviation, and Range of Th and Tc (Table 8) 39

TABLE 15b Mean, Standard Deviation, and Range of Tm and AT (Table 8) 39

TABLE 16 Mean and Standard Deviation of L (Table 8) 45

TABLE 1 7 Mean and Standard Deviation of Source Laboratory L (Table 7) 45

TABLE 18 Is a Factor Statistically Significant (FCDF > 95 %? Yes/No) 51

TABLE 19 Is there a Significant Correlation between X and a Laboratory Factor

I r | > 20 %? (Yes/No) 52

TABLE 20 Comparison of Fixed Temperature (297.15 K) Replicate Data with Certified

Values 54

TABLE 21 Relative Means and Standard Deviations for Replicates (297.1 5 K) Excluding

Outlying Data (Material 1 -Lab 1 and Material 3-Lab 4) 56

TABLE 22a Means for Replicate Data (297. 1 5 K) Excluding Outlying Data (Material 1 - Lab 1 and Material 3-Lab 4) 57

TABLE 22b Standard Deviations for Replicate Data (297.1 5 K) Excluding Outlying Data

(Material 1-Lab 1 and Material 3-Lab 4) 57

TABLE23 Multi-Temperature (280 K to 320 K) Data 64

TABLE 24 Summary Results of the Interlaboratory Comparison for the MultiTemperature Data 68

TABLE 25 Comparison of Multi-Temperature (280 K to 320 K) Data with Certified

Values 70

TABLE 26 Relative Ranges from Figure 26 Excluding Outlying Data Identified in

Table 24 71

VI
List of Figures

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

Figure 11a

Figure lib

Figure 12

Figure 13a

Figure 13b

Figure 13c

Figure 14

Figure 15

Figure 16

Figure 17

Figure 18

Figure 19

Figure 20

Figure 21

Figure 22

Figure 23

Figure 24

Figure 25

Figure 26

Figure 27

Figure 28

Multi-plot of bulk density versus specimen pair - source laboratory

(Materials 1,2,3,4) 10

Relative variation in specimen bulk density - source laboratory

(Materials 1,2,3,4) 11 Multi-plot of thermal conductivity versus bulk density - source laboratory

data (Materials 1,2,3,4) 13

Replicate data (297. 1 5 K) versus laboratory (Materials 1 ,2,3 ,4) 18

Replicate data (297.15 K) versus laboratory (Materials 1,2,3,4)

Error bars equal laboratory relative expanded uncertainty (Table 4) 20

Mean plot of replicate data (297.15 K) versus laboratory (Materials 1,2,3,4) 22

Standard deviation plot of replicate data (297.15 K) versus laboratory

(Materials 1,2,3,4) 23

Within- and between-laboratory variability versus grand means

(Materials 1,2,3,4) 25

Relative mean plot of replicate data (297.15 K) versus laboratory (Materials

1,2,3,4) 26

Relative standard deviation plot of replicate data (297.15 K) versus laboratory

(Materials 1,2,3,4) 27

Recipient laboratories versus source laboratory (Materials 1,2,3,4) 30

Relative deviations from source laboratory (Materials 1 ,2,3,4) 30

Cause-and-effect chart for laboratory test result (X) 33

Relative thermal conductivity versus material 36

Relative mean thermal conductivity versus material 36

Relative standard deviation thermal conductivity versus material 36

Thermal conductivity (297.15 K) as a function of bulk density (Materials

1,2,3,4) 38

Multi-plot of thermal conductivity versus test parameter (Materials 1,2,3,4) 40

Replicate data (297.15 K) as a function of mean temperature (Materials

1,2,3,4) 42

Replicate data (297.15 K) versus temperature difference (Materials 1,2,3,4)

43

Replicate data (297. 1 5 K) versus thickness (Materials 1 ,2,3,4) 44

Scatter plots of X (297.1 5 K) versus laboratory factors - Material 1 46

Scatter plots of X (297. 1 5 K) versus laboratory factors - Material 2 47

Scatter plots of X (297 A 5 K) versus laboratory factors - Material 3 48

Scatter plots of X (297'. 1 5 K) versus laboratory factors - Material 4 49

Relative deviations from certified values versus p (Materials 1,4) 55

Within- and between-laboratory variability versus grand means (Materials

1,2,3,4) excluding data from Material 1, Laboratory 1 and Material 3,

Laboratory 4 58

Multi-plot of thermal conductivity as a function of mean temperature

(Materials 1,2,3,4) 66

Multi-plot of relative deviations versus mean temperature (Materials 1,2,3,4) 67

Multi-plot of thermal conductivity versus test parameter (Materials 1,2,3,4) .. 69

Relative deviations from certified values versus Tm (Materials 1 ,4) 72

vm
1 Introduction

1.1 Problem Definition

A recent ASTM C-16 Workshop [1] on thermal insulation standard reference materials identified

the transferal of national reference materials and their acceptance across international boundaries

as a potential obstacle to global commerce. This (apparent) limitation with national and regional

reference materials and the continued expansion of global commerce has motivated several

national standards laboratories to develop a technical exchange of information by conducting

international comparisons. The purpose of this international comparison is to assess the

measurement variability among test results of different guarded-hot-plate apparatus located in national standards laboratories in Canada, France, Japan, United Kingdom, and United States. The laboratory participants were the National Research Council Canada (NRCC), Laboratoire

National d'Essais (LNE), Japan Testing Center for Construction Materials (JTCCM), National

Physical Laboratory (NPL), and National Institute of Standards and Technology (NIST),

respectively. The European Commission Institute for Reference Materials and Measurements

(IRMM) provided one of the reference materials and was an official observer.

1.2 Comparison Process

In order to foster confidence and credibility in these international measurements, this comparison was conducted using four different national reference materials. Two of the reference materials were issued by NIST; one by the European Commission IRMM; and one by JTCCM. Ten

specimens from each lot of material were selected and characterized by the issuing organization

(or delegate laboratory), paired by density, and a single specimen pair distributed to each

participant. The laboratory participants were requested to conduct five replicate measurements

of each material at a fixed temperature of 297.15 K (24 °C). In addition, each recipient

laboratory measured the each material at five specified temperatures from 280 K to 320 K. The

tests were to be conducted using either Test Method ISO 8302 [2] or ASTM C 177 [3]. All test data were recorded on official test forms and reported to NIST for analysis. This study was

organized in 1997 by NPL; material characterization by the issuing laboratories was completed

in 1998; participant measurements completed in 1999; and the resulting data analyzed in 2000 by

NIST.

1.3 Background

An interlaboratory, or collaborative, test program provides the participants with the means of

1) assessing the clarity of a particular test method, 2) verifying that the results are in agreement

with accuracy statements specified by the method, and 3) maintaining a periodic check of a group of laboratories [4,5]. These objectives have motivated several recent international

comparisons of guarded hot plate apparatus [6-8]. Each comparison has investigated a relatively

small number of thermal insulation materials over a specified temperature range (typically at or near 297 K). The comparisons have endeavored to minimize issues of material variability by

circulating the same pairs of thermal insulation materials among the laboratories following the

strict format of a "round robin" test program. Replicate measurements at fixed levels of

temperature were not requested. Although desirable, increasing the number of materials and

replicates adds a considerable burden to the participating laboratory and increasing the number

of laboratories adds a considerable burden to the coordination of the collaboration.

1
One of the most ambitious studies [6] was organized in 1978 and involved nearly 50 guardedhot-plate laboratories from Africa, Asia, Australia, Europe and North America. The study was

intended to determine the worldwide state-of-the-art in guarded hot plate measurements prior to the development of ISO standards. Because of the large number of laboratories involved, this

study can be considered the starting point for all modern international comparisons of guardedhot-plate apparatus. Participants measured the thermal conductivity of fibrous glass specimens

at mean temperatures of 283 K, 297 K, and a third temperature within the range from 273 K to

3 1 3 K. The results indicate that the relative standard deviation of the data from the fitted curve

is 2.4 % [6], although several data points deviate from the curve by more than 5 % and some by

more than 10 %. The original test plan envisioned a second comparison similar in scope to the

initial study to determine if an improvement in precision was realized after the approval of ISO

8302 [2]. To date, the follow-up study has not been completed.

More recent international comparisons [7,8] of guarded-hot-plate apparatus have emphasized a smaller number of laboratories, generally with participation from at least two national standard

laboratories. In one study [7], three pairs of glass-fiber specimens having thicknesses of 26 mm

and 75 mm and bulk densities of 44 kg/m and 53 kg/m were circulated to three laboratories. In the worst case, the relative standard deviation of the data from the fitted curve fit is less than

1.5 % and the largest difference between the sets of measurements is 2.2 % [71. In the second

study [8], one pair of glass-fiber specimens (159 kg/m ) and fibrous alumina silica (288 kg/m ) was circulated between two national standard laboratories in North America. The standard

deviations, multiplied by 2, for the fitted models of glass-fiber board and fibrous alumina silica

board are 1.4 % and 0.5 % [8], respectively. Both of these studies concluded that, although some

small systematic differences were present among the laboratories, the variations of the test data were less than the imprecision levels of ± 2 % to ± 5 % currently specified in ISO 8302 [2] and

ASTMC 177 [3].

1.4 Overview

This comparison is intended as another step in assessing the variability among international

guarded-hot-plate laboratories. In contrast to the "round-robin" format of the earlier studies [6-

8], this comparison distributed individual specimens of four different national reference materials

to each participant for measurement. Here, the primary goal is to assess and quantify the level of

variability in the guarded-hot-plate measurements and to encourage confidence and credibility in

international measurements of different national reference materials. This report describes the

test program, guarded hot plate laboratories, reference materials and their certification equations,

test method and equipment, material characterization, test results, and data analysis. The data

analyses include both statistical and engineering assessments. Final rankings for the materials

and laboratories are summarized, and recommendations for future comparisons are given.

2 Test Program

This section describes the specific objectives of the test program in context with the overall goal

of the comparison. Technical contacts and addresses are provided for the laboratories as well as a technical description of the reference materials and certified equations (where appropriate). A

summary of the test protocol given to the participants is also provided.
2. 1 Purpose and Objectives

The purpose of this interlaboratory comparison is to investigate the variability in test results

among guarded hot plate laboratories in Canada, France, Japan, United Kingdom, and United

States using different national reference materials. There are three primary objectives:

1) Characterize the material properties, specifically the bulk density and thermal conductivity,

of each sample of specimens distributed to the laboratories;

2) Quantify and assess the level of variability (both within- and between-laboratory) of the

fixed temperature (297.15 K) replicate data; and

3) Quantify the effect of temperature by comparison of the multi-temperature (280 K to 320 K) data.

2.

Laboratory Participants

Table 1 summarizes the participant laboratory's organization, country, and contact(s). The

addresses of the participants are provided in Appendix A. The final list of participants resulted

from a series of informal communications, meetings, and subsequent proposals initiated by the

National Physical Laboratory (NPL). In 1997, the National Institute of Standards and

Technology (NIST) agreed to assist in planning the interlaboratory comparison and to provide

statistical analyses of the test data.

TABLE 1 - Laboratory Participants

Organization Country Contact

1) Japan Testing Center for Construction Materials (JTCCM)

2) Laboratoire National d'Essais (LNE)

3) National Institute of Standards and Technology (NIST)

4) National Physical Laboratory (NPL)

5) National Research Council Canada (NRCC)

Japan

France

United States United Kingdom

Canada

Masayoshi Uezono

Gianni Venuti, Sylvie Quin

Robert Zarr David Salmon, Ronald Tye

Kumar Kumaran, Fitsum Tariku

European Commission Institute for Reference Materials

and Measurements (IRMM) (Observer only)

European

Commission

Jean Pauwels

2. 3 Reference Materials

The reference materials were selected to obtain a wide range - yet manageable number - of

insulation materials from Asia, Europe, and North America. Table 2 summarizes the reference

materials by designation, material description, (nominal) density, (nominal) thickness,

temperature range, and source. Materials 1, 2, and 3 were fibrous insulations covering a broad

range of densities; material 4 was a molded beads, expanded polystyrene board. Material 3,

which is a mixture of glass and mineral oxides fibers having high temperature capabilities, is currently undergoing an internal review process for certification. Each source laboratory was

responsible for characterizing 10 specimens of the reference material. In 1998, the European

Commission IRMM agreed to provide specimens of IRMM-440 (replacement lot for Certified

Reference Material 064) to NPL for characterization and distribution to the participants. As a

side note, the NIST Standard Reference Material Program (SRMP) has officially designated

SRM 1451 as obsolete due to historically low customer demand. NIST SRMP continues to offer

SRM 1452, which is from the same material lot as 1451. Specimens of SRM 1451 are currently

available from the NIST Building and Fire Research Laboratory.
TABLE 2 - Reference Materials

Density Thickness Temperature

Designation Description (kg/mJ ) (mm) (K) Source and Ref. 1)SRM+ 1451 Fibrous glass blanket 13 25 100 to 330 NIST [9] 2) IRMM-440: Resin-bonded glass fibre board 70 35 263 to 323 IRMM(viaLNE[10])

3) JTCCM candidate Mineral-oxide fiber board 200 25 JTCCM

4) SRM 1453 Expanded polystyrene board 38 13 285 to 310 NIST [11]

+ Standard Reference Material (SRM) issued by NIST.

^Certified Reference Material (CRM) issued by IRMM.

2.4 Certified Values for Reference Materials

A Certified Reference Material (CRM) is accompanied by a certificate having one or more

property values certified by a procedure which establishes traceability to an accurate realization

of the unit in which the property values are expressed, and for which each certified value is accompanied by an uncertainty at a stated level of confidence [12]. Certified values of thermal

conductivity for SRM 1451, IRMM-440. and SRM 1453 are described by the following general

model modified from Reference [9]:

*(Tm ,p) a\P+ a{Tm + a3 Tm + o4

(7)„-180) + a<e L 75 P

(1)

Here, X(Tm, p) is predicted thermal conductivity (W/m-K); p is the bulk density (kg/m3

); and, Tm

is the mean specimen temperature (K). The thermal transmission properties of heat insulators

determined from standard test methods typically include several mechanisms of heat transfer,

including conduction, radiation, and possibly convection. For that reason, some experimentalists

will include the adjective "apparent'' when describing thermal conductivity of thermal insulation.

However, for brevity, the term thermal conductivity will be used in this report.

Table 3 summarizes the regression coefficients (a,) and expanded uncertainties (U) at a coverage

factor of k = 2 for predicted values of IRMM-440, and SRM 1453. For SRM 1451 [9], the

uncertainty statement of ± 3 % was developed before current international guidelines on

expressing uncertainty became effective; therefore, a coverage factor is unavailable.

TABLE 3 - Regression Coefficients (Eg 1) for SRM 1451. IRMM-440. and SRM 1453

Designation a a. ^2 a3 a4 a5 U (k=2)

SRM 1451 -1.059xl0~4 1.378xl0"4 7.714xl0"5 8.472x1

0"9 1.339x10"' ± 3 %

+ IRMM-440: 0.0293949 0.0001060 2.047x1

0"7 ± 1 %

SRM 1453 6.3054xl0"4 -4.1993xl0"5 1.1650xl0"4 ± 1 .3 %

Coverage factor is unavailable. ^Temperature units are in [°C], not [K].

The official certification of IRMM-440 was finished after the completion of the data analysis of

this interlaboratory comparison. Thus, the certified equation and regression coefficients for

IRMM-440 are presented only for comparison purposes. The JTCCM "candidate" reference

material is currently undergoing certification processes and, consequently, certified values of

thermal conductivity are unavailable.

4
2. 5 Protocol

Using test methods ISO 8302 [2] and ASTM C 177 [3], a short test protocol was drafted and

subsequently approved by the participants for this comparison (see Appendix B). The protocol was partitioned into two sections. The first section covered the characterization by the source

laboratories providing reference materials and the second section covered the measurements

conducted by the participants. Each source laboratory provided one pair of specimens of

reference materials to each participant (5 pairs in total). In order to assess the material

variability, the density and thermal conductivity of each specimen pair was measured by the source laboratory at a mean temperature of 297.15 K (24 °C) and temperature difference of 20 K

(n - 5 measurements per material). Needless to say, the logistics of providing reference

measurements and subsequently delivering all specimens to the participants was time consuming.

The test protocol for the participants required a series of replicate and multi-temperature

measurements for each material. Initially, the thermal conductivity of each pair of specimens was determined five times at a (fixed) mean temperature of 297. 1 5 K (24 °C) and a temperature

difference of 20 K {n = 20 measurements for 4 materials). The operator was required to remove

the specimens from the apparatus after each measurement and re-install the specimens after

sufficient conditioning. After completion of the replicate measurements, thermal conductivity

measurements were conducted for each material at 280 K, 290 K, 300 K, 310 K, and 320 K and a temperature difference of 20 K (n = 20 measurements for 4 materials). Note that although the

multi-temperature tests were conducted in random order, the specimens were not removed from

the apparatus between temperature settings.

With exception of SRM 1451, the materials were to be tested at thicknesses determined by each

laboratory with the only provision that the pressure exerted on the specimens by the measuring

equipment was limited to a range between 1000 Pa and 2000 Pa. For SRM 1451, the test thickness was limited to 25.4 mm by utilizing spacer stops placed at the perimeter of the

specimen to prevent over compression of the material during testing. The use of spacer stops for

the other materials (for example, limiting plate movement due to specimen creep, if any) was left to the operator's discretion. The material characterization and test data were recorded in SI units on "official" data entry forms and returned to NIST. An annotated copy of each form is given in Appendices C and D, respectively. Upon receipt by NIST, the test data were input into

electronic spreadsheets, checked for consistency, and subsequently analyzed using graphical

exploration techniques.

3 Test Method and Apparatus

3. 1 Operating Principle

Measurements of thermal conductivity were determined in accordance with procedures in standard test methods, ISO 8302 [2] and/or ASTM C 177 [3], which are summarized briefly

here. For the double-sided mode of operation, two specimens having the same density, size, and

thickness are placed on the two sides of the guarded hot plate and clamped securely by the cold

plates. Ideally, the guarded hot plate and the cold plates provide constant temperature boundary

conditions to the surfaces of the specimens. With proper guarding in the lateral direction, the
apparatus is designed to provide one-dimensional heat flow (Q) through the meter area of the

pair of specimens. Additional guarding is provided by means of a temperature controlled

environmental chamber, edge insulation, linear guarding, or a combination of these. When in use, the environmental chamber ordinarily maintains the ambient air temperature at the same

value as the mean temperature (Tm) of the hot and the cold plates.

Under steady-state conditions, measurements of thermal conductivity (X) for the pair of

specimens are determined using the following equation:

0=A2A^f- (2)

where Q is the heat flow through the meter area of the specimens (W); 2A is the meter area normal to direction of heat flow, both sides (m ); AT is the temperature difference across the hot

(7/,) and cold surfaces (Tc ) of the specimens (K); and, L is the in-situ thickness of the pair of

specimens (m). Values of X are typically reported at the mean temperature of the hot and cold

plates, Tm = V*(Th + Tc).

For a single-sided mode of operation, a single specimen (selected from the pair) is placed

between the hot and cold plates of the apparatus. The other specimen is replaced with an

auxiliary piece of insulation that is placed between the hot and guard plate. The auxiliary guard

plate is maintained at the same temperature as the hot plate. With proper guarding in the lateral direction, the apparatus is designed to provide one-dimensional heat flow (O) through the meter

area of the single specimen. For determining X in the single-sided case, Eq 2 is modified slightly

by taking a meter area (A) coefficient of unity. In general, all other particulars of the test procedure are essentially the same as the double-sided mode of operation.

3.2 Equipment

Table 4 summarizes the pertinent features of the guarded hot plate (GHP) apparatus used in this

comparison as reported by the laboratory participants. The information covers four categories:

1) apparatus manufacturer, 2) principle (i.e., test method utilized), 3) relative expanded

uncertainty for the estimate of X, and 4) details of the apparatus components including plate

sizes, emittance, heaters, guarding, and temperature sensors. Most laboratories fabricated their

own apparatus; however, in one case (JTCCM), a commercial vendor fabricated one of the

apparatus. The laboratories conducted their tests utilizing the guarded hot plate principle,

following either the ISO 8302 [2] or ASTM C 177 [3] test method.

3.2.1 Uncertainty: The relative expanded uncertainty [13] (k =2) associated with measurement

estimates of X for each apparatus range from 1.0 % to 1.5 % (Table 4) and is used later for the

engineering analysis of the test data. One laboratory (JTCCM) did not report their estimated

uncertainty. The expanded uncertainty (U) defines an interval about the result of a measurement

(y) that may be expected to encompass a large fraction of the distribution of values (Y = y + U)

that could reasonably be attributed to the measurand (in this case, X). Here, the expanded

uncertainty corresponds to a level of confidence of 95 % by taking a coverage factor of k = 2

[13]. The relative expanded uncertainty is defined as Ul\y\, |y| * [13].
TABLE 4 - Guarded Hot Plate Apparatus

JTCCM LNE NIST NPL NRCC

Manufacturer

Eko Instruments Trading Co., Ltd. LNE NIST NPL NRCC

Principle GHP ISO 8302 ASTMC 177 ISO 8302 ASTMC 177

Relative Expanded

Uncertainty (k=2) (%)

Not reported 1.5 1.5(IRMM-440)

1.0 (other)

1.2 1.0

Plate size (mm) 300x300 610x610 1016 diameter 610x610 610x610

Meter plate size (mm) 150x150 300x300 406.4 diameter 305.2x305.2 250x250

Plate material Al Al Al

Hot - Cu

Cold-Al Al

Plate emittance 0.9 0.86 ±0.05

(k=2)

0.89 >0.9 0.89

Type of heater Distributed Distributed

1 Line source" Distributed" Distributed Edge guarding Condition air Note

4 Condition air Note' Glass-fiber Temperature sensor Type T Type K PRT Type E Type T

Operation mode 2-sided 2-sided 2-sided 1 -sided 2-sided

Isolated Ni/Cr heating resistance with a central metering area and a guard section

2 Line-heat source per ASTM C 1043 [14]: 1 ribbon heater in the meter plate, 2 swaged heaters in the guard ring

J Double sided copper printed circuit board

4 Edge insulation, temperature controlled peripheral guard and additional outer edge insulation

5 Linear temperature gradient edge guard and 100 mm expanded polystyrene

3.2.2 Components: As noted in Table 4, there is a wide variety in the design of the apparatus

components. The plates range in size (and geometry) from 300 mm square to 1016 mm in

diameter. Three of the apparatus plates, however, are 610 mm square. All of the apparatus have

different meter plate sizes (albeit the differences for LNE and NPL are small). Most of the

apparatus plates are fabricated from aluminum; one laboratory (NPL) utilizes a copper hot plate.

The plate emittances range from 0.86 to 0.9, or greater. The plate heaters are either distributed

(majority) or line-source [14]. In the case for distributed heaters, two laboratories provided

details on different heater constructions (see notes 1 and 3). Edge guarding of the plates was

accomplished by lateral insulation, linear guard, environmental chamber, or a combination of

these approaches. For temperature measurements, four apparatus utilize thermocouples, either

Type E (nickel-chrome/constantan), Type K (nickel-chrome/nickel-silicon), or Type T

* (copper/constantan). One laboratory (NIST) utilized platinum resistance thermometers (PRTs).

3.2.3 Control Stability: In addition to the information given in Table 4, each laboratory was

required to report their criteria to ensure that their data were, in fact, stable (i.e., in a state of

statistical control). The responses indicate that each laboratory has developed their own in-house

protocol for checking stability of their apparatus during operation. For example, JTCCM

requires a temperature difference less than 0.03 K over the last 5 readings taken at 30 min

intervals after 24 h steady-state conditions. LNE validates on a 16 h interval from thermal

resistance or thermal conductivity measurements using the following criteria: a relative standard

deviation 0.05 (%); and, a relative slope of 1.5xl0

-8 (% s~ ). NIST requires temperature stability

for each plate during the test period to be 0.005 °C, or better. During the same period, the

variation in the thermal conductivity data must be less than 0.5 %. NPL requires that the

temperature difference be stable to better than 0.03 °C over the last 10 readings taken at 1 h

intervals. NRCC requires 12 h of steady-state conditions and for each datum to differ from the

mean by no more than the relative (expanded, k = 2) uncertainty estimate for the measurement ( 1 %).
4 Material Characterization

The major goal of the material characterization was to quantify and, if possible, minimize the

density variability among specimens of the reference materials (Table 3) that were distributed to the recipient laboratories. This section analyzes the bulk density and thermal conductivity

measurements from the source laboratories and addresses the following questions:

1) What is the level of variability of bulk density for the reference materials? and,

2) What is the effect of the bulk density on thermal conductivity?

A secondary goal of the material characterization is to afford the opportunity for direct

comparison of source and recipient laboratory test data. The reader, however, is cautioned that

such a comparison is for informational purposes only. Although desirable, other material

properties (such as microstructure, mechanical properties, etc.) were not requested.

4.1 Bulk Density (Source Laboratories)

Table 5 summarizes the measurements of specimen mass (m), dimensions (x\, xi, L) and bulk

density

1 (p) reported to NIST by the source laboratories. The last column in Table 5 indicates

the recipient laboratory for the specimen pair. The data are grouped by material (1 to 4) and

coded using the following number assignments (hereafter in this report): 1) NIST SRM 1451;

2) IRMM-440; 3) JTCCM "candidate"; and, 4) NIST SRM 1453. Within each material group,

the data is ranked by density of the specimen pair. For brevity, the laboratories have been

assigned a number code (hereafter): 1) JTCCM; 2) LNE; 3) NIST; 4) NPL; and, 5) NRCC.

TABLE 5 - Physical Characteristics of Reference Materials Determined by Source Laboratories

. . . Source

Material ,

, Lab

Specimen

ID m

(g) (mm)

x2 (mm)L (mm)

P' (kg/m3

)

Recipient

Lab

1 j 1.1 133.7 611.7 610.0 25.58 14.01 4

1 j 1.2 134.2 613.0 611.0 25.49 14.06 4

1 3 2.1 133.5 610.7 611.7 25.51 14.01 2

1 3 2.2 134.8 611.7 611.3 25.56 14.11 2

1 3 3.1 135.5 611.7 611.3 25.56 14.17 1

1 3 3.2 135.7 612.7 612.0 25.50 14.19 1

1 3 4.1 135.0 611.0 611.3 25.49 14.18 3

1 3 4.2 134.9 610.7 608.3 25.57 14.20 3

1 3 5.1 135.3 609.7 611.0 25.55 14.22 5

1 3 5.2 135.4 609.0 611.0 25.51 14.27 5

6.1 6.2

7.1 7.2

8.1 8.2

9.1 9.2

10.1 10.2

859

859

859

878

3624

3683

909

910

916

939

597

597

597

597

1199

1198

597

596

597

597

598

596

596

598

1202

1201

596

598

599

596

34.94

35.02

35.01

35.01 34.98

34.98

34.97

34.83

34.83

34.83

68.9

69.0

68.9

70.3 71.9

73.2 73.0

73.3 73.6

75.8

1 In order to preserve the specimens for additional measurements, the source laboratory determined the bulk density

of the entire specimen and did not cut the meter section to determine the bulk density for the meter area. 8
TABLE 5 (continued)

Material Source Specimen m *1 x2 L P

Recipient

Lab ID (g) (mm) (mm) (mm) (kg/mJ ) Lab

3 1 11.1 4482 910 910 24.4 222 1 3 1 11.2 4390 910 910 23.9 222 1 3 1 12.1 4470 910 910 24.3 222 4

3 1 12.2 4413 910 910 23.8 224 4

3 1 13.1 4437 910 910 23.6 227 3 3 1 13.2 4462 910 910 23.7 227 3 3 1 14.1 4456 910 910 23.6 228 2

3 1 14.2 4495 910 910 23.7 229 2

3 1 15.1 4565 910 910 23.7 233 5

3 1 15.2 4501 910 910 23.3 233 5 4 3 16.1 190.6 611.0 611.0 13.48 37.87 4 4 3 16.2 191.5 611.0 611.0 13.52 37.94 4

4 3 17.1 190.3 611.0 610.3 13.42 38.03 5 4 3 17.2 192.4 611.0 611.0 13.50 38.18 5 4 3 18.1 193.7 611.0 611.3 13.60 38.13 3 4 3 18.2 186.4 611.0 611.0 13.08 38.17 3 4 3 19.1 193.2 611.0 610.7 13.46 38.47 1 4 3 19.2 193.4 611.0 610.7 13.46 38.51 1 4 3 20.1 191.8 611.0 610.7 13.30 38.65 2

4 3 20.2 194.5 611.0 611.0 13.48 38.65 2

Figure 1 plots the density measurements given in Table 5 versus specimen pair (1 to 20) for each

material. The plot character depicts the recipient laboratory for any given specimen pair. The

source laboratories determined the selection of the recipient laboratories for each specimen pair

by random lot. The graphs indicate that, for the most part, each pair of specimens was

reasonably well matched by bulk density. The grand mean ( p ) for each material is displayed as a solid horizontal line. Values for p , the grand standard deviation, and range are summarized in a text box for each material.

Figure 2 plots the relative differences of p (Table 5) and p (Figure 1) versus specimen pair for

materials 1 through 4. Again, the plot character depicts the recipient laboratory. Figure 2

provides a quick comparison of relative differences for all the materials. For materials 1, 2, 3,

and 4, the relative differences range from -1 % to +1%, -4 % to +5.5 %, -2 % to +2.5 %, and

-1 % to +1%, respectively (Figure 2). The effect of p on X is investigated in the next section.

Table 6 summarizes the results from Figures 1 and 2.

TABLE 6 - Summary Statistics for Bulk Density Determined by Source Laboratories

Summary Statistic Material 1 Material 2 Material 3 Material 4 p (kg/m3) 14.14 71.8 227 38.3 Grand SD (kg/m3

) 0.09 2.4 4.2 0.3 Relative Grand SD (%) 0.6 1.9 0.8 Range (kg/m J ) 0.26 6.9 11 O.S
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Figure 1 . Multi-plot of bulk density versus specimen pair - source laboratory (Materials 1,2,3, 4)

10
6.0

4.0 -

Id.

I Q.

2.0

0.0

-2.0

-4.0

-6.0

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I I II I I I I I I I I

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I I I I I I I I I I I I I I i I I I I I

1 2 3 4 5 6 7 8 9 10 1 1 12 13 14 15 16 17 18 19 20

Specimen Pair

Figure 2. Relative variation in specimen bulk density - source laboratory

(Materials 1,2, 3,4)

11
4. 2 Thermal Conductivity (Source Laboratories)

Table 7 summarizes measurements reported to NIST by the source laboratories for the hot (7),) and cold (Tc) plate temperatures, specimen heat flow (Q), thickness (I), meter area (A), and

thermal conductivity (A) at 297.15 K (24 °C) and a temperature difference of 20 K. Ideally, the

measurements of A. were determined following equivalent (or similar) procedures used later for

the comparison. Hence, laboratory 3 determined the thermal conductivity for each pair of

specimens (n = 5) in the double-sided mode of operation and laboratory 4 measured each

specimen individually (n = 10) in the single-sided mode. Note that laboratory 1 utilized a 900-

mm square guarded hot plate apparatus (450 mm square meter area) to measure each specimen

pair individually, which was a different apparatus than that used later in the comparison

(Table 4).

TABLE 7 - Thermal Conductivity (297. 15 K) of Reference Materials Determined by Source Laboratories

Material Source Specimen p

1 Th Tc Q L A X Recipient

Lab (Pair) (kg/m3 ) (K) (K) (W) (mm) (m2

) (W/m K) Lab

1 ij 1 14.0 307.15 287.15 4.089 25.53 0.1298 0.04021 4

1 3 2 14.1 307.15 287.15 4.152 25.51 0.1298 0.04079 2

1 3 3 14.2 307.15 287.15 4.163 25.53 0.1298 0.04095 1

1 3 4 14.2 307.15 287.15 4.121 25.53 0.1298 0.04053 3

1 3 5 14.2 307.15 287.15 4.087 25.53 0.1298 0.04020 5 2 4 6.1 68.9 305.2 288.1 1.486 34.48 0.09315 0.03212 2

2 4 6.2 69.0 305.0 288.1 1.488 34.42 0.09315 0.03232 2

2 4 7.1 68.9 305.3 288.2 1.482 34.46 0.09315 0.03204 4

2 4 7.2 70.3 305.2 288.1 1.484 34.23 0.09315 0.03206 4

2 4 8.1 71.9 305.3 288.1 1.494 34.43 0.09315 0.03223 3 2 4 8.2 73.2 305.3 288.1 1.493 34.47 0.09315 0.03226 3 2 4 9.1 73.0 305.2 288.1 1.492 34.41 0.09315 0.03218 5 2 4 9.2 /3.J 305.1 288.1 1.474 34.42 0.09315 0.0321 5 2 4 10.1 73.6 305.2 288.1 1.488 34.42 0.09315 0.03221 1 2 4 10.2 75.8 304.7 288.1 1.446 34.48 0.09315 0.03216 1 3 1 11.1 222 308.2 287.9 6.413 244 0.2025 Not Reported 1 3 1 11.2 222 307.9 287.9 6.269 23.9 0.2025 0.0370 1

*> 1 12.1 222 308.1 288.2 6.122 24.3 0.2025 0.0369 4

12.2 224 308.2 288.1 6.317 23.8 0.2025 0.0369 4

3 13.1 227 308.5 288.1 6.474 23.6 0.2025 0.0370 3

3 [ 13.2 227 308.2 288.1 6.426 23.7 0.2025 0.0375 3

3 14.1 228 307.7 288.1 6.272 23.6 0.2025 0.0373 2

3 14.2 229 307.9 288.0 6.351 23.7 0.2025 0.0373 2

3 I 15.1 233 308.5 287.9 6.610 23.7 0.2025 0.0376 5

3 1 15.2 233 308.0 287.9 6.536 23.3 0.2025 0.0374 5 4 3 16 37.9 307.15 287.15 6.489 13.49 0.1298 0.03372 4

4 3 17 38.1 307.15 287.15 6.483 13.46 0.1298 0.03361 5 4 3 18 38.2 307.15 287.15 6.545 13.34 0.1298 0.03363 3 4 3 19 38.5 307.15 287.15 6.466 13.46 0.1298 0.03351 1 4 3 20 38.7 307.15 287.15 6.487 13.39 0.1298 0.03347 2 Values taken from Table 5.

Figure 3 plots the thermal conductivity (from Table 7) as a function of their respective bulk

densities (p) (from Table 5) for each material. The plot character depicts the recipient laboratory

for the specimens thereby facilitating a direct comparison with later results from the recipient

laboratories.

12
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Figure 3. Multi-plot of thermal conductivity versus bulk density - source laboratory

(Materials 1,2, 3,4)

13
Figure 3 indicates that, for these particular specimens, the A.-p relationship is weak (or

negligible) for materials 1 and 2; positive for material 3; and, negative for material 4. For

materials 2 and 4, these results are consistent with previous findings from References [10] and

[11], respectively. Material 2 has been specifically manufactured such that values of X are

essentially independent of p from 283 K to 293 K [10]. For material 4, the negative A.-p

relationship is consistent with the negative density term [11] given in Table 3. For material 1, however, the certification equation [9] indicates a definitive A,-p relationship (Table 3), not

evident in Figure 3. One possible explanation is that the meter-area p affected the test results for

material 1 . In general, the results of Figure 3 would be more representative of the measured X if the meter-area p was used, especially if there was significant within-specimen variability for

material 1. Significant within-specimen variability could also affect the test results from

apparatus having significantly different meter areas (for example, laboratories 1 and 3).

The main goal of characterizing each sample of reference material by a source laboratory was to provide the recipient laboratories with closely equivalent sets of test specimens. Further, by

having an issuing laboratory conduct thermal conductivity measurements on each specimen,

there is an opportunity for a direct comparison of the source and recipient laboratories. An

analysis of these data (for informational purposes only) will be presented in the next section.

Finally, it is important to note that the material characterization data were only released to the

participants at the conclusion of the test program.

5 Analysis of Fixed Temperature (297.15 K) Replicate Data

This section provides a tabulated listing of the fixed temperature (297.15 K) replicate data and

the corresponding statistical analyses of the data. The primary goal of the analyses is to provide

the laboratory participants with diagnostic tools for examination of their data. The analyses are motivated by the central theme of the comparison: How do the laboratories behave across the

four materials? With respect to this question, the following analyses are provided:

1

)

Presentation of laboratory data;

2) Graphical exploration of laboratory test data by material;

3) Assessment of the engineering significance of the laboratory test data by material;

4) Detailed statistical analysis of the location and variation of the test data;

5) An ensuing ranking of the laboratories by location and variation; and,

6) Comparison of source and recipient laboratory test data.

5. 1 Presentation ofLaboratory Data

Table 8 summarizes the measurements for the specimen bulk density (p), hot (7/,) and cold (Tc) plate temperatures, specimen heat flow (Q), thickness (I), meter area (A), and thermal

conductivity (X) at 297.15 K (24 °C) and a temperature difference of 20 K. The data in Table 8 were entered in an electronic spreadsheet and report values for X were checked by recalculation.

For convenience, values of p have been rounded to 3 significant digits and each value represents

the average of the pair of specimens (for a double sided test). The number of significant digits

for the other parameters is tabulated (here and elsewhere) as received from the laboratory. Any

certainty for the 5

th significant digit for values of X cannot be assigned, but the digit is included

for the subsequent analyses of the results.

14
TABLE 8 - Fixed Temperature (297.15 K) Replicate Data

Material Lab Replicate P

T„ Tc Q L A I Tm AT

(kg/m 3 ) (K) (K) (W) (mm) (m2 ) (W/m K) (K) (K)

1 13.4 307.20 286.73 1.622 25.4 0.0225 0.04473 296.97 20.47

2 13.4 307.01 286.74 1.612 25.4 0.0225 0.04489 296.88 20.27

3 13.4 303.16 286.59 1.299 25.4 0.0225 0.04425 294.88 16.57 4 13.4 303.23 286.54 1.306 25.4 0.0225 0.04417 294.89 16.69

5 13.4 307.20 286.54 1.623 25.4 0.0225 0.04434 296.87 20.66

2 1 14.1 307.14 287.18 5.806 25.40 0.090085 0.04101 297.16 19.96

2 2 14.1 307.17 287.16 5.824 25.40 0.090085 0.04104 297.17 20.01

2 3 14.1 307.19 287.18 5.824 25.40 0.090085 0.04105 297.19 20.01

2 4 14.1 307.20 287.20 5.824 25.40 0.090085 0.04103 297.20 20.00

2 5 14.1 307.19 287.21 5.824 25.40 0.090085 0.04109 297.20 19.98

3 1 14.2 307.15 287.15 4.124 25.51 0.1298 0.04052 297.15 20.00

3 z 14.2 307.15 287.15 4.126 25.52 0.1298 0.04055 297.15 20.00

3 3 14.2 307.15 287.15 4.126 25.52 0.1298 0.04056 297.15 20.00

3 4 14.2 307.15 287.15 4.127 25.52 0.1298 0.04056 297.15 20.00

3 5 14.2 307.15 287.15 4.126 25.52 0.1298 0.04056 297.15 20.00

4 1 14.1 306.47 287.54 2.8766 25.42 0.09315 0.0415 297.01 18.93 4 2 14.1 306.63 287.57 2.8770 25.37 0.09315 0.0411 297.10 19.06 4 3 14.1 306.65 287.58 2.8793 25.37 0.09315 0.0411 297.12 19.07 4 4 14.1 306.64 287.57 2.8765 25.37 0.09315 0.0411 297.11 19.07 4 5 14.1 306.60 287.57 2.8714 25.37 0.09315 0.0411 297.09 19.03

5 1 14.4 307.15 287.17 1.988 25.35 0.0625 0.04035 297.16 19.98

5 2 14.4 307.16 287.14 1.987 25.39 0.0625 0.04030 297.15 20.02

5 3 14.4 307.14 287.13 1.985 25.39 0.0625 0.04029 297.14 20.01

5 4 14.4 307.12 287.16 1.981 25.39 0.0625 0.04031 297.14 19.96

5 5 14.4 307.12 287.15 1.985 25.36 0.0625 0.04034 297.14 19.97

2 1 79.2 307.21 286.22 0.891 34.5 0.0225 0.03254 296.72 20.99

2 2 79.2 307.12 286.20 0.885 34.5 0.0225 0.03243 296.66 20.92

2 3 79.2 307.45 286.27 0.899 34.5 0.0225 0.03254 296.86 21.18

2 4 79.2 307.47 286.25 0.899 34.5 0.0225 0.03248 296.86 21.22

2 5 79.2 307.47 286.27 0.900 34.5 0.0225 0.03255 296.87 21.20

2 2 1 69.9 307.15 287.20 3.329 34.41 0.090085 0.03186 297.18 19.95

2 2 2 69.9 307.17 287.17 3.340 34.41 0.090085 0.03189 297.17 20.00

2 2 3 69.9 307.20 287.12 3.351 34.41 0.090085 0.03188 297.16 20.08

2 2 4 69.9 307.20 287.14 3.351 34.41 0.090085 0.03189 297.17 20.06

2 2 5 69.9 307.24 287.25 3.339 34.41 0.090085 0.03191 297.25 19.99

2

-*j 1 73.8 307.15 287.15 2.356 34.83 0.1298 0.03161 297.15 20.00

2 3 2 73.8 307.15 287.15 2.362 34.82 0.1298 0.03168 297.15 20.00

2 3 3 73.8 307.15 287.14 2.362 34.82 0.1298 0.03167 297.15 20.01

2 3 4 73.8 307.15 287.14 2.365 34.82 0.1298 0.03170 297.15 20.01

2 5 73.8 307.15 287.15 2.360 34.82 0.1298 0.03164 297.15 20.00

2 4 1 70.0 306.16 287.30 1.6364 34.38 0.09315 0.0320 296.73 18.86 2 4 2 70.0 306.15 287.31 1.6379 34.34 0.09315 0.0321 296.73 18.84 2 4 3 70.0 306.19 287.31 1.6435 34.34 0.09315 0.0321 296.75 18.88

2 4 4 70.0 306.16 287.31 1.6358 34.35 0.09315 0.0320 296.74 18.85 2 4 5 70.0 306.09 287.29 1.6380 34.33 0.09315 0.0321 296.69 18.80 2 5 1 74.6 307.04 287.14 1.161 34.14 0.0625 0.03188 297.09 19.90

2 5 2 74.6 307.17 287.14 1.182 34.14 0.0625 0.03223 297.16 20.03

2 5 3 74.6 307.14 287.15 1.182 34.14 0.0625 0.03232 297.15 19.99 2 5 4 74.6 307.15 287.17 1.181 34.14 0.0625 0.03229 297.16 19.98

2 5 5 74.6 307.15 287.17 1.181 34.14 0.0625 0.03228 297.16 19.98

15
Material Lab Replicate P Th Tc Q L A X Tm AT

(kg/m3 ) (K) (K) (W) (mm) (m2 ) (W/m K) (K) (K)

3

1 213 307.09 286.36 1.328 25.3 0.0225 0.03602 296.73 20.73

3 2 213 307.32 286.36 1.360 25.3 0.0225 0.03648 296.84 20.96

3 3 213 307.48 286.35 1.363 25.3 0.0225 0.03627 296.92 21.13

3 4 213 306.83 286.31 1.352 25.3 0.0225 0.03704 296.57 20.52

3 5 213 306.90 286.34 1.351 25.3 0.0225 0.03694 296.62 20.56

3 2 1 228 307.17 287.26 5.611 23.48 0.090085 0.03674 297.22 19.91

3 2 2 228 307.21 287.36 5.596 23.48 0.090085 0.03673 297.29 19.85

3 2 3 228 307.18 287.32 5.610 23.44 0.090085 0.03677 297.25 19.86

3 2 4 228 307.22 287.26 5.640 23.45 0.090085 0.03676 297.24 19.96

3 2 5 228 307.12 287.25 5.609 23.45 0.090084 0.03675 297.19 19.87

3 3 1 225 307.15 287.15 3.958 23.73 0.1298 0.03617 297.15 20.00

3 3 2 225 307.15 287.15 3.921 23.76 0.1298 0.03588 297.15 20.00

3 3 225 307.15 287.15 3.949 23.88 0.1298 0.03633 297.15 20.00

3 3 4 225 307.15 287.15 3.952 23.77 0.1298 0.03618 297.15 20.00

3 3 5 225 307.15 287.15 3.962 23.76 0.1298 0.03625 297.15 20.00

3 4 1 223 306.26 287.48 2.5446 24.10 0.09315 0.0350 296.87 18.78

3 4 2 223 306.23 287.47 2.5399 24.09 0.09315 0.0350 296.85 18.76

3 4 3 223 306:27 287.46 2.5442 24.11 0.09315 0.0350 296.87 18.81

3 4 4 223 306.25 287.48 2.5403 24.11 0.09315 0.0350 296.87 18.77

3 4 5 223 306.19 287.46 2.5352 24.09 0.09315 0.0350 296.83 18.73

3 5 1 230 307.14 287.14 1.963 23.48 0.0625 0.03688 297.14 20.00

3 5 2 230 307.14 287.14 1.965 23.48 0.0625 0.03691 297.14 20.00

3 5

ij 230 307.13 287.15 1.960 23.48 0.0625 0.03687 297.14 19.98

3 5 4 230 307.15 287.13 1.963 23.48 0.0625 0.03685 297.14 20.02

3 5 5 230 307.17 287.15 1.961 23.48 0.0625 0.03680 297.16 20.02

4 1 39.8 306.50 285.80 2.347 13.5 0.0225 0.03401 296.15 20.70

4 2 39.8 306.92 286.41 2.347 13.5 0.0225 0.03433 296.67 20.51 4 3 39.8 306.21 285.19 2.347 13.5 0.0225 0.03350 295.70 21.02

4 4 39.8 306.38 285.56 2.347 13.5 0.0225 0.03382 295.97 20.82

4 5 39.8 306.57 285.80 2.347 13.5 0.0225 0.03390 296.19 20.77

4 2 1 38.6 307.15 287.15 9.046 13.43 0.090085 0.03369 297.15 20.00

4 2 2 38.6 307.16 287.11 9.065 13.44 0.090085 0.03369 297.14 20.05

4 2 3 38.6 307.14 287.18 9.028 13.43 0.090085 0.03372 297.16 19.96

4 2 4 38.6 307.14 287.13 9.045 13.42 0.090085 0.03368 297.14 20.01 4 2 5 38.6 307.20 287.16 9.065 13.42 0.090085 0.03368 297.18 20.04

4 3 1 38.2 307.15 287.15 6.557 13.33 0.1298 0.03367 297.15 20.00

4 3 2 38.2 307.15 287.15 6.578 13.33 0.1298 0.03378 297.15 20.00

4 3 3 38.2 307.15 287.15 6.576 13.33 0.1298 0.03377 297.15 20.00

4 3 4 38.2 307.15 287.15 6.575 13.33 0.1298 0.03376 297.15 20.00

4 3 5 38.2 307.15 287.15 6.578 13.32 0.1298 0.03377 297.15 20.00

4 4 1 38.8 305.66 287.90 4.2130 13.17 0.09315 0.0335 296.78 17.76 4 4 2 38.8 305.69 287.87 4.2328 13.25 0.09315 0.0338 296.78 17.82 4 4 3 38.8 305.77 287.90 4.2410 13.26 0.09315 0.0338 296.84 17.87 4 4 4 38.8 305.69 287.89 4.2290 13.20 0.09315 0.0337 296.79 17.80

4 4 5 38.8 305.67 287.88 4.2296 13.14 0.09315 0.0336 296.78 17.79 4 5 1 38.5 307.12 287.13 3.168 13.36 0.0625 0.03387 297.13 19.99 4 5 2 38.5 307.13 287.16 3.169 13.34 0.0625 0.03386 297.15 19.97 4 5 3 38.5 307.12 287.14 3.170 13.34 0.0625 0.03386 297.13 19.98 4 5 4 38.5 307.13 287.14 3.171 13.35 0.0625 0.03389 297.14 19.99

4 5 5 38.5 307.13 287.13 3.172 13.35 0.0625 0.03388 297.13 20.00

16
5.2 Graphical Exploration ofLaboratory Data

Figure 4 plots the measurements of A, at 297.15 K versus laboratory (1 to 5) for the 4 materials.

The replicate observations for each laboratory, shown as x characters, are slightly offset along

the x-axis to assess any trends in the run-sequence of an individual laboratory. In examining the

laboratory data for each material, the central question under investigation is, do the five

laboratories behave similarly across the four materials? or, (if the laboratories behave differently

from material to material), is there a laboratory-material interaction? There are two independent

but related questions in determining the behavior of laboratories from material to material: 1) Is there a change in location (that is, mathematical mean) of the laboratory data? and, 2) Is there a change in variation (standard deviations) of the laboratory data? Examination of these two

questions for the data in Figure 4 will provide an answer for the central question under

investigation (i.e., How do the five laboratories behave across the four materials?).

The principal conclusion from Figure 4 is that the behavior of the laboratories does, in fact,

change from material to material. As observed in the plots, the location and variation of each set of laboratory data changes from material to material. For example, laboratory 5 is lowest and

relatively precise for material 1 , and higher with respect to the other laboratories and less precise

for material 2. In short, there is a laboratory-material interaction. Since the breadth of this

interaction was not entirely anticipated to the extent observed in the data (for example, material

1, laboratory 1). the most immediate response is, why? What are the principal causes for the

laboratory-material interaction? A helpful plan of attack is to refine the problem by focusing

attention on the extreme values of the data set with respect to location and variation. For each

material, Table 9 summarizes the laboratories with the highest and lowest mean values, the

highest variation (i.e., noise), and apparent outliers.

TABLE 9 - Summary of the Interlaboratory Comparison

Material High Lab Low Lab Noisy Lab Outlying Lab

1 1 5 1 —

2 1 3 — 5 (1 observation)

-> — 4 1 —

4 — — 1 —

From Table 9, the major results from the interlaboratory comparison are summarized below as a

set of primary questions.

1)

2)

3)

4)

5)

6)

Ql: For 2 of the 4 materials, laboratory 1 is high, why?

Q2: For material 1, laboratory 5 is low, why?

Q3: For material 2, laboratory 3 is low, why?

Q4: For material 3, laboratory 4 is low, why?

Q5: For 3 of the 4 materials, laboratory 1 is noisy, why?

Q6: For material 2, laboratory 5 appears to have one outlying observation, why?

The answers to this set of questions are of considerable interest and will guide the presentation of

more detailed analyses presented later in this report (Section 6). These analyses investigate the

effects of material factors (including bulk density, etc.) as well as other factors on X. Before

proceeding with these detailed analyses, however, it is extremely useful to investigate the

engineering significance of the test data given in Figure 4.

17
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Figure 4. Replicate data (297.15 K) versus laboratory (Materials 1, 2, 3, 4)

18
5.

3

Engineering Significance ofLaboratory Data

Based on the results of Figure 4, an appropriate question is, are the differences in the laboratory

test data significant from an engineering viewpoint? In other words, are the differences less than

some acceptable minimum level of engineering significance? An engineering viewpoint requires

some assessment of the uncertainty for laboratory values of A,. From Table 4, recall that for

laboratories 2, 3, 4, and 5 the estimates for their relative expanded uncertainties, based on current

international guidelines [13], were 1.5 %, 1.5 % for material 2 and 1.0 % for the other materials,

1.2 %, and 1.0 %, respectively. (Laboratory 1 did not report an uncertainty for their values of X.)

For comparison purposes, the relative expanded uncertainties (U) given in Table 4 are presented

as symmetric error bars for the data given in Figure 4. It is important to note that the estimates

for U reported by each laboratory have been determined independently of this comparison.

Figure 5 again plots the measurements of X at 297.15 K, shown as x characters, versus laboratory

(1 to 5) for each material. As before, the replicate observations for a given laboratory are

slightly offset along the x-axis. For laboratories 2, 3, 4, and 5, the data points include symmetric

error bars representing the respective laboratory's estimate of U(X). As stated earlier, £/ defines an interval about the result of a measurement that may be expected to encompass a large fraction

of the distribution of values that could easily be attributed to the measurand [13] (i.e., X). For a coverage factor of k - 2, £/ defines a 95 % level of confidence within which the value of thermal

conductivity is confidently believed to reside [13].

Examination of the data in Figure 5 confirms the primary findings from the graphical analysis

shown in Figure 4. That is, there are systematic differences among the laboratory data for

materials 1, 2, and 3. For these materials there are several cases where the differences among the

data points lie outside the ranges covered by the error bars, most notably for materials 1 and 3. In contrast, however, the differences for material 4 among laboratories 2, 3, 4, 5, and 4 of the 5 observations for laboratory 1 appear to be insignificant at the uncertainty levels given in Table 4. Also, on a positive note, almost all the individual variation noted within a laboratory lies within

the error bars given for the laboratory. An exception is noted for material 2, laboratory 5.

The evaluation of sources for the systematic differences (effects due to differences in specimens,

equipment, procedure, etc.) noted in Figure 5 is described in Section 6. Further diagnosis of the

laboratory replicate data, including a detailed investigation of the location (means) and variation

(standard deviations) for the data, is summarized below.

5.

4

Detailed Investigation ofLaboratory Location and Variation

The general conclusions from Figures 4 and 5 are examined further by the application of the

mean and standard deviation plots to the thermal conductivity data. The mean plot provides

quantitative information for the question: Is there a change in the laboratory means across

laboratories? Likewise, the standard deviation plot provides quantitative information for the

question: Is there a change in the laboratory variation across laboratories? In the first case, the

change in location of the mean is associated with a systematic difference between laboratories.

For the second case, independent replicate measurements are generally used to provide estimates

of within- (and also between-) laboratory precision. The analyses of these statistics will be

presented graphically, tabulated, and used to rank the laboratories.

19
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Figure 5. Replicate data (297.15 K) versus laboratory (Materials 1, 2, 3, 4)

Error bars equal laboratory relative expanded uncertainty (Table 4)

20
Figure 6 plots the mean ( X ) value for each laboratory (where n = 5 observations) for materials 1 through 4. The grand mean (I) for each material (n = 25 observations) is shown as a horizontal

line. For reference, summary statistics that include J , grand standard deviation, and range are provided in a text box for each material. Ideally, the differences between X and X should be

small, indicating close agreement among the laboratories, and randomly scattered about the

horizontal line. An examination of the plots reveals that the locations of the means (with respect

to the laboratories) change from material to material. Ranking the materials by the magnitude of

their differences (by using either the grand standard deviation or range) reveals the following

order (from highest to smallest): 1, 3, 2, and 4.

Figure 7 plots the standard deviation for each laboratory (n = 5 observations) for materials 1 through 4. Here, each point represents the within-laboratory variability for five (independent)

observations, which, in most cases, is quite small. The grand standard deviation for each

material (n = 25 observations), shown as a solid horizontal line, includes both within- and

between-laboratory variability. An examination of the plots reveals that the variability within a laboratory also changes from material to material. It is interesting to note that for materials 1, 2,

and 3, the grand standard deviation is larger than the laboratory standard deviations and, for

material 4, is comparable to the laboratory standard deviations.

Tables 10a and 10b summarize the results of Figures 6 and 7, respectively. The last row in each

table provides the respective grand or "pooled" statistic (n = 25 observations) for each material

(across all laboratories). Likewise, the last column in each table provides the respective grand or "pooled" statistic (n = 25 observations) for each laboratory (across all materials). As a note of

clarification, the pooled standard deviation for each material in Table 10b is determined

differently than the grand standard deviation presented in Figures 6 and 7. The results given

Table 10 provide quantitative verification of the core conclusions given in Table 9.

TABLE 1 0a - Means for Replicate Data (297. 1 5 K)

Material 1 Material 2 Material 3 Material 4 Lab

Lab I I X X Average

(W/m K) (W/m K) (W/m K) (W/m K) (W/m K)

1 0.04448 0.03251 0.03655 0.03391 0.03686

2 0.04104 0.03189 0.03675 0.03369 0.03584

3 0.04055 0.03166 0.03616 0.03375 0.03553

4 0.04118 0.03206 0.03500 0.03368 0.03548

5 0.04032 0.03220 0.03686 0.03387 0.03581

Grand 0.04151 0.03206 0.03626 0.03378 0.03591

TABLE 10b- Standard Deviations for Replicate Data (297.15 K)

Material 1 Material 2 Material 3 Material 4 Pooled

Lab SD(k) SD(A.) SD(X) SD(X) SD

(W/m K) (W/m K) (W/m K) (W/m K) (W/m K)

1 0.00032 0.00005 0.00043 0.00030 0.00031

2 0.00003 0.00002 0.00002 0.00002 0.00002

0.00002 0.00004 0.00017 0.00005 0.00009

4 0.00018 0.00005 0.00000 0.00013 0.00011

5 0.00003 0.00018 0.00004 0.00001 0.00009

Pooled 0.00016 0.00009 0.00021 0.00015 0.00016

21
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22
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Figure 7. Standard deviation plot of replicate data (297.15 K) versus laboratory

(Materials 1,2, 3,4) 23
With regard to location, the last column in Table 10a (lab average across all four materials)

indicates that laboratory 1 is consistently higher than the other laboratories. On the average

across all four materials, laboratories 2 and 5, and 3 and 4, are closely paired and each pair of

laboratories differs by about 0.8%. With regard to variation, the last column in Table 10b

indicates that laboratory 1 is consistently noisy across all four materials. Laboratories 3, 4, and 5 exhibit similar levels of variability while laboratory 2 is extremely precise (by nearly a factor of

5 in comparison to the other three laboratories) across all four materials.

The summary statistics given in the last row of Tables 10a and 10b (as well as Figures 6 and 7)

motivate the following question of interest: Does the measurement precision vary with the

thermal conductivity of the materials being measured? To answer this question, we plot the

imprecision for each material and include both within-laboratory variability (pooled standard

deviations) and within- and between-laboratory variability (grand standard deviation) versus the

grand means of each material.

Figure 8 plots both the pooled (within-laboratory) and grand standard deviations (within- and

between-laboratory) versus the grand means of the thermal conductivities for materials 1 through

4. Each data point is depicted by a plot character equal to material. The results of Figure 8

would seem to indicate that the between-laboratory variability increases with the thermal

conductivity of the materials. As will be shown later in Figure 24, this trend is an artifact of

extremely high and low sets of data for materials 1 and 3, respectively, (as summarized in Table

9). The within-laboratory variability, however, is approximately the same across all levels of

thermal conductivity.

For comparison purposes, it is useful to determine the mean and standard deviation statistics

(Figures 6 and 7, respectively) on a relative basis (%). Figure 9 plots the relative mean for each

laboratory (n — 5 observations) for materials 1 through 4. The relative mean is defined as the

percentage difference between A (lab mean) and J (grand mean). With the exception of the

extremely high and low means for materials 1 (laboratory 1) and 3 (laboratory 4), respectively,

most of the laboratory means are within 1.5 % of the grand mean for each material.

Figure 10 plots the relative standard deviations for each laboratory (n = 5 observations) for

materials 1 through 4. Each point represents the within-laboratory variability and the grand

standard deviation for each material (n = 25 observations), shown as a solid horizontal line,

includes both within- and between-laboratory variability. With the exception of one point

(material 3, laboratory 1) all of the relative laboratory standard deviations are less than 1 % and

several are less than 0.5 %. The grand relative standard deviations range from approximately

0.5 % (material 4) to 3.7 % (material 1).

Tables 1 la and lib summarize the results of Figures 9 and 10, respectively. The last row in each

table provides the respective relative range (maximum minus minimum relative mean) or pooled

statistic (n = 25 measurements) for each material across all laboratories. Likewise, the last column in each table provides the respective grand or "pooled" statistic (n = 25 observations) for

each laboratory across all materials. In both tables, curious (or anomalous) results for a

particular laboratory, relative to the other laboratories, are tagged with a superscript number.

24
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Figure 8. Within- and between-laboratory variability versus grand means (Materials 1, 2, 3, 4)

25
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26
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(%) uojjBiAaa pjBpuBis aA|}B|ey (%) uoijBiAea pjBpuBis aA|jB|ay

Figure 10. Relative standard deviation plot of replicate data (297.15 K) versus laboratory

(Materials 1, 2, 3, 4)

27
TABLE 1 la- Relative Means for Replicate Data (297.15 K)

Material 1 Material 2 Material 3 Material 4 Lab

Lab Mean Mean Mean Mean Average

(%) (%) (%) (%) (%)

1 7.1' 1.4 0.8 0.39 2.4 2 -1.1 -0.6 1.3 -0.26 -0.2

3 -2.3 -1.3 -0.3 -0.09 -1.0

4 -0.8 0.0 -3.5 -0.30 -1.2

5 -2.9 0.4 1.6 0.27 -0.2

Range 10.0 2.7 5.1 0.69 3.6 High; "Marginally low

TABLE lib -Relative Standard Deviations for Replicate Data (297.15 K)

Material 1 Material 2 Material 3 Material 4 Pooled

Lab SD SD SD SD SD

(%) (%) (%) (%) (%)

1 0.71' 0.16 1.19' 0.89' 0.83 2 0.07 0.06 0.04 0.05 0.06

3 0.04 0.11 0.47

2 0.13 0.25 4 0.43

2 0.17 0.00J 0.39

2 0.30

5 0.06 0.56' 0.11 0.04 0.29 Pooled 0.37 0.28 0.57 0.44 —

Grand 3.74 0.95 1.97 0.49 —

High; "Marginally high; ^Artificially low

In general, the treatment of anomalous (or outlying) data can be handled either by retaining,

correcting, or deleting the data. Obviously, none of these options are completely satisfactory;

however, the third option (deletion) is acceptable when a physical cause can be identified to explain the behavior of the data. As will be seen later, some of the above test data will

eventually be classified as outlying (and excluded), but only because of a physical or engineering

reason. For these diagnostic analyses, the inclusion of all test data (curious or otherwise) allows

the opportunity to rank laboratories as presented below.

5. 5 Laboratory and Material Rankings

Using the results of Tables 10 and 11, the laboratory and material rank by location and variation

are summarized in Tables 12a, 12b, and 12c, respectively. Note that the rankings given in Tables

12a and 12b verify (and augment) the core conclusions given in Table 9.

TABLE 12a- Laboratory Ranking by Location

Rank

Material 1 LocationMaterial 2 LocationMaterial 3 Location

Material 4 Location

1 (highest) Lab 1* 1 5 1 2 4 5 2 5

3 2 4 1 3 4 3 2 2

5 (lowest) 5 3 4 4

* Cell entry is the coded laboratory identifier.

28
TABLE 12b - Laboratory Ranking by Variation

Rank

Material 1 Variation

Material 2

Variation

Material 3 VariationMaterial 4

Variation

1 (highest) Lab 1* 5 1 1 2 4 4 3 4

3 2 1 5 3 4 5 3 2 2

5 (lowest) 3 2 4 5

Cell entry is the coded laboratory identifier.

TABLE 12c - Material Ranking by Location and Variation

Rank

Location

Material (W/m-K)

Variation

Material (W/m-K)

1 (highest) 1 0.04151 1 0.00155

2 3 0.03626 3 0.00072

3 4 0.03378 2 0.00030

4 (lowest) 2 0.03206 4 0.00017

The results from Tables 12a and 12b succinctly demonstrate that the rankings for location and

variation are not consistent across all materials (even though laboratory 1 dominates many of the

#1 rankings). In other words, for a particular laboratory there is a change in location and

variation from material to material. The physical reasons for this behavior are explored in detail

in the next section.

The location rankings from Table 12c for materials 1 through 4 are in general agreement with

current measurement results in the literature. The variation rankings contain information on

between-laboratory variability and, unfortunately, are somewhat skewed because of high and low

sets of data for materials 1 (laboratory 1) and 3 (laboratory 4), respectively. Elimination of this

data as outlying would suggest that the between-laboratory variability for all materials would be

comparable.

5. 6 Comparison ofSource and Recipient Laboratory Data

This section presents a direct comparison (for informational purposes only) of thermal

conductivity data obtained from the source and recipient laboratories for materials 1 through 4. Figure 1 1 a plots thermal conductivity measurements from the recipient laboratories (Table 8) versus measurements from the source laboratories (Table 7). The plot character depicts the

(recipient) laboratory. The materials (1 through 4) are identified by their corresponding number.

A dashed line located at 45 degrees to the horizontal and vertical axes indicates perfect

agreement between the recipient and source laboratories. Values that fall below the line indicate

that the recipient measurements are low with respect to the source measurements. Conversely,

values above the line indicate that the recipient measurements are high with respect to the source measurements. For material 1, the recipient measurements are either spread along the line or high; for material 2, the values are slightly low; for material 3, low; and, for material 4, near or on the line. It is interesting to note that the values for material 1 are spread out along the

horizontal axis in comparison to material 2, for example. Figure 1 lb plots the relative deviations

of the recipient measurements from the 45-degree line.

29
0.045 -

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co

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10 -

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<D (D © Material

(D ©

i i

(D

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Source

1

0.030 0.035 0.040

X Source Laboratory (W/m-K)

0.045

Figure 11 . a) Recipient laboratories versus source laboratory (Materials 1,2,3, 4)

b) Relative deviations from source laboratory (Materials 1, 2, 3, 4)

30
6 Assessment of Fixed Temperature (297.15 K) Replicate Data

A complete and thorough assessment of the fixed temperature (297.15 K) replicate data relies on

both statistical and engineering analyses of the data. A descriptive statistical analysis quantifies

differences in the location and variation of the data, thereby ranking the data and identifying

curious or anomalous data points. Descriptive statistics provide minimal, if any, information on why the data points behave as observed. As mentioned previously, anomalous data points were

not discarded purely on the basis of outlier statistics in order to examine all the test data.

An engineering analysis, in contrast, attempts to determine the underlying cause(s) for the

behavior of the test data noted in the statistical analyses. In this regard, this section conducts the

following analyses:

1) Presentation of (secondary) laboratory factors;

2) Evaluation of the major sources of variation;

3) Detailed investigation of the effect of laboratory factors on X; 4) Comparison of the laboratory test data with certified values; and,

5) Comparison of the laboratory test data with precision indices from standard test methods

[2,3]

Before proceeding with the analyses, we re-present the set of primary questions identified in the

statistical analysis of the data. The answers to these questions are of considerable interest and

will guide the presentation of more detailed analyses. Specific questions will be answered later in the next section.

1) Ql : For 2 of the 4 materials, laboratory 1 is high, why?

2) Q2: For material 1, laboratory 5 is low, why?

3) Q3: For material 2, laboratory 3 is low, why?

4) Q4: For material 3, laboratory 4 is low, why?

5) Q5: For 3 of the 4 materials, laboratory 1 is noisy, why?

6) Q6: For material 2, laboratory 5 appears to have one outlying observation, why?

6.1 Presentation of (Secondary) Laboratory Factors

As investigated in the previous section, the primary factors of interest for the fixed temperature

(297.15 K.) replicate data are laboratory (5 levels) and reference material (4 levels). (The effect

of temperature as a primary factor, from 280 K to 320 K, is discussed later.) Ideally,

interlaboratory comparisons are designed to investigate within- and between-laboratory

variability of the primary factors by minimizing the effects of other (secondary) laboratory

factors. Thus, the resulting variability in the test data may be attributed to unavoidable random

errors present in every experimental test method. The effects of different settings for such

secondary laboratory factors will cause systematic differences in the test data. In this

comparison, the effect on A. across laboratories is systematic in nature and is most likely due to differences across settings within one (or more) laboratory factor(s). It is important to identify

(and subsequently estimate the effect of) the secondary laboratory factors present in this

comparison.

31
The cause-and-effect diagram is an extremely effective tool for identifying and classifying the

laboratory factors that affect a test result. Figure 12 illustrates a typical cause-and-effect diagram

showing major sources of variation and underlying laboratory factors for this comparison. The

major sources of variation are shown in text boxes and include 1) procedure; 2) specimen;

3) equipment; and, 4) measurement, among others. Here, procedure refers to a particular

technique utilized by a laboratory. Specimen refers to the material properties affecting

variability in X. In this case, specimen only includes the effect of bulk density and excludes any

affects due to the different levels of the primary factor material. Equipment covers the

component differences noted in Table 4 and measurement covers all properties measured in-situ

in the guarded-hot-plate apparatus (see Appendix D) for the determination of X. Obviously, this

list is not all-inclusive; the effects associated with operator and environment are not considered.

The underlying laboratory factors identified and classified in Figure 12 are summarized in

Table 13 with their respective source classification. Each factor is also classified by data type,

quantitative (numeric) or qualitative (categories). This distinction is important for subsequent

statistical analyses. The list of factors is not intended to be all-inclusive and, in some cases, there

is some redundancy among factors in different classifications (for example, note the similarity in

the factors - meter plate size and meter area - classified under equipment and measurement,

respectively).

TABLE 13 - Laboratory Factors Affecting the Measurement Variability of A. Laboratory Factors Data Type Source Classification

12

3

Steady-state conditions

Conditioning of specimen

Measurement technique for surface temperatures

Qualitative

Quantitative

Qualitative

]

f Procedure

J 4 Bulk density (p) Quantitative r Specimen

56

789

10

11

Plate size Meter plate size Plate emittance

Type of heater Edge guarding

Temperature sensor Operation mode

Quantitative

Quantitative

Quantitative

Qualitative

Qualitative

Qualitative

Qualitative

1

r Equipment

(see Table 4)

J 12

1314

1516

17

1819

Th (Hot surface)

Tc (Cold surface)

Tm (Mean temperature)

AT (Temperature difference)

L (In-situ specimen thickness)

Q (Specimen heat flow)

A (Meter Area)

q (Specimen heat flux, Q/A)

Quantitative

Quantitative

Quantitative

Quantitative

Quantitative

Quantitative

Quantitative

Quantitative

1

\ Measurement

J We will systematically step through each line in Table 13, performing two analyses. The first analysis evaluates the underlying factors of three major sources of variation - procedure,

specimen, and measurement. The second analysis is a comprehensive statistical analysis of

correlation and variance for all 19 factors given in Table 13.

32
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CD DC ^

.Q -H^ CO C/) _l ^

i_3 /CD

CD 55 O

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Q. CD

CD W

Figure 12. Cause-and-effect chart for laboratory test result (X)

33
6.2 Evaluation ofMajor Sources of Variation

6.2.1 Procedure: Figure 1 2 identifies three procedural factors that may have caused variations in

the test results: 1) differences in defining steady-state conditions; 2) specimen conditioning; and,

3) the technique for measuring the temperature difference across the specimen.

6.2.1.1 Steady-State Conditions: A discussion of the laboratory equipment revealed that each

laboratory has developed similar, but not identical, in-house procedures for obtaining steadystate conditions (i.e., short-term control stability) of their respective apparatus. The procedures

are based on typical guidelines for settling time and measurement interval established in ISO

8302 [2] and ASTM C 177 [3] test methods. Since the procedures involve different groups of

parameters and stabilization times, a complete laboratory-to-laboratory comparison is not

possible. In general, however, the procedural differences reported among the laboratories for

obtaining steady state are small and, therefore, not believed to be a significant source of the

systematic differences observed in the data.

6.2.1.2 Specimen Conditioning: The laboratory environments for specimen conditioning were

unspecified in the test protocol (Appendix B) and left to the individual laboratories. Although

not requested, laboratory 2 included their specimen conditioning data with their original report

forms. Similar data were requested from the other laboratories after completion of this study.

Table 14 summarizes the available, data. Although the data are too sparse for definitive

conclusions, in general, ambient conditioning of these materials plays little or no role. The

fibrous material does not pick up moisture sufficient to have an effect and the presence of a binder allows only a small amount (0.3 % to 0.4 % by mass fraction). Likewise, polystyrene

(closed-cell) foam does not pick up moisture under most laboratory ambient conditions.

TABLE 14 - Conditioning Environments for Specimens (Post-Comparison, except Lab 2)

Lab Material 1 Material 2 Material 3 Material 4 T(°C) RH (%) T(°C) RH (%) T(°C) RH (%) T(°C) RH (%)

12' 23 50 23 50 23 50 23 50

3 23 20 24 30 23 30 24 25

4

5 Laboratory 2 dried specimens of materials 1, 2, and 3 in an oven at 70 °C prior to conditioning

6.2.1.3 Surface Temperature Measurement Technique: With respect to surface temperature,

two different techniques were utilized in this comparison for the surface temperature

measurement: 1) permanent sensors affixed to the apparatus; and, 2) removable sensors affixed

to the specimen. Both ISO 8302 [2] and ASTM C 177 [3] provide recommended techniques to determine the temperature difference across a specimen. For non-rigid specimens, the

temperature difference is usually determined using temperature sensors permanently mounted in

the heating and cooling surfaces . For rigid specimens, the temperature difference may be

determined by mounting sensors flush (typically by cutting grooves) in the specimen surfaces.

Temperature sensors such as thermocouples are typically installed in grooves cut in the surfaces of the plates. For

laboratory 3, a platinum resistance thermometer is actually installed in the guard-gap on the perimeter of the meter

plate in accordance with ASTM practice C 1043 [14]. 34
Four of the five laboratories utilized the first technique, that is, temperature sensors permanently

mounted in the heating and cooling surfaces. After submission of their test data, laboratory 1 reported that the surface temperatures of their specimens were measured using 0.2 mm diameter

thermocouples (Type T) placed directly on the surface of the specimen with adhesive tape. For

the replicate measurements, the thermocouples were removed and reapplied prior to each

measurement. It is surmised that much of the variability observed in Figure 4 could be attributed

to this measurement technique of affixing thermocouples to the surface of the specimen. In an

early comparison of guarded hot plates, Robinson and Watson [15] noted that discrepancies

could result between conductivity values obtained using temperatures from plate surfaces and

those measured using surface thermocouples. Intuitively speaking, the surface mounted

technique would seem to have inherently more variation than sensors permanently affixed to the

apparatus and, thus, contribute to less precise levels of replication.

This premise is investigated by plotting the laboratory test results for X on a relative basis (%)

versus material as illustrated in Figure 13a. The five laboratory replicates are plotted

sequentially for each material. Note that for laboratory 1, the relative differences from the grand

mean are substantially different across the four materials (Figure 13b) and the relative standard

deviations are high for materials 1, 3, and 4 (Figure 13c). As noted before, materials 1, 2, and 3 are fibrous materials having average bulk densities of 14 kg/m3

, 72 kg/m3

, and 227 kg/m3

, respectively (Figure 1). Material 1 is a flexible blanket and materials 2 and 3 are semi-rigid

boards of increasing rigidity. By contrast, material 4 is expanded polystyrene in the form of a semi-rigid board having relatively smooth surfaces in comparison to the fibrous materials. The

results in Figure 13 would tentatively suggest an interaction between the surface measurement

technique of affixing the sensors to the materials and the type of material.

The approach of adhering fine-diameter temperature sensors to the specimen surface appears to have contributed to measurement differences and may be an unintended extension of the test procedures specified in the ISO and ASTM standard test methods [2,3]. Further measurements

comparing different techniques for determining the temperature difference across a test specimen

would be extremely useful. With regard to ISO 8302 [2] and ASTM C 177 [3] standard test methods, the appropriate sections on determination of the temperature difference should be re- examined for clarity and revised if necessary.

6.2.2 Specimen: The inclusion of bulk density (p) with the other factors in Table 13 is necessary, even though a substantial effort was undertaken by the source laboratories to issue well-matched

specimens of a homogeneous sample of each reference material (Figures 1 and 3, respectively).

Many of the specimens, however, were subsequently cut smaller for the different plate sizes

(Table 4) involved in this comparison. Within-specimen variability, if present, could contribute

to differences in density between the source and recipient laboratories. Furthermore, variability

between specimen and meter area bulk densities may also be present. As mentioned earlier,

there was no provision included in the protocol (Appendix B) for determining the bulk density of

the meter area of the specimen. Since the meter area bulk density is more representative of the

measured thermal conductivity, future comparisons should, if possible, request the determination

of the meter area bulk density for the analysis of the A,-versus-p data. For the samples of

reference materials released to the participants, the pertinent question becomes: Is there a specimen bulk density effect within a material for the fixed temperature (297.15 K) replicate

data?

35
12 3 4

Material

Figure 13. a) Relative thermal conductivity versus material;

b) Relative mean thermal conductivity versus material;

c) Relative standard deviation thermal conductivity versus material

36
Figure 14 plots X versus specimen p for each material. Vertical dashed lines denote the initial density range measured by the source laboratory (Table 5). For materials 1 and 4, predicted

values of X(Tm,p) at 297.15 K from Eq 1 are shown as solid lines. The predicted values for

material 1 increased from 0.04039 W/m K to 0.04138 W/m K (about 2.5 %) over the range of p

from 13.4 kg/m3 to 14.4 kg/m3

. For material 4, the change in X(Tm,p) was less than 0.1 %.

Unfortunately, a definitive analysis of Figure 14 is problematic for the following reasons.

1) Figure 14 indicates a negative X-p relationship for material 1, positive for material 2, and

weak for material 3. In contrast, Figure 3 (source lab data) indicates the ^-p relationship

was weak for materials 1 and 2; and, positive for material 3. These differences suggest

that either within-specimen variability is significant (particularly for material 1), or the

results of Figure 14 are perhaps skewed by the densities reported by laboratory 1, or both.

2) The bulk densities reported by laboratory 1 are either consistently a minimum or maximum value across all four materials, why? A partial explanation is available from

the results given in Figure 1 for materials 2 and 3. Laboratory 1 received specimen pairs

for materials 2 and 3 having the maximum and minimum density, respectively, for each

material (Figure 1).

3) The bulk densities reported by laboratory 1 are, in some cases, considerably outside the

ranges provided by the source laboratories in Figure 1. Were there problems with the

density measurement, part from the metering section issue? Further information on this

issue, and the above, from laboratory 1 is on request.

Although unrelated to density, there are other noteworthy issues concerning some of the

specimens, which are discussed here. The comments below were reported by laboratory 4.

1) For material 3, laboratory 4 reported values of X that are 3.5 % below the grand mean for

material 3 (Table 11.) In the comment section of their official test report form, laboratory

4 reported that, "this material had completely delaminated on arrival so that the test specimen consisted of two pieces which were always aligned in the same orientation with

respect to each other whilst testing." Since no other laboratories reported similar

experiences, this set of data for material 3 is considered sufficiently different from the

other specimens to warrant rejection as an outlying observation.

2) For material 4, laboratory 4 reported values of X that are relatively imprecise when

compared to their own data for the other 3 materials. In the comments section of their

official test report form, laboratory 4 reported that the higher variability in the data

"could (be) due to an increased uncertainty associated with the measurement thickness of

about 13 mm." The laboratory noted that "this sample is thinner than the limit of 25 mm

set for minimum specimen thickness in accordance with ISO 8302 [2]." This condition is simply noted since this data is only affected marginally.

Finally, some final comments on material types and density levels are in order. Although this

comparison studied four reference materials, there were only two types of materials: fibrous

glass (p = 3 levels) and cellular expanded polystyrene (p = 1 level). In hindsight, future

comparisons may alternatively consider balancing the number of levels of p for each material type

37
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Figure 14. Thermal conductivity (297.15 K) as a function of bulk density (Materials 1, 2, 3, 4)

38
or, at a minimum, consider 2 levels of p per material. In addition, if possible, it would probably

be useful to characterize the microstructure (pore size, fiber diameter, etc.) of each material and

determine the extent of within-specimen variations of bulk density.

6.2.3 Equipment: Figure 12 identifies several equipment factors (from Table 4) that may have

caused variation in the test result. The effects of these factors are investigated later as part of the

comprehensive analysis of all the laboratory factors.

6. 2.

Measurement: This section investigates six of the eight factors identified in Figure 12: Th, Tc , T„„ AT, L (in-situ), and q. Values for these parameters were requested as part of the official returns from the laboratories (Appendix C) and tabulated in Table 8. The analysis is carried out

in two parts:

1) A check of the protocol execution given in Appendix B; and,

2) An in-depth analysis of Tm, AT, and L (in-situ).

6.2.4.1 Check of Protocol Execution: Figure 15 is a sequence of plots for X versus the

thermal test parameters; 7)„ Tc , Tm, AT, L, and, q. The first four plots (Figures 15a to 15d) check

how effectively the laboratories executed the test protocol (Appendix B) to obtain target

temperatures of Tm = 297.15 K (24 °C) and AT= 20 K (regardless of material). Dashed vertical

lines indicate target temperatures in the first four plots. For example, Figure 15a (7),) indicates a

target temperature of 307.15 K (34 °C).

The data indicate that laboratory 1 was low with respect to both 7), and Tc, and that laboratory

4 was low. for T/, but high for Tc. The net effect, as shown in Figures 15c and 15d, was that

laboratory 1 was significantly low for Tm and high and low for AT. Laboratory 4 was slightly

low for Tm (<0.5 K) and low for AT. The other laboratories were generally tightly clustered

about the respective target temperatures. Table 15 summarizes the laboratory statistics for the

mean, standard deviation, and range for values of Th, Tc,, Tm and AT given in Figures 15a to 15d.

TABLE 15a - Mean, Standard Deviation, and Range of Th and Tc (Table 8)

Lab

Th Th - 307.15 SD(7*) Range Tc Tc - 287.15 SD(rc) Range

(K) (K) (K) (K) (K) (K) (K) (K)

1 306.64 -0.51 1.23 4.32 286.24 -0.91 0.39 1.55 2 307.18 0.03 0.03 0.12 287.20 0.05 0.07 0.25

3 307.15 0.00 0.00 0.00 287.15 0.00 0.00 0.01 4 306.17 -0.98 0.33 0.99 287.56 0.41 0.22 0.61

5 307.14 -0.01 0.03 0.13 287.15 0.00 0.01 0.04

TABLE 15b - Mean, Standard Deviation, and Range of T„, and AT (Table 8)

Lab

Tm T -297.15 m SD(rw) Range AT A7/-20 SD(A7) Range

(K) (K) (K) (K) (K) (K) (K) (K)

1 296.44 -0.71 0.64 2.09 20.39 0.39 1.32 4.65

2 297.19 0.04 0.04 0.15 19.98 -0.02 0.06 0.23

3 297.15 0.00 0.00 0.00 20.00 0.00 0.00 0.01 4 296.86 -0.29 0.14 0.43 18.61 -1.39 0.49 1.31 5 297.14 -0.01 0.02 0.07 19.99 -0.01 0.03 0.13

39
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Figure 1 5. Multi-plot of thermal conductivity versus test parameters (Materials 1,2,3, 4)

40
Figure 15e plots X versus L for all the laboratories. Horizontal lines have been inserted that

delineate the thermal conductivity (A.) ranges of the four materials (shown as ©,©,(D, and ©,

respectively). (Note that these lines are not shown in Figures 15a to 15d, although the same

ranges do apply.) A target thickness of 25.4 mm was specified only for material 1 (Appendix B).

The thicknesses for the other materials were unspecified in the test protocol and measured by the

laboratories as received. These thickness measurements are in close agreement except for the

few cases that are discussed below.

Figure 15f plots X versus q for all the laboratories. Horizontal lines have been inserted that

delineate the thermal conductivity (X) ranges of the four materials (shown as ©,©,(D, and ©,

respectively). It is interesting to note that laboratories 1 and 2 reported values of q that were

essentially twice the values determined by the other laboratories. These differences are merely a discrepancy in the accounting for the factor of 2 given in Eq 2, and indicate that further clarity

for the definition of q is needed in either the test protocol (Appendix B), or the standard test methods [2,3], or both.

6.2.4.2 Mean Temperature (TJ: Figure 16 plots X as a function of Tm for each material. For

the fixed-temperature replicate data, all laboratories were requested to test the specimens at a mean temperature of 297.15 K (24 °C). Examination of the plots reveals that the data, for most

laboratories, are near 297.15 K (24 °C). As discussed previously (Figure 15), laboratories 1 and

4 reported mean temperatures that are consistently lower than the other laboratories. There are

also other interesting trends in the data. For material 2, the direction of variation for laboratories

3 and 5 is vertical and for laboratory 2, horizontal. In some cases, these variations change

direction from material to material (for example, note directional change in variability for

laboratories 2 and 4 for materials 3 and 4). The reason(s) for these trends is not known.

6.2.4.3 Temperature Difference (AT): Figure 17 plots X versus AT" for each material. All

laboratories were requested to test their specimens at a temperature difference of 20 K,

regardless of material (and mean temperature). Examination of the plots reveals that the data, for

most laboratories, are near 20 K. As discussed previously (Figure 15), laboratories 1 and 4

reported temperature differences that were consistently higher (about 1 K) and lower (about 1 K

to 2 K), respectively, than the other laboratories. For material 1 , laboratory 1 reported 2

observations that were about 3 K low. In some cases, as was observed in Figure 16, variations in

direction changed from material to material (for example, note directional change in variability

for laboratory 4 from materials 3 to 4). The reason(s) for these trends is not known.

6.2.4.4 Thickness (L): Figure 18 plots X versus L for each material. With the exception of

material 1, all laboratories were requested to measure the specimen thickness as received.

A target thickness of 25.4 mm was specified for material 1 (Appendix B). All laboratories

reported such thicknesses to 2 decimal places - with the exception of laboratory 1 which

reported 1 decimal place (Table 8). For laboratory 1, there is no variation in any of the

measurements of thickness (perhaps due to the rounding). The thickness data for laboratory 2 is generally quite tight for the fibrous glass materials. The same statement applies for laboratory 5. except for material 1 . Both laboratories 2 and 5, however, report more variation in L for material

4 (cellular expanded polystyrene). For material 1, laboratory 3 is about 0.4 % higher than the

other laboratories. Requesting additional information on in-situ thickness measurement

techniques would be useful for future interlaboratory comparisons.

41
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Figure 16. Replicate data (297.15 K) as a function of mean temperature (Materials 1, 2, 3, 4)

42
£

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Figure 17. Replicate data (297.15 K) versus temperature difference (Materials 1, 2. 3, 4)

43
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Figure 18. Replicate data (297.15 K) versus thickness (Materials 1, 2, 3, 4)

44
Table 16 summarizes the laboratory statistics for the mean and standard deviation of L by

material. Superscripts ( H

) and ( L

) designate the high and low laboratory means, respectively, for

each material. The grand mean and standard deviation (n = 25 observations per material) are given in the last row of Table 16.

TABLE 16 - Mean and Standard Deviation of L (Table 8)

Material 1 Material 2 Material 3 Material 4 Lab L SD(L) L SD(L) L SD(L) L SD(I)

(mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm)

1 25.4 0.0 34.5 0.0 25.3

H 0.0 13.5

H 0.0 2 25.40 0.00 34.41 0.00 23.46 L 0.02 13.43 0.01

3 25.52 H 0.00 34.82

H 0.00 23.78 0.06 13.33 0.00 4 25.38

L 0.02 34.35 0.02 24.10 0.01 13.20

L 0.05

5 25.38

L 0.02 34.14L 0.00 23.48 0.00 13.35 0.01 Grand 25.41 0.06 34.44 0.25 24.02 0.76 13.36 0.11

H High value for material;L Low value for material

With the exception of material 3, the values for the grand standard deviations in Table 16 are

relatively small. On a relative basis (dividing the grand standard deviations by their respective

grand mean), the relative standard deviations are 0.2 %, 0.7 %, 3.2 %, and 0.8 % for materials 1, 2, 3, and 4, respectively. For comparison, Table 17 provides summary thickness statistics for the source laboratory data given in Table 7.

TABLE 17 - Mean and Standard Deviation of Source Laboratory L (Table 7)

Source Lab

L SD(Z.) Rel. SD(I)

Material (mm) (mm) (%)

1

->j 25.53 0.01 0.04 2 4 34.42 0.07 0.2

3 1 23.8 0.3 1.4 4 13.43 0.06 0.4

6. 3 Detailed Investigation ofLaboratory Factors

In contrast to the previous evaluation and discussion of major sources of variation identified in

the cause-and-effect chart (Figure 12), this comprehensive statistical analysis of the 19

laboratory factors (from Table 13) addresses two questions:

1

)

Is there a factor effect on XI and,

2) What is the relationship between the response variable (X) and a factor?

Results of the analysis are presented by graphical analysis of the data as illustrated in Figures 19,

19, 20, and 21 for materials 1, 2, 3, and 4, respectively. Each figure contains 20 scatter plots of X

(vertical axis) versus the factors 1 through 19 (horizontal axis) as given in Table 13. As a point

of reference, the first plot of each figure graphs X versus the primary factor laboratory.

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49
For a given material, each plot provides a correlation coefficient (r) (for quantitative x-axis data

only) and an analysis of variance (ANOVA) cumulative probability for X and the laboratory

factor of interest. Values of r near ± 100 % and values of the ANOVA cumulative probability near 100 % both are indications of factor significance. The following information is provided to

assist in interpreting the graphical analysis.

The plot character in all plots is laboratory (1 to 5). With no loss of interpretability, the tic marks

and tic labels have been purposely omitted for conciseness. For a given material, the limits of

the vertical axis are the same for all 20 plots so as to assist comparability. For example, the

vertical axis limits for all plots for material 1 (Figure 19) are 0.040 W/m-K to 0.045 W/m-K. The

horizontal limits change depending on what factor is plotted. For example, in the first plot of

Figure 19, the horizontal axis varies from 1 to 5; whereas, in the fifth plot (X versus plate size),

there are three horizontal axis values (300 mm, 610 mm, and 1016 mm as taken from Table 4).

From an interpretation point of view, participating laboratories are encouraged to peruse each

plot and relate their own laboratory values of X to specific factors. By way of example (using

Figure 19 for material 1 as a starting point for illustrative purposes), laboratory 1 appears to be

high relative to the other four laboratories. It is of use to consider what laboratory factors may

contribute to this high set of observations. In this regard, it is desirable to enumerate those

factors in which laboratory 1 is unique, i.e., in which no other laboratories share that factor.

Hence, for example, laboratory 1 has the following unique settings:

1) Plot 3: surface measurement technique is 1 (affixing thermocouples to specimen);

2) Plot 4: lowest p;

3) Plot 5: smallest plate size;

4) Plot 6: smallest meter plate size;

5) Plot 13: lowest cold plate temperature (Tc); 6) Plot 17: smallest Q; and,

7) Plot 18: smallest meter area (A).

Note that the above items 3), 4), and 7) all share the same common dimensionality. The net

effect is that the above factors serve to verify previous conclusions.

On the other hand, perusal of certain plots would suggest that other factors would not serve as an

explanation for the high observations reported by laboratory 1 . Thus, any future settings shared

with laboratory 1 would suggest that the factor might be eliminated as a prime candidate for

causing high values of X. For example, laboratories 1 and 4 both having the same plate

emittance (plot 7) suggests exclusion, as would laboratories 1, 2, 3, and 5 sharing the same

(double-sided) mode of operation (plot 11).

Figures 19 through 22 are replete with information dealing with both consistency and anomaly.

Participant laboratories are encouraged to use Figures 1 9 to 22 (and the upcoming Tables 1 8 and

19) for self-assessment.

6.3.1 Analysis of Variance: Question 1 from this section can be re-phrased: Do different levels of

a factor yield significantly different X's from one another. The analysis of variance (ANOVA)

procedure examines the statistical significance of a factor on X. The term FCDF (F-cumulative

distribution function) given in Figures 19 through 22 is the percent point of the F-distribution

50
[16, p. 117]; only FCDF values above 95 % are considered significant (at the 5 % level). It is important to note that values of FCDF are based on the assumption that the variances of the

treatments

3 are constant across treatments. This is decidedly not the case for many plots and so

the numeric values of FCDF should be used for indicative purposes only. An advantage of the

ANOVA analysis is that it is applicable to both types of data: quantitative (numeric) or

qualitative (categorical). Table 18 summarizes the results of the ANOVA procedure.

TABLE 18 - Is a Factor Statistically Significant? (FCDF> 95 %? Yes/No)

Laboratory Factors Material 1 Material 2 Material 3 Material 4 Laboratory (primary) Y Y Y N

12

Steady-state conditions

Conditioning of specimen

Measurement technique for surface temperatures

Y

Incomplete

Y

Y

Incomplete

Y

Y

Incomplete

N

N

Incomplete

Y

4 Bulk density (p) Y Y Y N

56

7

89

10

11

Plate size Meter plate size Plate emittance

Type of heater Edge guarding

Temperature sensor Operation mode

Y

Y

Y

N

Y

N

N

Y

Y

Y

Y

N

Y

N

N

Y

Y

N

Y

Y

Y

N

N

N

N

N

Y

N

12

1314

1516

17

18

19

T„

Tc T

AT

L

Q

A

Q

Y

Y

Y

Y

N

Y

Y

Y

N

N

N

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

Y

N

N

N

N

From Table 18, the single most important conclusion is that, for material 4, the primary factor

laboratory is not statistically significant. This is not the case for materials 1, 2, and 3 - there is statistically significant difference across the 5 laboratories.

Further examination of Table 18 above indicates that many of the 19 (secondary) laboratory

factors are significant. Significance, however, does not necessarily imply causation - especially

given the fact that many correlations exist among the factors themselves. (For example, if T/, is significant and/or Tc is significant, then it is not surprising that Tm and/or AT would also be

significant.) Finding the root significant factor(s) is done by using results from Table 18 in

conjunction with engineering judgement (and possibly additional tests) by the participating

laboratories.

6.3.2 Correlation: Question 2 from this section deals with relationships between A. and a factor.

The simplest case, asks whether a linear relationship exists between X and a factor. The

correlation coefficient (r) is a measure of linear relatedness between two variables. A perfect

A treatment is a particular combination of levels of the factors involved in an experiment [171. 51
linear relationship yields a correlation coefficient of ± 1 00 %. A lack of relationship yields a

correlation coefficient of zero (0 %). Because of the large quantity of replicate data for the five

laboratories (n = 100 per plot), values of \r\ > 20 % are statistically significant at the 5 % level

[16, p. 185 and p. 557].

In the context of linear regression between X and a factor, the correlation coefficient is related to the slope of the fitted line. If the slope is positive (or negative), the correlation coefficient will

be positive (or negative). If the slope is zero, the correlation coefficient will be zero.

Table 19 summarizes the results of the correlation analysis. In cases where the data for the factor on the x-axis is qualitative (as identified in Table 13), the correlation coefficient is meaningless

and was not included. Values of r with a "high" level of correlation (arbitrarily selected for |r| >

90 %) are shown in boldface italics.

TABLE 19 - Is there a Significant Correlation between X and a Laboratory Factor? (\r\ >20 %? Yes/No)

Laboratory Factors Material 1 Material 2 Material 3 Material 4 Laboratory (primary) ... ... ... ...

1 Steady-state conditions — ... ... —

2 Conditioning of specimen Incomplete Incomplete Incomplete Incomplete

-> Measurement technique for surface temperatures 4 Bulk density (p) Y (-98 %) Y (+63 %) N Y (+30 %)

5 Plate size Y (-76 %) Y (-89 %) N Y (-29 %)

6 Meter plate size Y (-77 %) Y (-94 %) Y (-3 1 %) Y(-41 %)

7 Plate emittance Y (+36 %) Y (+44 %) Y (-47 %) Y (+25 %)

8 Type of heater — — — ...

9 Edge guarding — — ... ...

10 Temperature sensor — — ... ...

11 Operation mode — ... ... ...

12 T„ Y (-5 1 %) N Y (+82 %) Y (+27 %)

13 Tc Y (-73 %) Y (-70 %) Y (-43 %) Y (-26 %)

14 T1 m Y (-62 %) Y (-53 %) Y (+36 %) N

15 AT Y (-33 %) Y (+46 %) Y (+73 %) Y (+34 %)

16 L N Y (-49 %) N Y (+39 %)

17 Q Y (-47 %) Y (-75 %) N Y (-42 %)

18 A Y (-76 %) Y (-94 %) Y (-35 %) Y (-44 %)

19 Q Y (+69 %) Y (+43 %) Y (+53 %) N

The values given in Table 19 indicate that for all materials there are several factors correlated

with X. Fortunately, many of the numeric values of |r| are small. For materials 1 and 2, however,

there are a few factors highly correlated with X (> 90 %) that call for further investigation. Note

that high correlation does not imply causality, only a linear association. In general, these results are somewhat unexpected and indicate that future interlaboratory comparisons should probably

require additional protocols to minimize the effects of undesired laboratory factors.

52
6. 4 Comparison with Certified Values

The comparison of measured values of X with certified values, X(Tm, p), provides another useful

method for evaluating the differences among the laboratories from an engineering perspective.

Values of X(Tm, p) for materials 1 and 4 (SRMs 1451 and 1453, respectively) were determined

from Eq 1 using the measured values of Tm and p

provided by each participant (Table 8). The

corresponding uncertainties of ± 3 % and ± 1.3 % for materials 1 and 4, respectively, were used

to establish cut-off bounds for the evaluation of anomalous values of A. reported earlier. The

certification equation for material 2 [10] became available after this analysis was completed and

is not included. Material 3 is currently undergoing certification process and, therefore, the

certification equation is unavailable.

Table 20 summarizes the measurements for materials 1 and 4 given previously in Table 8 for p, Tm, AT, X, as well as computed values of X(Tm, p) from Eq 1, and the corresponding differences

(absolute and relative) between X and X(Tm, p). The data are partitioned by material, laboratory,

and replicate number (i.e., laboratory run sequence). For materials 1 and 4, the relative

differences range from approximately -0.2 % to +8.5 % and -0.2 % to +2.4 %, respectively.

Figure 23 plots the relative differences of X and X(Tm, p) versus p for materials 1 and 4,

respectively. Here the plot character represents the laboratory and horizontal solid lines indicate

the cut-off bounds for the (expanded) uncertainty levels for each CRM. For materials 1 and 4,

the (expanded) uncertainties are ±3% (coverage factor unavailable) and ± 1.3% (coverage

factor of k = 2), respectively.

Figure 23a reveals that the relative differences for the replicate data from laboratories 2, 3, 4, and

5 are entirely within the uncertainty levels (± 3 %) for material 1 . With the exception of one

observation from laboratory 4, the differences from the certified values for these laboratories are

less than 1.3 %. Although the agreement among these laboratories is quite encouraging, the

differences for laboratory 1 are considerably outside the uncertainty levels for SRM 1451. For

material 1, the data from laboratory 1 are considered sufficiently different (+7.2 % to +8.5 %)

from the certified values to warrant rejection as an outlying observation.

Figure 23b reveals that the relative differences for the replicate data from laboratories 2, 3, 4, and

5 are entirely within the uncertainty levels (± 1.3 %) for material 4. For these laboratories, the

differences from the certified values are less than 0.8 %. Although the agreement among these

laboratories is quite encouraging, the differences for laboratory 1 require further analysis. For

laboratory 1 , 3 of the 5 replicate observations, including the mean value, from laboratory 1 are within the uncertainty levels. Therefore, the differences for laboratory 1 are considered

acceptable and within the CRM uncertainty levels for material 4. In general, the agreement

among the laboratories for material 4 (SRM 1453) is strongly encouraging.

53
TABLE 20- Comparison of Fixed Temperature (297.15 K) Replicate Data with Certified Values

Materia] Lab Replicate P Tm AT X KTms p) Difference Difference

(kg/m3 ) (K) (K) (W/m-K) (W/m-K) (W/m-K) (%)

1 13.35 296.97 20.47 0.04473 0.04138 0.00335 8.09

2 13.35 296.88 20.27 0.04489 0.04136 0.00353 8.54

*5 13.35 294.88 16.57 0.04425 0.04088 0.00337 8.24 4 13.35 294.89 16.69 0.04417 0.04088 0.00329 8.04

5 13.35 296.87 20.66 0.04434 0.04136 0.00299 7.22 2 1 14.10 297.16 19.96 0.04101 0.04064 0.00037 0.90

2 2 14.10 297.17 20.01 0.04104 0.04064 0.00040 0.97 2 3 14.10 297.19 20.01 0.04105 0.04065 0.00040 0.99 2 4 14.10 297.20 20.00 0.04103 0.04065 0.00038 0.93 2 5 14.10 297.20 19.98 0.04109 0.04065 0.00044 1.08

3 1 14.15 297.15 20.00 0.04052 0.04059 -0.00007 -0.18

3 2 14.15 297.15 20.00 0.04055 0.04059 -0.00004 -0.10

3 3 14.15 297.15 20.00 0.04056 0.04059 -0.00003 -0.08

3 4 14.15 297.15 20.00 0.04056 0.04059 -0.00003 -0.08

3 5 14.15 297.15 20.00 0.04056 0.04059 -0.00003 -0.08 4 1 14.13 297.01 18.93 0.0415 0.04058 0.00092 2.27 4 2 14.13 297.10 19.06 0.0411 0.04060 0.00050 1.23 4 3 14.13 297.12 19.07 0.0411 0.04061 0.00049 1.22 4 4 14.13 297.11 19.07 0.0411 0.04060 0.00050 1.22 4 5 14.13 297.09 19.03 0.0411 0.04060 0.00050 1.24

5 1 14.37 297.16 19.98 0.04035 0.04039 -0.00004 -0.10

5 2 14.37 297.15 20.02 0.04030 0.04039 -0.00009 -0.21

5 3 14.37 297.14 20.01 0.04029 0.04038 -0.00009 -0.23

5 4 14.37 297.14 19.96 0.04031 0.04038 -0.00007 -0.18

5 5 14.37 297.14 19.97 0.04034 0.04038 -0.00004 -0.11 4 1 39.8 296.15 20.70 0.03401 0.03346 0.00055 1.66 4 2 39.8 296.67 20.51 0.03433 0.03352 0.00081 2.41 4 3 39.8 295.70 21.02 0.03350 0.03341 0.00009 0.26 4 4 39.8 295.97 20.82 0.03382 0.03344 0.00038 1.13 4 5 39.8 296.19 20.77 0.03390 0.03346 0.00044 1.30 4 2 1 38.6 297.15 20.00 0.03369 0.03363 0.00006 0.19

4 2 2 38.6 297.14 20.05 0.03369 0.03363 0.00006 0.19 4 2 3 38.6 297.16 19.96 0.03372 0.03363 0.00009 0.27 4 2 4 38.6 297.14 20.01 0.03368 0.03363 0.00005 0.16 4 2 5 38.6 297.18 20.04 0.03368 0.03363 0.00005 0.15 4 3 1 38.2 297.15 20.00 0.03367 0.03364 0.00003 0.08 4 3 2 38.2 297.15 20.00 0.03378 0.03364 0.00014 0.40 4 3 3 38.2 297.15 20.00 0.03377 0.03364 0.00013 0.37 4 3 4 38.2 297.15 20.00 0.03376 0.03364 0.00012 0.34 4 3 5 38.2 297.15 20.00 0.03377 0.03364 0.00013 0.37 4 4 1 38.8 296.78 17.76 0.0335 0.03357 -0.00007 -0.22 4 4 2 38.8 296.78 17.82 0.0338 0.03357 0.00023 0.67 4 4 3 38.8 296.84 17.87 0.0338 0.03358 0.00022 0.65 4 4 4 38.8 296.79 17.80 0.0337 0.03358 0.00012 0.37 4 4 5 38.8 296.78 17.79 0.0336 0.03357 0.00003 0.08 4 5 1 38.5 297.13 19.99 0.03387 0.03363 0.00024 0.72

4 5 2 38.5 297.15 19.97 0.03386 0.03363 0.00023 0.68

4 5 3 38.5 297.13 19.98 0.03386 0.03363 0.00023 0.68 4 5 4 38.5 297.14 19.99 0.03389 0.03363 0.00026 0.77 4 5 5 38.5 297.13 20.00 0.03388 0.03363 0.00025 0.74

54
Material 1

10.0

5.0 -

<c^

CL

, E <^

o.o -

-5.0 -

- -

I

I I I i

1

1

Character = Laboratory

- Uncertainty Limits

4

I

4

a a

a)

I i i i i

13.0 13.5 14.0

P (kg/m3 14.5 15.0

3.0

2.0 -

1.0 -

a.

I

a. tf °-°

<<<

-1.0

-2.0

-3.0

b)

38.0

Material 4

Expanded Uncertainty Limits (k=2)

38.5 39.0

P (kg/m3)

39.5 40.0

Figure 23. Relative deviations from certified values versus p

(Materials 1 , 4)

55
6. 5 Comparison with Standard Test Method Precision Indices

Both ISO 8302 [2] and ASTM C 177 [3] provide statements of uncertainty (precision) of ± 2 %

for measurements near room temperature. In addition, ISO 8302 [2] specifies a reproducibility

4

of better than ± 1 % for independent replicate measurements near room temperature. This

section evaluates the question: Are the differences among laboratories at 297.15 K significant in

comparison with accepted uncertainty and precision statements of the standard test methods for

guarded-hot-plate apparatus [2,3]?

From previous analyses, two sets of laboratory data are sufficiently different to warrant rejection as outlying observations - data sets for material 1, laboratory 1 (5 observations); and, material 3,

laboratory 4 (5 observations). Table 21 excludes these observations and re-computes the

laboratory relative means and the grand relative standard deviations previously given in Table 1

1

for the affected materials.

TABLE 21 - Relative Means and Standard Deviations for Replicates (297.15 K)

Excluding Outlying Data (Material 1-Labl and Material 3-Lab 4)

Material 1 Material 2 Material 3 Material 4 Lab Mean SD Mean SD Mean SD Mean SD

(%) (%) (%) (%) (%) (%) (%) (%)

1 — ... 1.4 0.16 -0.1 1.19' 0.39 0.89' 2 0.7 0.07 -0.6 0.06 0.5 0.04 -0.26 0.05

3 -0.5 0.04 -1.3 0.11 -1.1 0.47

2 -0.09 0.13 4 1.0 0.43

2 0.0 0.17 — — -0.30 0.39

2

5 -1.1 0.06 0.4 0.56

1 0.8 0.11 0.27 0.04 Grand — 0.91 — 0.95 — 0.95 — 0.49 Range 1.8 — 2.7 — 1.9 — 0.69 —

'High; "Margina ly high

From Table 21, note that the ranges of laboratory means for materials 1, 2, 3, and 4 are 1.8 %,

2.7 %, 1.9 %, and 0.69 %, respectively. The corresponding half-ranges for materials 1, 2, 3, and

4 are ± 0.9 %, ± 1.4 %, ± 1.0 %, and ± 0.35 %, respectively, which are all less than the

ISO/ASTM uncertainty (precision) statements of ± 2 %. With the exception of one set of data

(material 3, laboratory 1), the laboratory standard deviations are all less than 1 % (Table 21),

which are less than the reproducibility limit of ± 1 % given in ISO 8302 [2].

At this point, it is constructive to re-compute the summary statistics for the replicate data,

excluding the above outlying observations (material 1, laboratory 1 and material 3, laboratory 4).

Tables 22a and 22b exclude these observations and re-present the laboratory means and grand

standard deviations previously given in Tables 10a and 10b, respectively. The last row in each

table provides the recomputed values for the respective grand or "pooled" statistic for each

material (across all laboratories). The last column in each table provides the recomputed values

for the respective grand or "pooled" statistic for each laboratory (across all materials). As noted

in the last row of Table 22a, the grand mean for material 1 has decreased and increased for

material 3 when compared to previous values (Table 10a). Values for the grand standard

deviations (last row, Table 22b) have decreased for materials 1 and 3. The "pooled" values for

the lab standard deviations have decreased for materials 1 and increased slightly for material 3.

ASTM defines this quantity as repeatability.

56
TABLE 22a - Means for Replicate Data (297.15 K)

Excluding Outlying Data (Material 1-Labl and Material 3-Lab 4)

Material 1 Material 2 Material 3 Material 4 Lab

Lab I I I I Average

(W/m K) (W/m K) (W/m K) (W/m K) (W/m K)

1 — 0.03251 0.03655 0.03391 —

2 0.04104 0.03189 0.03675 0.03369 0.03584

3 0.04055 0.03166 0.03616 0.03375 0.03553

4 0.04118 0.03206 — 0.03368 —

5 0.04032 0.03220 0.03686 0.03387 0.03581

Grand 0.04077 0.03206 0.03658 0.03378 0.03591

TABLE 22b - Standard Deviations for Replicate Data (297.15 K)

Excluding Outlying Data (Material 1-Labl and Material 3-Lab 4)

Material 1 Material 2 Material 3 Material 4 Pooled

Lab SDW SD(?i) SD(X) SD(X) SD

(W/m K) (W/m K) (W/m K) (W/m K) (W/m K)

1 — 0.00005 0.00043 0.00030 0.00031

2 0.00003 0.00002 0.00002 0.00002 0.00002

3 0.00002 0.00004 0.00017 0.00005 0.00009

4 0.00018 0.00005 — 0.00013 0.00013

5 0.00003 0.00018 0.00004 0.00001 0.00009

Pooled 0.00009 0.00009 0.00023 0.00015 0.00016

Grand 0.00037 0.00030 0.00035 0.00017 —

Figure 24 re-plots both the "pooled" (within-laboratory) and grand standard deviations (withinand between-laboratory) (last two rows from Table 22b, respectively) versus the grand means

(Table 22a) of the thermal conductivities for materials 1 through 4. Each data point is depicted

by a plot character equal to material. The results of Figure 22 indicate that the betweenlaboratory variability is approximately the same across all levels of thermal conductivity. This

result is reassuring for the four materials studied in this comparison. The within-laboratory

variability, however, is approximately the same across all levels of thermal conductivity and is, as expected, less than the between-laboratory variability for each material.

7 Summary Findings for Replicate Data (297.15 K)

This section summarizes the important findings of the replicate data analysis. The principal

conclusion from the comparison of the replicate data is that the behavior of the laboratories does,

in fact, change from material to material. As observed initially in Figure 4, the location and, to a

lesser extent, variation of each set of laboratory data does change from material to material. In

short, there is a laboratory-material interaction. This conclusion was verified by a re- examination of the data that included the engineering levels of expanded uncertainty for each

laboratory (Figure 5). Subsequent analyses were guided by a set of primary questions

(formulated from the results of Figure 4) that represent the core results of this interlaboratory

comparison.

57
0.0020

* 0.0015

E

cg

'I 0.0010

CD Q

T3

L.

CO T3C

03 55 0.0005

0.0000

Character = Material

O Between-laboratory variability

Within-laboratory variability

Excluded data: Material 1, Laboratory 1 Material 3, Laboratory 4

®

CD ©

m

0.032 0.034 0.037 0.039

Grand Mean (W/m-K)

0.042

Figure 24. Within- and between-laboratory variability versus grand means (Materials 1, 2, 3, 4)

Excluding data from Material 1, Laboratory 1 and Material 3, Laboratory 4

58
7.1 Descriptive Statistics

Descriptive statistics are used to summarize the fixed-temperature (297.15 K) replicate data and

to subsequently rank order the laboratories and materials. The results of this detailed statistical analysis quantify the changes in location and variation (observed in Figures 4 and 5). These

results, which are drawn from Tables 10 and 11, are summarized below using a shorthand

notation (M = material, L = laboratory). The changes in location were greatest for material 1, a

fibrous-glass blanket and smallest for material 4, a semi-rigid expanded polystyrene board.

• Laboratory location rank by material (relative mean in parentheses) from Table 1 1

• Ml: LI (7.1 %), L4 (-0.8 %), L2 (-1.1 %), L3 (-2.3 %), L5 (-2.9 %);

• M2: LI (1 .4 %), L5 (0.4 %), L4 (0.0 %), L2 (-0.6 %), L3 (-1 .3 %);

• M3: L5 (1.6 %), L2 (1.3 %), LI (0.8 %), L3 (-0.3 %), L4 (-3.5 %); and,

• M4: LI (0.39 %). L5 (0.27 %), L3 (-0.09 %), L2 (-0.26 %), L4 (-0.30 %).

• Laboratory variation rank by material (relative standard deviation in parentheses) from

Table 11:'

• Ml: LI (0.71 %), L4 (0.43 %), L2 (0.07 %), L5 (0.06 %), L3 (0.04 %);

• M2: L5 (0.56 %), L4 (0.17 %), LI (0.16 %), L3 (0.1 1 %), L2 (0.06 %);

• M3: LI (1.19 %), L3 (0.47 %), L5 (0.1 1 %), L2 (0.04 %), L4 (0.0 %); and,

• M4: LI (0.89 %), L4 (0.39 %), L3 (0.13 %), L2 (0.05 %), L5 (0.04 %)

• Material variation rank (grand relative standard deviation in parentheses) from Table 1 1

• Ml (3.74 %), M3 (1.97 %), M2 (0.95 %), and M4 (0.49 %)

• Anomalous data points:

• High location and variation: (M 1 , L 1

• High variation: (M2, L5); (M3. LI); and, (M4, LI)

• Low location and artificially low variation: (M3, L4)

• Marginal data points:

• Marginally high variation: (Ml. L4); (M3, L3); and (M4, L4)

7.2 Assessment

The assessment of the fixed-temperature (297.15 K) replicate data was guided by the six core

questions presented above. The systematic effects noted in the data (Figures 4 and 5) indicate

the presence of one or more secondary factors. Applying a cause and effect diagram (Figure 12).

(secondary) laboratory factors were identified and systematically investigated using statistical and engineering techniques. The results for questions 1 through 6 are presented below.

01: For 2 of the 4 materials, laboratory 1 is high, why? It is surmised that, for laboratory 1, much of the within-laboratory variability observed in the test data (Figures 4 and 5) could be

attributed to the measurement technique of affixing thermocouples directly to the specimen for

surface temperatures. In an early comparison of guarded hot plates, Robinson and Watson [15]

noted that discrepancies could result between conductivity values obtained using temperatures

from plate surfaces and those measured using surface thermocouples. This technique introduces

several potential sources of variation to the temperature difference across the specimen:

59
1) operator/procedural judgement in precisely locating the sensor for each replicate;

2) relocation of sensor could place the sensor in different proximity to local material

inhomgenieities;

3) different levels of clamping pressure could result in temperature variations if the

thermocouples were not in intimate contact with the plates; and,

4) (potential) error due to incorrect determination of the separation distance corresponding

to the temperature difference across the specimen.

With the above concerns, one could make an effective argument that this technique would seem

to have inherently more variation than sensors permanently affixed to the apparatus (as utilized

by the other laboratories) and, thus, contribute to less precise levels of replication. This premise was investigated by plotting the laboratory test results for X on a relative basis (%) versus

material (Figure 13). For laboratory 1, the relative differences from the grand mean are substantially different across the four materials (Figure 13b) and the relative standard deviations

are high for materials 1, 3, and 4 (Figure 13c). Materials 1, 2, and 3 are fibrous materials having

average bulk densities of 14 kg/m , 72 kg/m3

, and 227 kg/m3, respectively. Material 1 is a

flexible blanket and materials 2 and 3 are semi-rigid boards of increasing rigidity. Material 4 is a semi-rigid expanded polystyrene board having relatively smooth surfaces in comparison to the

fibrous materials. The results in Figure 13 would tentatively suggest an interaction between the

surface measurement technique of affixing the sensors to the materials and the type of material.

02: For material 1, laboratory 5 is low, why? Referring to Figure 14, there is, unfortunately, a small density effect for specimen sample that was distributed. The value for X is low because the

bulk density of the specimen was high.

03: For material 2, laboratory 3 is low, why? The only insight to this finding is given in Figure 20, which indicates an extremely high negative correlation between X and meter plate size

(as well as the two other related factors). The reader is strongly cautioned, however, that

correlation does not imply causality.

Q4: For material 3, laboratory 4 is low, why? The answer was provided by laboratory 4 in their

official report form. In the comments section of their official test report form, laboratory 4

reported that, "this material had completely delaminated on arrival so that the test specimen

consisted of two pieces which were always aligned in the same orientation with respect to each

other whilst testing."

Q5: For 3 of the 4 materials, laboratory 1 is noisy, why? The answer is given above (see

question 1).

06: For material 2, laboratory 5 appears to have one outlying obseryation, why? The answer to

this question is currently unknown.

7.2.1 Anomalous Data Points: Analyses of the anomalous data points above revealed that two

sets of data points (10 % of the replicate data) were outlying data sets (and eventually omitted).

For interlaboratory studies, it is extremely helpful (and inevitably necessary) for the laboratories

in question to present their own explanations for the behavior of the test results. To their credit,

laboratories 1 and 4 did provide explanations (see below) for their anomalous data.

60
Ml, LI : After submission of their test data, laboratory 1 reported that the surface

temperatures for determinations of specimen AT were measured using 0.2 mm diameter

thermocouples placed directly on the surface of the specimen with adhesive tape. In contrast,

the other laboratories utilized temperature sensors permanently mounted in the heating and

cooling surfaces. Further, this set of data was significantly different (by 8 %) from certified

values for material 1 and therefore classified as an outlying data set. For material 1, all of

other laboratory data was entirely within the bounds of the CRM uncertainty limits of ± 3 %.

M3, L4: As reported by laboratory 3, the reason this data set was identified as an outlying set data was attributed to specimen failure. The specimen was found delaminated upon arrival.

No other laboratory reported this condition for the same material. As a side comment, this one incident of delamination could present a dilemma for future "certification" of material 3. One occurrence can be attributed as an accident (i.e., handled badly during shipment, etc). If the occurrences are more regular, the material may be unsuitable as a reference material.

Two of the other sets of anomalous data points (M3, LI and M4, LI) were attributed to the

technique used to measure the temperature difference across the specimens (see Question 1, above). The underlying cause(s) for the last set of anomalous data points (M2, L5) are undetermined.

7.2.2 Marginal Data Points: The underlying cause(s) for the marginal data points identified in the statistical analysis are unknown.

7. 2.

3

Laboratory Factors: The contribution of any (secondary) laboratory factors was

systematically investigated using a cause-and-effect diagram. The analysis was covered in two

parts: an engineering assessment of the major sources of variation that included a check of the

protocol execution; and, a comprehensive statistical analysis of 19 laboratory factors using

correlation analysis and analysis of variance (ANOVA).

Check ofProtocol Execution:

• Checking the execution of the protocol revealed that, for some laboratories, there were deviations in obtaining the target temperatures for the hot and cold surfaces. As

a result the mean temperature (Tm) and temperature differences (AT) were slightly

different than the target temperatures for some laboratories.

• For the report values of q (heat flux), two laboratories reported values that were

essentially twice the values of the other laboratories for a given material. This was

merely a bookkeeping discrepancy and did not affect the final determination of

thermal conductivity. Still, this discrepancy indicates that additional clarification is needed in the standard test methods [2,3] concerning the definition of heat flux and

what quantity is to be reported.

7.2.4 Comparison ofA with Certified Values: Certified values were available for materials 1 and

4, fibrous-glass blanket (SRM 1451) and expanded polystyrene board (SRM 1453), respectively.

For material 1, the mean values of X for 4 of the 5 laboratories deviated from certified values by

less than the ± 3 % uncertainty limits. For material 4, the mean values of X for 5 of the 5 laboratories were less than the ± 1 .3 % relative expanded uncertainties (k = 2).

61
7.2.5 Comparison with Standard Test Methods Precision Indices: When the outlying data sets are excluded (for the reasons noted above), the ranges of laboratory means for materials 1, 2, 3,

and 4 are 1.8 %, 2.7 %, 1.9 %, and 0.69%, respectively (Table 21). The corresponding halfranges for materials 1, 2, 3, and 4 are ± 0.9 %, ± 1.4 %, ± 1.0 %, and ± 0.35 %, respectively,

which are all less than the ISO/ASTM uncertainty (precision) statements of ± 2 %. With the

exception of one set of data (material 3, laboratory 1), the laboratory standard deviations are all less than 1 % (Table 21), which are all less than the reproducibility limit of ± 1 % given in ISO

8302 [2].

7. 2.

6

Procedural Recommendations for Future Comparisons:

• It would be useful to have additional information on the measurement technique(s)

used by individual laboratories participating in the comparison (for example, in-situ

techniques for thickness measurements, etc). In a related issue, the list of factors

investigated here was not exhaustive. For example, other factors that could be

important are: 1) major differences in gap size between metering and guard and how

the gap was filled; 2) what areas were used to calculate A. if, in fact, there were gap

width differences; and, 3) how well was edge guarding undertaken - could moisture

condensation be a factor? A standardized list of requested factors would be

extremely useful.

• One laboratory utilized an alternative technique for the measurement of the

temperature difference across the specimen. The results suggest that this technique of

placing temperature sensors directly on the specimens is inherently less precise than

using sensors permanently mounted in the heating and cooling surfaces. Both ISO

and ASTM may wish to address this issue with greater clarity in their respective

standards [2,3].

• The five laboratories used slightly different criteria for establishing settling and

equilibrium times for taking test data. Both ISO and ASTM may wish to address this

issue in their respective standards [2.3].

• Two of the laboratories computed values of q approximately one-half the values

determined by the other three laboratories. Both ISO and ASTM may wish to address

this issue in their respective standards [2,3].

• In future comparisons, laboratories should follow an agreed upon (or standardized)

method for computing the expanded uncertainties (U) of their measured values of

thermal conductivity (k).

• In order to minimize some of these procedural differences in the future, the respective

ISO and ASTM technical committees may wish to develop standard practices for

conducting an interlaboratory comparison specifically for guarded hot plate

apparatus. These standard practices should include standard test protocols, forms for

reporting data (including expanded uncertainties (U)), and ancillary information (such

as test equipment, etc.). Such activities will need to consider that ISO and ASTM

have different definitions for some statistical terms, such as reproducibility and

repeatability.

62
8. Analysis of Multi-Temperature (280 K to 320 K) Data

The third primary factor investigated in this interlaboratory comparison is temperature,

specifically, single-point measurements for each material from 280 K to 320 K. The single-point

data precludes the rigorous descriptive statistical analysis performed for the replicate data at 297.15 K. Nonetheless, the analyses are driven by the same central theme for the fixedtemperature replicate data: How do the laboratories behave across the four materials? With

respect to this question, the following analyses are provided:

1

)

Presentation of laboratory data;

2) Graphical exploration of laboratory test data versus temperature by material;

3) An ensuing ranking of the laboratories by location and variation;

4) Comparison of the thermal conductivity measurements with certified values; and,

5) Comparison of the thermal conductivity measurements with the precision indices from

standard test methods [2,3]

8.

1

Presentation ofLaboratory Data

Table 23 summarizes the measurements for the specimen bulk density (p), hot (7),) and cold (Tc) plate temperatures, specimen heat flow (0, thickness (L), meter area (A), thermal conductivity

(A,), mean temperature (Tm), and temperature difference (of 20 K). The tabulated data are partitioned by material, laboratory, and run sequence. All laboratories, except 4, reported a run sequence from low to high Tm. Note that for all materials, laboratory 4 did not report data at 320 K. The value for p has been rounded to 3 significant digits and represents the average of the

pair of specimens (for a double-sided test). The number of significant digits for the other

parameters is tabulated as received from the laboratory. Any certainty for the 5

l significant digit

for values of X cannot be assigned, but the digit is included for the subsequent analyses of the

results. The data in Table 23 were entered in an electronic spreadsheet and reported values for X

were checked by recalculation.

8.2 Graphical Exploration ofLaboratory Data

Figure 25 plots the measurements of X versus Tm for the 4 materials. The observations for each

laboratory are shown as characters 1, 2, 3, 4, and, 5, respectively. In examining the laboratory

data for each material, the central question under investigation is again, do the five laboratories

behave similarly across the four materials? Or, (if the laboratories behave differently across the

four materials), is there a laboratory-material interaction? There are two independent but related

questions in determining the behavior of laboratories from material to material: 1) Is there a change in location of the laboratory data? and, 2) Is there a change in variation of the laboratory

data? Examination of these two questions for the data in Figure 25 is provided by a linear

regression analysis of the data. For comparison purposes, the data in Figure 25 were fit with the

following model:

X = b + b, Tm ( 3 )

Figure 26 plots the relative deviations from the fitted curve for each data point.

63
TABLE 23 - Multi-Temperature (280 K to 320 K) Data

Material Lab Run P Th Tc Q L A X Tm AT

Seq. (kg/m3 ) (K) (K) (W) (W) (m2 ) (W/m K) (K) (K)

1 13.4 290.22 270.48 1.441 25.4 0.0225 0.04120 280.35 19.74

2 13.4 299.95 279.90 1.526 25.4 0.0225 0.04296 289.92 20.05

3 13.4 309.89 289.68 1.641 25.4 0.0225 0.04583 299.79 20.21 4 13.4 320.30 299.77 1.785 25.4 0.0225 0.04908 310.03 20.53

5 13.4 329.35 309.69 1.849 25.4 0.0225 0.05309 319.52 19.66

2 1 14.1 290.17 270.07 5.282 25.40 0.090016 0.03707 280.12 20.10

2 2 14.1 300.14 280.09 5.585 25.40 0.090056 0.03929 290.12 20.05

2 3 14.1 310.16 290.19 5.911 25.40 0.090097 0.04171 300.18 19.97 2 4 14.1 320.19 300.17 6.292 25.40 0.090138 0.04428 310.18 20.02

2 5 14.1 330.13 310.21 6.649 25.40 0.090178 0.04700 320.17 19.92

3 1 14.2 290.15 270.14 3.720 25.52 0.1297 0.03656 280.15 20.01

3 2 14.2 300.15 280.15 3.9541 25.49 0.1297 0.03883 290.15 20.00

3 3 14.2 310.15 290.15 4.196 25.53 0.1298 0.04125 300.15 20.00

3 4 14.2 320.15 300.15 4.449 25.57 0.1299 0.04381 310.15 20.00

3 5 14.2 330.15 310.15 4.715 25.62 0.1299 0.04654 320.15 20.00

4 3 14.1 290.43 270.34 2.7613 25.38 0.09315 0.0374 280.39 20.09

4 4 14.1 300.26 280.16 2.9285 25.39 0.09315 0.0397 290.21 20.10

4 1 14.1 309.07 290.48 2.8712 25.42 0.09315 0.0422 299.77 18.59

4 2 14.1 319.72 300.44 3.1669 25.44 0.09315 0.0448 310.08 19.28

5 1 14.4 290.06 270.05 1.820 25.39 0.0625 0.03695 280.06 20.01

5 2 14.4 299.96 279.98 1.922 25.39 0.0625 0.03908 289.97 19.98

5 3 14.4 310.00 290.01 2.022 25.39 0.0625 0.04111 300.01 19.99

5 4 14.4 320.01 300.01 2.149 25.39 0.0625 0.04364 310.01 20.00

5 5 14.4 330.01 310.03 2.281 25.39 0.0625 0.04637 320.02 19.98

2 1 79.2 290.54 269.91 0.835 34.5 0.0225 0.03103 280.23 20.63

2 2 79.2 300.39 279.27 0.871 34.5 0.0225 0.03162 289.83 21.12

2 3 79.2 310.17 289.09 0.904 34.5 0.0225 0.03288 299.63 21.08

2 4 79.2 320.10 299.06 0.931 34.5 0.0225 0.03392 309.58 21.04

2 5 79.2 330.00 309.05 0.973 34.5 0.0225 0.03561 319.52 20.95

2 2 1 69.9 290.13 270.11 3.135 34.42 0.090015 0.02993 280.12 20.02

2 2 2 69.9 300.13 280.18 3.243 34.42 0.090056 0.03107 290.16 19.95

2 2 69.9 310.12 290.11 3.372 34.42 0.090097 0.03219 300.16 20.01

2 2 4 69.9 320.13 300.23 3.485 34.42 0.090137 0.03343 310.18 19.90

2 2 5 69.9 330.16 310.17 3.636 34.42 0.090178 0.03470 320.17 19.99

2 3 1 73.8 290.15 270.15 2.215 34.77 0.1297 0.02966 280.15 20.00

2 3 2 73.8 300.15 280.15 2.296 34.79 0.1297 0.03077 290.15 20.00

2 3 3 73.8 310.15 290.15 2.384 34.83 0.1298 0.03197 300.15 20.00

2 3 4 73.8 320.15 300.15 2.469 34.88 0.1299 0.03318 310.15 20.00

2 3 5 73.8 330.15 310.15 2.563 34.93 0.1299 0.03449 320.15 20.00

2 4 3 70.0 289.76 270.58 1.5659 34.36 0.09315 0.0301 280.17 19.18 2 4 4 70.0 300.14 280.40 1.6740 34.36 0.09315 0.0313 290.27 19.74

2 4 1 70.0 309.71 290.28 1.7071 34.39 0.09315 0.0324 300.00 19.43 2 4 2 70.0 319.69 300.14 1.7803 34.41 0.09315 0.0336 309.92 19.55

2 5 1 74.6 290.00 269.98 1.119 34.14 0.0625 0.03054 279.99 20.02

2 5 2 74.6 299.98 280.00 1.156 34.14 0.0625 0.03160 289.99 19.98

2 5 3 74.6 309.98 290.00 1.198 34.14 0.0625 0.03277 299.99 19.98

2 5 4 74.6 319.98 300.00 1.245 34.14 0.0625 0.03401 310.00 19.98

2 5 5 74.6 330.01 310.01 1.288 34.14 0.0625 0.03517 320.01 20.00

64
Material Lab Run P Th Tc Q L A X Tm AT

Seq. (kg/m3 ) (K) (K) (W) (W) (m2

) (W/m K) (K) (K)

3 1 213 290.35 270.03 1.295 25.3 0.0225 0.03583 280.19 20.32

3 2 213 300.10 279.36 1.332 25.3 0.0225 0.03611 289.73 20.74

3 3 213 310.15 289.24 1.390 25.3 0.0225 0.03737 299.70 20.91

3 4 213 320.01 299.17 1.432 25.3 0.0225 0.03863 309.59 20.84

3 5 213 329.88 308.95 1.477 25.3 0.0225 0.03968 319.42 20.93

3 2 1 228 290.15 270.06 5.386 23.41 0.090015 0.03486 280.11 20.09

3 2 2 228 300.14 280.15 5.541 23.41 0.090056 0.03602 290.15 19.99

3 2 3 228 310.13 290.20 5.683 23.41 0.090097 0.03706 300.17 19.93

3 2 4 228 320.12 300.20 5.844 23.41 0.090137 0.03810 310.16 19.92

3 2 5 228 330.15 310.16 6.035 23.41 0.090178 0.03918 320.16 19.99

3 3 1 225 290.15 270.15 3.736 23.76 0.1297 0.03420 280.15 20.00

3 3 2 225 300.15 280.15 3.866 23.74 0.1297 0.03534 290.15 20.00

3 3 3 225 310.15 290.15 3.996 23.69 0.1298 0.03647 300.15 20.00

3 3 4 225 320.15 300.15 4.124 23.71 0.1299 0.03766 310.15 20.00

3 3 5 225 330.15 310.15 4.233 23.68 0.1299 0.03861 320.15 20.00

3 4 1 223 289.70 270.73 2.4387 24.00 0.09315 0.0331 280.21 18.97

3 4 2 223 299.31 280.54 2.4896 24.03 0.09315 0.0342 289.92 18.77

3 4 3 223 309.13 290.39 2.5607 24.05 0.09315 0.0353 299.76 18.74

3 4 4 223 319.07 300.26 2.6511 24.08 0.09315 0.0364 309.66 18.81

3 5 1 230 289.84 270.03 1.849 23.48 0.0625 0.0351 279.93 19.81

3 5 2 230 299.99 279.98 1.926 23.48 0.0625 0.03616 289.99 20.01

3 5 230 309.97 289.97 1.975 23.48 0.0625 0.03714 299.97 20.00

3 5 4 230 320.02 300.00 2.032 23.48 0.0625 0.03814 310.01 20.02

3 5 5 230 329.96 309.98 2.086 23.48 0.0625 0.03922 319.97 19.98

4 1 39.8 290.03 270.04 2.233 13.5 0.0225 0.03310 280.04 19.99 4 2 39.8 298.98 278.87 2.230 13.5 0.0225 0.03327 289.92 20.11

4 3 39.8 309.73 288.75 2.394 13.5 0.0225 0.03424 299.24 20.98

4 4 39.8 320.90 298.55 2.644 13.5 0.0225 0.03549 309.72 22.35

4 5 39.8 330.58 308.64 2.686 13.5 0.0225 0.03673 319.61 21.94

4 2 1 38.6 290.10 270.12 8.540 13.41 0.090015 0.03184 280.11 19.98 4 2 2 38.6 300.10 280.17 8.808 13.41 0.090056 0.03292 290.14 19.93 4 2 3 38.6 310.16 290.18 9.130 13.41 0.090097 0.03403 300.17 19.98 4 2 4 38.6 320.15 300.21 9.424 13.41 0.090138 0.03517 310.18 19.94 4 2 5 38.6 330.14 310.19 9.764 13.41 0.090178 0.03639 320.17 19.95 4 3 1 38.2 290.15 270.15 6.167 13.32 0.1297 0.03164 280.15 20.00

4 3 2 38.2 300.15 280.15 6.420 13.28 0.1297 0.03282 290.15 20.00

4 3 3 38.2 310.15 290.15 6.642 13.31 0.1298 0.03405 300.15 20.00

4 3 4 38.2 320.15 300.15 6.851 13.38 0.1299 0.03532 310.15 20.00

4 3 5 38.2 330.15 310.15 7.070 13.43 0.1299 0.03655 320.15 20.00

4 4 3 38.8 289.10 271.16 4.0270 13.12 0.09315 0.0316 280.13 17.94

4 4 4 38.8 298.96 281.08 4.1588 13.15 0.09315 0.0328 290.02 17.88

4 4 2 38.8 308.63 290.86 4.2638 13.17 0.09315 0.0339 299.75 17.77 4 4 1 38.8 318.73 300.92 4.4184 13.22 0.09315 0.0352 309.82 17.81 4 5 1 38.5 290.00 270.03 2.997 13.36 0.0625 0.03208 280.01 19.97 4 5 2 38.5 299.99 280.00 3.097 13.36 0.0625 0.03312 290.00 19.99

4 5

*5J 38.5 309.99 290.03 3.192 13.36 0.0625 0.03419 300.01 19.96

4 5 4 38.5 320.00 300.02 3.297 13.36 0.0625 0.03528 310.01 19.98

4 5 5 38.5 329.99 310.00 3.410 13.36 0.0625 0.03647 320.00 19.99 Note: Laboratory 4 did not report data at 320 K.

65
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(Materials 1,2,3,4)

66
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67
As observed before with the replicate data, the principal conclusion from Figure 26 is that the

behavior of the laboratories does, in fact, change from material to material. For the four plots,

the location and variation of each set of laboratory data changes from material to material. In

short, there is a laboratory-material interaction over the range of temperatures from 280 K to 320 K. By focusing attention again on the extreme values of the data set with respect to location

and variation in Figure 26, we will attempt to verify and, possibly, augment the conclusions

obtained from the replicate data. Table 24 summarizes the maximum and minimum values, the

level of variation (i.e., noise), and apparent outliers for each material.

TABLE 24 -Summary Results of the Interlaboratory Comparison for the Multi-Temperature Data

Material High Lab Low Lab Noisy Lab Outlying Lab

1 1 (Outlier) 5,3 1 1 (280 K, 320 K)

2 1,5 1 1 (280 K, 320 K)

1 4 (Outlier) 1 1 (280 K)

4 1 2,3,4 1 1 (280 K)

The results from Table 24 and Table 9 are not identical indicating that there are other interactions

between temperature and (some or all of) the factors identified previously. These results are investigated briefly further below.

8.3 Check ofProtocol Execution

Figure 27 is a sequence of plots for X versus T/„ Tc , Tm, AT, L, and, q. The first four plots

(Figures 27a to 27d) check how effectively the laboratories executed the test protocol

(Appendix B) to obtain target temperatures of Tm = 280 K, 290 K, 300 K, 310 K, and 320 K and

AT = 20 K (regardless of Tm or material). The dashed vertical lines indicate target temperatures.

Large horizontal offsets from the dashed lines indicate a laboratory deviation from the test protocol (Appendix B). In general, as seen previously (Figure 15) with the fixed temperature

(297,15 K) data, laboratories 1 and 4 appear not to adhere to the test temperature protocol as well

as laboratories 2, 3, and 5 (Figure 27d).

8.

4

Comparison with Certified Values .

Values of X{Tm, p) for materials 1 and 4 (SRMs 1451 and 1453, respectively) were determined

from Eq 1 using the measured values of T,„ and p provided by each participant (Table 23).

Table 25 summarizes the measurements for materials 1 and 4 for p, Tm, AT, X, and computed

values of X(Tm, p), and the corresponding differences (absolute and relative) between A. and X(Tm, p). The data are partitioned by material, laboratory, and run sequence. Note that for material 4,

calculations outside the range of certified values 285 K to 310 K (Table 2) are shown as in

italics. The corresponding uncertainties of ± 3 % and ± 1.3 % for materials 1 and 4, respectively, were used to establish cut-off bounds for the evaluation of anomalous values of X. The

certification equation for material 2 [10] became available after this analysis was completed and

is not included. Material 3 is currently undergoing certification process and, therefore, the

certification equation is unavailable.

68
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69
TABLE 25 - Comparison of Multi-Temperature (280 K to 320 K) Data with Certified Values

Material Lab Run P Tm AT X MTm ,p) Difference Difference

Seq. (kg/m3

) (K) (K) (W/m-K) (W/m-K) (W/m-K) (%)

1 13.35 280.35 19.74 0.04120 0.03757 0.00364 9.68

2 13.35 289.92 20.05 0.04296 0.03972 0.00324 8.16

3 13.35 299.79 20.21 0.04583 0.04206 0.00377 8.96 4 13.35 310.03 20.53 0.04908 0.04463 0.00445 9.97

5 13.35 319.52 19.66 0.05309 0.04712 0.00596 12.65 2 1 14.10 280.12 20.10 0.03707 0.03688 0.00019 0.52

2 2 14.10 290.12 20.05 0.03929 0.03904 0.00025 0.63

2 3 14.10 300.18 19.97 0.04171 0.04135 0.00036 0.88

2 4 14.10 310.18 20.02 0.04428 0.04376 0.00052 1.19 2 5 14.10 320.17 19.92 0.04700 0.04630 0.00070 1.52

3 1 14.15 280.15 20.01 0.03656 0.03684 -0.00028 -0.77

3 2 14.15 290.15 20.00 0.03883 0.03901 -0.00018 -0.45

3 3 14.15 300.15 20.00 0.04125 0.04129 -0.00004 -0.10

3 4 14.15 310.15 20.00 0.04381 0.04370 0.00011 0.26

3 5 14.15 320.15 20.00 0.04654 0.04623 0.00031 0.68 4 1 14.13 299.78 18.59 0.0422 0.04122 0.00098 2.37 4 2 14.13 310.08 19.28 0.0448 0.04370 0.00110 2.51 4 14.13 280.39 20.09 0.0374 0.03691 0.00049 1.32 4 4 14.13 290.21 20.10 0.0397 0.03904 0.00066 1.69

5 1 14.37 280.06 20.01 0.03695 0.03666 0.00029 0.80

5 2 14.37 289.97 19.98 0.03908 0.03878 0.00030 0.78

5

-> 14.37 300.01 19.99 0.04111 0.04104 0.00007 0.16

5 4 14.37 310.01 20.00 0.04364 0.04343 0.00021 0.49

5 5 14.37 320.02 19.98 0.04637 0.04593 0.00044 0.96 4* / 7 39.8 280.04 19.99 0.03310 0.03158 0.00152 4.80

4 1 2 39.8 288.92 20.11 0.03327 0.03262 0.00065 1.99 4 1 3 39.8 299.24 20.98 0.03424 0.03382 0.00041 1.23 4 1 4 39.8 309.72 22.35 0.03549 0.03504 0.00045 1.28 4 1 5 39.8 319.61 21.94 0.03673 0.03619 0.00053 1.47

4 2 / 38.6 280.11 19.98 0.03184 0.03164 0.00020 0.62 4 2 2 38.6 290.14 19.93 0.03292 0.03281 0.00011 0.33 4 2 3 38.6 300.17 19.98 0.03403 0.03398 0.00005 0.15 4 2 4 38.6 310.18 19.94 0.03517 0.03515 0.00002 0.07 4 2 5 38.6 320.17 19.95 0.03639 0.03631 0.00008 0.22 4 5 / 38.2 280.15 20.00 0.03164 0.03166 -0.00002 -0.08 4 3 2 38.2 290.15 20.00 0.03282 0.03283 -0.00001 -0.03 4 3 3 38.2 300.15 20.00 0.03405 0.03399 0.00006 0.17 4 3 4 38.2 310.15 20.00 0.03532 0.03516 0.00016 0.46 4 3 5 38.2 320.15 20.00 0.03655 0.03632 0.00023 0.62 4 4 1 38.8 309.83 17.81 0.0352 0.03509 0.00011 0.30 4 4 2 38.8 299.75 17.77 0.0339 0.03392 -0.00002 -0.06 4 </ J 38.8 280.13 17.94 0.0316 0.03163 -0.00003 -0.11 4 4 4 38.8 290.02 17.88 0.0328 0.03279 0.00001 0.04 4 5 7 38.5 280.02 19.97 0.03208 0.03164 0.00044 1.40 4 5 2 38.5 290.00 19.99 0.03312 0.03280 0.00032 0.98 4 5 3 38.5 300.01 19.96 0.03419 0.03397 0.00022 0.66 4 5 4 38.5 310.01 19.98 0.03528 0.03513 0.00015 0.43 4 5 5 38.5 320.00 19.99 0.03647 0.03629 0.00018 0.49

""Values in italics are compared with extrapolated predicted values.

70
Figures 28a and 28b plot the relative differences of X and X(Tm, p) versus Tm for materials 1 and

4, respectively. The plot character represents the laboratory and horizontal solid lines indicate

the cut-off bounds for the (expanded) uncertainty levels for each SRM: ± 3 % for material 1 and

± 1.3 % for material 4. Figure 27a reveals that the relative differences for the multi-temperature

data from laboratories 2, 3, 4, and 5 are entirely within the uncertainty levels (± 3 %) for

material 1 . As was the case for the fixed-temperature replicate data, the multi-temperature data

from laboratory 1 was considered sufficiently different (+8.2 % to 12.7 %) from the certification

values to warrant rejection as outlying data and, therefore, are excluded from the plot. It is interesting to note that the slopes for most of the laboratories are positive indicating an

increasing difference from the certified values at lower temperatures. The change in slope for

laboratory 5 at 300 K indicates a temperature interaction. In general, the agreement among these

laboratories over the temperature range of 280 K to 320 K is quite encouraging.

Figure 28b reveals that the relative differences for the multi-temperature data from laboratories

2, 3, 4, and 5 are entirely within the uncertainty levels (± 1.3 %) for the certified temperature

limit of 285 K to 310 K for material 4 (SRM 1453). For laboratory 5, one data point at 280 K is marginally outside if the uncertainty limits are extrapolated. For laboratory 1 , one data point at 290 K is outside the uncertainty limits. The two extreme points for laboratory 1 at 280 K and

320 K are outside if the uncertainty limits are extrapolated. The values at 280 K and 290 K for

laboratory 1 are considered sufficiently different from all other data points on the plot to warrant

rejection as outlying data. Further examination of the slopes reveals that there is a change in

slope (most notably for laboratories 4 and 5) indicating a temperature interaction at lower

temperatures. A final conclusion of Figure 28b is that the differences among the laboratories are affected substantially as the mean temperature decreases from room-temperature conditions.

Again, the agreement among these laboratories, for most of the data over the temperature range

of 280 K to 320 K, is quite encouraging.

8. 5 Comparison with Standard Test Method Precision Indices

At mean temperatures other than room temperature, both ISO 8302 [2] and ASTM C 177 [3]

provide statements of uncertainty (precision) statements that range from ± 3 % to ± 5 %. This

section evaluates the question: Are the differences among laboratories from 280 K to 320 K

significant in comparison with accepted uncertainty and precision statements of the standard test methods for guarded-hot-plate apparatus [2,3]? Further examination of Figure 26, and excluding

the outlying data identified in Table 24, yields the ranges summarized in Table 26.

TABLE 26 - Relative Ranges from Figure 26 Excluding Outlying Data Identified in Table 24

Material 1 Material 2 Material 3 Material 4 Minimum (%)

Maximum (%)

Range (%)

-3.7

-0.6

3.1

-1.8 + 1.3

3.1

-1.1

+2.1

3.2

-1.1 +0.9

1.0

The corresponding half-ranges for materials 1, 2, 3, and 4 are ± 1.6 %, ± 1.6 %, ± 1.6 %, and

±0.5 %, respectively, which are all less than the ISO/ASTM uncertainty (precision) statements

of±3%to±5%.

71
Material 1

Q.

CL

, E

<<<

c<

CL

r<

5.0

4.0

3.0

2.0

1.0

0.0

-1.0

-2.0

-3.0

-4.0

-5.0

280.0

5.0

4.0

3.0

2.0

1.0

0.0

-1.0

-2.0

-3.0

-4.0

-5.0

280.0

Character = Laboratory

,— Uncertainty Limits

290.0

290.0

300.0

TJK)

Material 4

310.0 320.0

Expanded Uncertainty Limits (k=2)

300.0

T„(K)

310.0 320.0

Figure 28. Relative deviations from certified values versus Tm (Materials 1 , 4)

72
9 Conclusions and Recommendations

This international comparison investigated the variability in thermal conductivity results among

guarded hot plate laboratories in Canada, France, Japan, United Kingdom, and United States

using four national reference materials provided by the participants. The four national reference

materials were SRM 1451 (fibrous-glass blanket), IRMM-440 (resin-bonded glass fibre board),

JTCCM "candidate" high-density fibrous glass board, and SRM 1453 (expanded polystyrene

board). The goal of the comparison was to assess effects of three primary factors - laboratory,

material; and, temperature - on the measurement results. The test plan addressed three primary

objectives:

1) Characterize the sample of specimens distributed to the participants;

2) Quantify the level of variability of replicate measurements at 297.15 K (24 °C); and,

3) Quantify the effect of temperature over the range from 280 K to 320 K.

The underlying causes for the behavior of the data was investigated using a cause-and-effect

diagram that identified 19 (secondary) laboratory factors that may have caused the variation in

the test results. The 19 factors were examined individually and collectively using graphical

analysis, correlation analysis, and analysis of variance (ANOVA).

9. 1 Results

The results from the comparison are summarized as follows.

• The thermal conductivity test data (Figures 4 and 5) indicates that there is a laboratory-to- laboratory difference for each of the materials (except material 4, SRM 1453).

• As expected (and as designed in), there is a material-to-material difference. Material 1, SRM

1451, was the highest thermal conductivity; material 2, IRMM-440, was the lowest. This

material-to-material difference was greater than the laboratory-to-laboratory difference.

• The laboratory effect changed from material to material; that is, there is a material-laboratory

interaction (Figures 4 and 5).

• The materials differed with respect to variability (Table 12c): material 4 (SRM 1453) was the

least variable, followed by material 2 (IRMM-440); material 3 (JTCCM "candidate"); and,

material 1 (SRM 1451).

• The dominant factor affecting the laboratory results was procedural in nature. In particular, a

significant location and variation shift was experienced by a laboratory that affixed

temperature sensors directly to the specimen surface as opposed to permanent sensors affixed

to the apparatus plates. This result is in agreement with test results from a previous

interlaboratory comparison of guarded hot plate apparatus [15].

• Two fixed temperature (297.15 K) replicate data sets were identified as outlying (laboratory 1, material 1 (SRM 1451) and laboratory 4, material 3 (JTCCM "candidate"). These outliers were respectively identified by 1) comparison with the certified values for SRM 1451; and.

2) laboratory notes indicating a specimen (of material 3) failure (i.e., delamination).

73
If the two outlying data sets of the fixed temperature (297.15 K) replicate data are excluded

(for reasons noted above), the maximum differences (Table 21) among the laboratories are

1.8 %, 2.7 %, 1.9 %, and 0.69 % for SRM 1451, JTCCM "candidate", IRMM-440; and, SRM

1453, respectively.

The results of the multi-temperature (280 K to 320 K) data (Table 24) were consistent with

the results observed for the fixed-temperature (297.15 K) replicate data. In addition, the

results indicated that disagreement among the laboratories tended to increase as mean

temperatures decreased from room-temperature (297.15 K) conditions.

The five laboratories may each be affected differently by the various 19 within-laboratory

factors identified herein. The heretofore-presented graphical and statistical analyses are meant to serve as a diagnostic foundation for further perusing by the participants.

9.2 Recommendations

Recommendations are provided for guidance in conducting future interlaboratory comparisons,

international or otherwise, as follows.

• Future comparisons of guarded hot plate laboratories should:

1) Begin planning the interlaboratory comparison with a cause-and-effect diagram. Identify

as many of the laboratory factors that differ from laboratory-to-laboratory; and, minimize,

by all means possible, the effects of these (secondary) laboratory factors.

2) In preparing the experimental design, consider the tradeoffs for replicate data at fixed

temperature(s) versus single-point data at multiple temperatures. If possible, obtain

replicate data at temperatures other than 297.15 K (24 °C).

3) Specify in the scope the purpose of the comparison, for example, 1) to assess the clarity of

a particular test method; 2) to maintain a periodic check of a group of laboratories; 3) to develop precision and bias statements; etc.

4) Develop an unambiguous test protocol that requires reporting of test data with official test forms. Specify the number of decimal points to be reported for each parameter. Specify

whether the bulk density is to be reported for the meter area or entire specimen.

5) Using the cause-and-effect diagram (Step 1, above) specify what auxiliary information

should be reported, for example, conditioning environment, additional information on

apparatus in-situ thickness measurement, etc.

6) Investigate different material types using a balanced number of levels for bulk density for

each material type. In anticipation of future comparisons, begin a tracking system to identify new national and regional reference materials.

74
7) If possible, include additional laboratories (although this will result in increased test time

and additional burdens for the coordinating organization).

8) Attempt, if possible, to reduce the cumulative time of the comparison. (Can this 5 -year

effort (initiation-to-final report) be shortened?)

The relevant task groups that revise standard test methods for guarded hot plates (ISO 8302

[2] and ASTM C 177 [3]) should:

1) Avoid (or minimize) vagueness in their respective test methods. Standardize the usage of

statistical terms in ISO 8302 and ASTM C 177.

2) Develop, as stand-alone documents, standard practices for conducting an interlaboratory

comparison with information specific to guarded-hot-plate apparatus. These practices

should include standard test protocols, forms for reporting data (including expanded

uncertainties (£/)), and ancillary information (such as test equipment, etc.). Note that the

statistical terminology should be consistent among standard bodies.

3) Specifically, clarify a) the criteria for establishing settling and equilibrium time for taking

data so that such information may be standardized; b) the procedure for the measurement

of surface temperatures (i.e., when an alternate technique may or may not be utilized);

and, c) definition for heat flux.

In regard to future test materials and matters of equivalence, future international comparisons

should be conducted by including either SRM 1453 or IRMM-440.

10. Acknowledgements

The authors gratefully acknowledge the efforts of Dr. Eric S. Lagergren who developed the test plan utilized in this comparison. We also appreciate the cooperation, openness, professionalism,

and hard work of the three material characterization laboratories: Japan Testing Center for

Construction Materials, National Institute of Standards and Technology, and the National

Physical Laboratory; and, the five participating laboratories: Japan Testing Center for

Construction Materials, Laboratoire National d'Essais, National Institute of Standards and

Technology, National Physical Laboratory, and National Research Council Canada. The authors

appreciate the donation of one material (IRMM-440) by the European Commission Institute for

Reference Materials and Measurements.

11. References

1. McCaa, D. J. "Standard Reference Materials: C 518 Heat Flow Meter," Standard Reference

Materials: Issues and Concerns for the Future, ASTM C-16 Workshop, New Orleans,

Louisiana (1996).

75
2. ISO 8302. "Thermal Insulation - Determination of Steady-State Areal Thermal Resistance

and Related Properties - Guarded Hot Plate Apparatus," International Organization for

Standardization

.

3. ASTM C 177. "Standard Test Method for Steady-State Heat Flux Measurements and

Thermal Transmission Properties by Means of the Guarded Hot Plate Apparatus," Annual

Book ofASTMStandards, Vol. 04.06.

4. Youden W.J. "The Collaborative Test," NBS Special Publication 300 - Volume 1 (1 969).

5. Youden W.J. "Ranking Laboratories by Round-Robin Test," NBS Special Publication 300 -

Volume 1 (1969).

6. Smith, D. R. "Thermal Conductivity of Fibrous Glass Board by Guarded Hot Plates and Heat

Flow Meters: An International Round-Robin," International Journal of Thermophysics (18):

1557-1573(1997).

7. Salmon, David, Silberstein Anne, and Kumar Kumaran, "Report on Inter-Laboratory

Comparison of Guarded Hot Plate Measurements," Journal of Thermal Insulation and

Building Envelopes, (18):289-300 (1995).

8. Zarr, R. R., Kumaran, M. K., Lagergren, E. S., "NIST/NRC-Canada Interlaboratory

Comparison of Guarded Hot Plate Measurements: 1993-1997," NISTIR 6087 (1997).

9. Hust, J.G. "Standard Reference Materials: Glass Fiberblanket SRM for Thermal Resistance,"

NBS Special Publication 260-103 (1985).

10. Quin, S. Venuti, G., DePonte, F., and A. Lamberty. "Certification of a Resin-Bonded Glass

Fibre Board for Thermal Conductivity between -10 °C and +50 °C," EUR 19572 EN.

11. Zarr, R.R., Davis, M.W., and Anderson, E.H. "Room-Temperature Thermal Conductivity of

Expanded Polystyrene Board for a Standard Reference Material," NISTIR 5838 (1996).

12. ISO Guide 30. (1992).

13. ISO. "Guide to the Expression of Uncertainty in Measurement," ISO (1993).

14. ASTM C 1043. "Standard Practice for Guarded-Hot-Plate Design Using Circular Line-Heat

Sources," Annual Book oj'ASTM Standards, Vol. 04.06.

15. Robinson H. E., and Watson, T. W. "Interlaboratory Comparison of Thermal Conductivity

Determinations With Guarded Hot Plates," ASTM STP 119, pp. 36-44 (1951).

16. Snedecor, George W., and Cochran, William G. Statistical Methods, 6

th Edition, Iowa State

University Press, Ames, Iowa, USA (1967).

17. Mendenhall, W., and Sinchich, T. Statistics for Engineering and the Sciences, 3

r Edition , Dellen Publishing Company, San Francisco, California, USA (1992).

76
Appendix A - Participants' Addresses

1) Japan Testing Center for Construction Materials (JTCCM)

Attn: Masayoshi Uezono

Physical Testing Section Central Laboratory

5-21-20, Inari, Soka, Saitama, Japan 340

2) Laboratoire National d'Essais (LNE)

Attn: Gianni Venuti

Departement Energie et Metrologie Thermique

5, Avenue Enrico Fermi

F-78190 Trappes, France

3) National Physical Laboratory (NPL)

Attn: David Salmon

Thermophysical Properties Section

CBTM, Building 16

Queens Road, Teddington, Middlesex, UK TW1 1 OLW

4) National Institute of Standards and Technology (NIST)

Attn: Robert Zarr

100 Bureau Drive, MS 8632

Building 226, Room B 320

Gaithersburg, MD 20899-8632 USA

5) National Research Council Canada (NRCC)

Attn: Dr. M. K. Kumaran

M-24 chemin Montreal Road

Ottawa, Ontario K1A0R6 Canada

6) European Commission - Joint Research Centre

Institute for Reference Materials and Measurements (IRMM)

Attn: Dr. Jean Pauwels

Retieseweg, B-2440 GEEL, Belgium

77
Appendix B - Test Protocols

Protocol for Suppliers of Materials

1) For each material, measure each pair of specimens at a mean temperature of Tm = 24 °C and

temperature difference of AT = 20 K.

2) Send 1 pair of each material to the participants. Send test results by letter carrier to the

address below.

Protocol for Participants

1) Conduct all tests with a single operator.

2) For all 4 materials, one material at a time, conduct 5 independent replicate measurements at a mean temperature of Tm = 24 °C and temperature difference of AT = 20 K.

Note - The replicate measurements are intended to be independent measurements (i.e., capture

within-laboratory variability by including typical laboratory/apparatus noise factors). Therefore, the

specimen should be removed from the apparatus before proceeding with the next test and conditioned.

All pertinent parameters should be fixed as close as possible for each test and the tests should be

completed in the shortest time period possible.

3) For all 4 materials, one material at a time, conduct a series of 5 tests at the following mean

temperatures: 280 K, 290 K, 300 K, 310 K, 320 K; each test at a temperature difference of

AT = 20 K.

Note - These tests are not independent, but should be conducted in a random order. 4) For SRM 1451, compress the low-density, glass fiber blanket insulation (13 kg/m3

) to a test thickness of 25.4 mm using rigid spacer stops to limit plate separation. For the other test materials:

a) limit the pressure exerted on the specimens by the measuring equipment to 1 000 Pa to 2000 Pa; and,

b) use, when necessary, appropriate spacers to avoid any creep.

5) For each measurement, estimate the relative expanded uncertainty (coverage factor, k = 2), see the ISO Guide to the Expression Uncertainty in Measurement, International Organization

for Standardization, Geneva, Switzerland, 1993.

Note - Estimates for relative expanded uncertainty at the same coverage factor (k = 2) are important

in order to establish consistent error bars in plotting the data. 6) Complete the appropriate test report for the material tested and when all the measurements

have been completed return all test reports by letter carrier to: NIST

Attn: Robert R. Zarr

Building 226, Room B320

Gaithersburg, MD 20899 USA

Note - Test data will be checked initially for consistency (i.e., no missing data, etc.) by R.

Zarr and subsequently forwarded to Dr. James J. Filliben for analysis.

Questions?, call or contact Robert R. Zarr, (301)-975-6436, fax: (301)-975-5433, or e-mail:

rzarr@nist.gov

78
Appendix C

MATERIAL CHARACTERIZATION REPORT FORM

INTERNATIONAL INTERLABORATORY COMPARISON

Date:

(To be completed ONLY by supplier of material)

Instructions: The preferred units are indicated. You may use other units, but you must specify

the units. Return one form for each material measured. The letters a and b refer to the pair of

specimens tested. Follow the test procedure from either ASTM Test Method C 177 or ISO 8302.

Report variations in test procedure, if any.

Laboratory Name:

Material:

Specimen Characteristics:

1 2 3 4 5

Sent to: a b a b a b a b a b

ID#

m(g)

x (mm)

y (mm)

L (mm)

p (kg m"

J

)

Specimen Data (297 K, AT = 20 K, 5 pairs):

1 2 3 4 5

Th (K)

Tc(K)

Q(W)

L (mm)

A(mz

) MWm-'K"1 )

Comments:

Do you correct specimen thickness for thermal expansion? (circle one)

Do you correct meter area for thermal expansion? (circle one)

Describe plate material, coating or paint, and emittance:

Other (over, or include separate sheet, if necessary):

[Y/N]

[Y/N]

79
Appendix D

TEST REPORT FORM

INTERNATIONAL INTERLABORATORY COMPARISON

Date:

Instructions: The preferred units are indicated. You may use other units, but you must specify

the units. Return one form for each material measured. The letters a and b refer to the pair of

specimens tested. Follow the test procedure from either ASTM Test Method C 177 or ISO 8302.

Report variations in test procedure, if any.

Laboratory Name:

Material:

Specimen Characteristics:

Mass (g):

Size, if circular - average diameter (mm):

if not circular - average length (mm):

average width (mm):

Specimen test thickness, in-situ (mm):

Specimen bulk density (kg-m"

3

):

Replicate Data (297 K, AT = 20 K, 5 replicates):

1 2 3 4 5

Th (K)

TC (K)

Q(W)

L (mm)

A(m')

^(Wm'K 1 )

Temperature Data (280 K, 290 K, 300 K, 310 K, 320 K, AT = 20 K):

1 2 3 4 5

Th (K)

TC (K)

Q(W)

L (mm)

A(mz

) ^(W-m"'K"')

Tm (K)

Comments:

Do you correct specimen thickness for thermal expansion? (circle one)

Do you correct meter area for thermal expansion? (circle one)

Describe plate material, coating or paint, and emittance:

80

[Y/N]

[Y/N]
Appendix E - Postscript

Update After Completion Of Analysis Of Data

On August 8, 2001, several of the guarded hot plate laboratory participants met in Cambridge,

Massachusetts, USA (in conjunction with the 26 International Thermal Conductivity

Conference/ 14

th International Thermal Expansion Symposium) to discuss the analysis of the data

in this report, as well as future activities.

With regards to the analysis of the data, a request was prepared for additional information from

Laboratory 1, focusing, in particular, on the measurement of specimen thickness and the

certification status of material 3. In response, Laboratory 1 indicated that in-situ (or as-tested)

measurement of thickness is difficult and that the thickness (/) used for specimen density was the same as the thickness (L) used for the test. In addition, Laboratory 1 indicated that their existing

apparatus is old and control is problematic and, therefore, a new guarded-hot-plate apparatus is currently under construction. Information on material 3 indicated that material has now been

treated with a surface coating.

With regards to future activities, one of the outcomes of the meeting was the recommendation

that future comparisons be conducted as "key comparisons" currently coordinated under the

umbrella of the Bureau International des Poids et Mesures (BIPM) as part of the international

Mutual Recognition Agreement (MRA). David Salmon from the National Physical Laboratory

agreed to pursue the activity. As a direct result of this inquiry, the Consultative Committee for

Thermometry (under the BIPM) established a new Working Group 9 on Thermophysical

Properties. Further interactions with this working group are anticipated.

81



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