Dynamic Force Measurement:

Instrumented Charpy Impact Testing

C. M. McCowan

J. D. Splett

E. Lucon 

NISTIR 6652
 

CONTENTS 

NISTIR 6652

Dynamic Force Measurement:

Instrumented Charpy Impact Testing

C. N. McCowan 

Materials Reliability Division 

Materials Science and Engineering Laboratory 

J. D. Splett 

Statistical Engineering Division 

Information Technology Laboratory 

National Institute of Standards and Technology 

325 Broadway 

Boulder, CO 80305 

E. Lucon 

Reactor Material Research Department 

 Institute of Nuclear Material Science 

SCK•CEN (Belgian Nuclear Research Centre) 

Mol, Belgium 

January 2008

U.S. Department of Commerce 

Carlos M. Gutierrez, Secretary 

National Institute of Standards and Technology 

 James M. Turner, Acting Director 
iii 

CONTENTS 

1. SUMMARY............................................................................................................................. 1

2. BACKGROUND..................................................................................................................... 2

3. TEST PLAN............................................................................................................................ 2

3.1. OBJECTIVE.......................................................................................................................... 2 

3.2. DESIGN ............................................................................................................................... 2 

3.3. REPORTING......................................................................................................................... 3 

3.4. TESTING DETAILS............................................................................................................... 3 

3.5. PARTICIPANTS .................................................................................................................... 3 

4. RESULTS & DISCUSSION.................................................................................................. 4

4.1. MAXIMUM FORCE............................................................................................................... 4 

4.2. FORCES AT GENERAL YIELD............................................................................................. 17 

5. REFERENCES ..................................................................................................................... 27

APPENDIX A. ............................................................................................................................. 28
1 

Dynamic Force Measurement: 

Instrumented Charpy Impact Testing 

C. N. McCowana

 and J. D. Splettb 

National Institute of Standards and Technology 

325 Broadway 

Boulder, CO 80305 

E. Luconc

SCK•CEN (Belgian Nuclear Research Centre) 

Mol, Belgium

Maximum forces measured on impact reference materials in round robin testing 

are reported. These dynamic results are compared with static force calibration 

of instrumented strikers. One machine in the round robin was identified as an 

outlier by the dynamic force measurement results, indicating that dynamic testing 

may be a useful approach to check the performance of the instrumented machine 

and measurement system. Repeatability (95 %) and reproducibility limits of 0.45 

kN and 2.16 kN, respectively, were determined for the high energy specimens. 

Key Words: Charpy impact; dynamic force measurement; instrumented impact 

testing 

1. Summary 

The maximum forces measured by the machines in this round robin are in good agreement. This 

general result shows that the static force calibration of instrumented strikers is quite robust, and 

that the various striker designs evaluated here performed in a predictable manner. One machine 

in the round robin was identified as an outlier by the dynamic force measurement results, 

indicating that dynamic testing may be a useful approach to check the performance of the 

instrumented machine and measurement system. 

It is not clear if differences observed between strikers with 2 mm and 8 mm radii are of practical 

significance. More data are needed to fully evaluate this variable. 

The certified value determined for the maximum force of the low energy (LL-103) specimens is 

32.97 ±0.75 kN (±2.3 %), with an expanded uncertainty of 1.84 kN (5.6 %). The specimens 

have a 95 % uncertainty interval of ±6 %. 

 a Materials Reliability Division, Materials Science and Engineering Laboratory 

b Statistical Engineering Division, Information Technology Laboratory 

c

 Reactor Material Research Department, Institute of Nuclear Material Science 
2 

The certified value determined for the maximum force of the high energy (HH-103) specimens is 

24.06 ±0.28 kN (±1.2 %), with an expanded uncertainty of 0.70 kN (2.9 %). The specimens 

have a 95 % uncertainty interval of ±3 %. 

The precision of the maximum force measured for the HH-103 specimens is higher than that 

measured for the LL-103 measurements. The 95 % repeatability and reproducibility limits for the 

HH-103 measurements were 0.45 kN and 2.16 kN, respectively (compared with 1.90 kN and 

5.96 kN for LL-103). 

The mean general yield values for the HH-103 and LL-103 specimens were 19.60 kN and 30.84 

kN, respectively. The 95 % repeatability and reproducibility limits for the HH-103 

measurements were 2.30 kN and 3.59 kN, respectively (compared with 2.09 kN and 9.60 kN for 

LL-103). 

The low variation associated with the HH-103 specimen makes it suitable for use as a material 

for dynamic force verification. 

 

2. Background 

Instrumented strikers for impact machines are calibrated with statically applied loads, traceable 

to certified load cells. This static calibration method has been found to work quite well. 

However, in some cases it may be convenient to check the performance of the machine, striker, 

and force measurement system using a verification specimen. Currently NIST does not offer a 

certified reference material that can be used to verify the performance of an instrumented impact 

machine. 

3. Test Plan 

3.1. Objective 

The round robin was conducted primarily to evaluate the suitability of using Charpy verification 

materials as dynamic force verification materials, and to establish certified reference values for 

the maximum force measured for these two steels in an instrumented impact test. These steels 

are expected to provide dynamic force verification at two levels of maximum force (around 25 

and 30 kN). In addition, the precision of the data are evaluated in terms of repeatability and 

reproducibility according to ASTM E 691-05. 

3.2. Design 

Specimens from batches of high (HH-103) and low (LL-103) energy level Charpy V-notch 

verification specimens are tested on instrumented Charpy pendulum impact machines. The 

specimens have already been certified by NIST for absorbed energy using conventional Charpy 

pendulum impact machines. The batch sizes for these high and low energy specimens are such 

that, following this round robin, about 800 to 900 specimens can be certified as force verification 

specimens and some reserve specimens can be held for future stability testing, etc. 
3 

3.3. Reporting 

This summary report on the testing will be distributed to the participants and cited on certificates 

developed for the specimens. The summary report is public information, and participants are 

encouraged to write journal articles based on the results of the testing. 

3.4. Testing Details 

o Materials: Two steels (LL-103 low energy and HH-103 high energy)

o Specimens: Standard size ASTM E23 Charpy V-notch specimens (10 mm x 10 mm x 55 

mm)

o Anvil Geometry: The ASTM E23 or ISO 148 anvil geometry

o Striker Geometry: Testing on either 2 mm or 8 mm radius striker geometries 

o Machine Type: Testing on instrumented pendulum impact machines 

o Test Procedure: Testing conducted in accordance with ASTM E23 and ASTM work item 

WK383 (Method for Instrumented Impact Tests of Metallic Materials) or ISO 148 – 1 and 

ISO 14556

o Test Matrix: Ten specimens at each energy level tested for each striker geometry used

o Test Temperature: Room temperature

o Test Time: Test the specimens within 3 months of receiving them

 

Table 1. Materials and machines.

Materia

l 

Machine 

type 

Striker 

geometry 

(mm) 

Number of 

specimens 

Steel 1 8 10 

LL-103 

Pendulum 

2 10 

Steel 2 8 10 

HH-103 

Pendulum 

2 10 

3.5. Participants 

Table 2. Participants.

Contact Laboratory 

Wolfgang Böhme Fraunhofer Institute for Mechanics of Materials 

Harald Diem MPI University of Stuttgart 

Enrico Lucon SCK⋅CEN, Institute of Nuclear Materials 

Chris McCowan National Institute of Standards and Technology 

Václav Mentl SKODA Research 

Hans-Werner Viehrig Forschungszentrum Rossendorf 

 
4 

4. Results and Discussion 

4.1. Maximum Force 

A total of 10 specimens were tested on each of 8 Charpy machines for the force verification 

round robin. The data were evaluated from averaged force-signals according to ISO 14556 or 

ASTM WK383. The raw data from the round robin are shown in Appendix A. Two sets of ten 

verification specimens were tested with machine #8 (identified as 8a and 8b in Appendix A). 

The measurements for machine #8 were combined since there is no statistical difference between 

the averages of the two sets and no apparent trend in the data. Machine #2 and machine #8 use 

an 8 mm striker, the remaining machines all use a 2 mm striker. Figures 1 and 2 display the 

maximum force for low-energy and high-energy specimens, respectively. 

The data appear to be fairly consistent among machines, with the exception of machine #4, 

which has test results that are much lower than the rest of the data for both low and high 

energies. Since machine #4 produces consistently low values, we exclude it from further 

analyses. 

4.1.1. Striker Radius 

Figures 3 and 4 display the force data versus striker radius for low and high energies, 

respectively. 

Figures 3 and 4 indicate that striker radius may have some effect on maximum force. We 

performed a t-test to determine if the mean of the data from machines having an 8 mm striker is 

statistically different from the mean of data from machines with 2 mm strikers for each energy 

level. Based on the t-test (using the Satterthwaite method for unequal variances [1]), the 8 mm 

striker mean is statistically different from the 2 mm striker mean for both low and high energies 

(p < 0.0001). Figure 5 displays the means of each group along with error bars (twice the 

standard error of the mean, or 2 ). s n

The error bars in Figure 5 do not overlap for either low or high energy, also indicating that there 

is a significant difference between 2 mm and 8 mm striker means. In addition, the figure shows 

that the 8 mm striker means are higher than the 2 mm striker means. 

 

A t-test using combined machine data may not be the best way to examine striker differences 

because of the large sample sizes in each group. The t-test will always find a difference between 

groups if the sample sizes are large enough since the uncertainty of the mean decreases as the 

sample size increases. An alternative to the t-test is to determine if the two 8 mm striker 

machines have large influence on the consensus value [2]. If both machines with 8 mm strikers 

are highly influential, then there is evidence that there are striker differences. Table 3 lists the 

“hat” value, standardized residual, and Cook’s D for each machine and energy level. 
5 

Figure 1. Low-energy maximum force for eight machines. 

Figure 2. High-energy maximum force for eight machines. 
6 

 

Figure 3. Maximum force versus striker radius for low-energy specimens.

Figure 4. Maximum force versus striker radius for high-energy specimens. 
7 

Figure 5. Maximum force means and associated error bars (twice the standard error of the mean) for both 

low and high energy striker means. 

Table 3. Hat value, standardized residual, and Cook’s D for each machine and energy level. 

Low Energy High Energy 

Machine Hat 

Value

Std Residual Cook’s D Hat 

Value

Std 

Residual 

Cook’s 

D 

1 0.14 0.1 0.001 0.14 -1.1 0.185 

2 0.14 1.8 0.501 0.14 1.4 0.324 

3 0.14 0.8 0.011 0.14 -0.6 0.062 

5 0.14 -0.5 0.047 0.14 1.2 0.220 

6 0.14 -0.7 0.078 0.14 -0.0 0.000 

7 0.14 -1.5 0.372 0.14 -1.4 0.329 

8 0.14 0.0 0.000 0.14 0.5 0.048 

 
8 

A machine is considered influential if the hat value is greater than 0.29, or if the standardized 

residual is larger than the absolute value of 2, or if Cook’s D is larger than 0.445. None of the 

quantities listed in Table 3 exceed the guidelines for detecting influential machines, indicating 

that it may not be necessary to calculate a separate consensus value for each striker type. 

Although means for the two striker radii are statistically different for both energy levels based on 

a t-test, there is no evidence of striker differences based on an analysis of influence quantities. 

Thus, it is not clear if striker differences are of practical significance. Additional data from 

machines with 8 mm strikers would be helpful in deciphering the striker effect. For now, we will 

proceed with computing the certified reference value as if the striker radius has no effect. 

4.1.2. Certified Reference Value 

The certified reference value was determined by use of the Paule-Mandel method for computing 

a consensus value [3]. The consensus value depends on the assumption that all Charpy machines 

in the study are “good” and that no single machine is thought to produce better results than the 

others. The consensus value is a weighted mean in which the weights account for both withinmachine and between-machine variation. The certified reference value (consensus value) Y

~ is 

computed from 

i

k

i i

Yi Y

ω

∑ ω= = ~ 1 , (1) 

where k is the number of machines, ωi is the weight for the i

th machine, and Yi is the average of 

the measurements for the i

th machine. The standard uncertainty of the certified reference value is 

∑=

= k

i i

u Y

1

1 )

~

(

ω

. (2) 

The estimated weight for the i

th machine is 

2

2

1

b

i

i

i

s

n

s

+

ω = , (3) 

where 2

i s is the usual sample variance of the i

th machine, ni is the number of test results for the 

i

th machine, and 2

b s is the estimated variance between machines. The between-machine variance 

estimate is determined by an iterative procedure [3]. We used the “consensus means” command 

in a statistical analysis package called DATAPLOT [4] to compute the between-machine 

variance. Table 4 lists certified reference values, associated uncertainties, coverage factors, and 

expanded uncertainties corresponding to 95 % uncertainty intervals for low and high energy 

specimens. 
9 

Figure 6. Low-energy maximum force for final set of machines with certified reference value (middle 

line). The top and bottom horizontal lines represent the 95 % uncertainty interval for the certified value. 

 

Figure 7. High-energy maximum force for final set of machines with certified reference value (middle 

line). The top and bottom lines represent the 95 % uncertainty interval for the certified reference value. 
10 

Table 4. Certified reference values, standard uncertainty, coverage factor, and expanded uncertainty. 

Energy level 

Certified 

reference value 

(kN) 

Standard 

uncertainty (kN) Coverage factor, 

k 

Expanded 

uncertainty (kN) 

Low 33.00 0.76 2.447 1.86 

High 24.06 0.28 2.447 0.70 

The coverage factor for both low and high energy levels is based on a t-table value for 7−1=6 

degrees of freedom and a 95 % two-sided uncertainty interval. The data, certified reference 

value, and 95 % uncertainty bounds for low and high energy data are shown in Figures 6 and 7. 

We also computed the reference value for just the machines having 2 mm strikers to compare 

with the reference value based on all machines. The reference values based on just the machines 

having 2 mm strikers were lower by 2.1 % and 1.1 % for low and high energy, respectively. 

Thus, the reference value is not substantially altered by including machines with 8 mm strikers. 

4.1.3. Repeatability and Reproducibility 

The data from this round robin are also useful in estimating the precision of maximum force 

measurements. The precision is evaluated according to the terms of repeatability and 

reproducibility defined in ASTM E 691-05. The procedures in E 691 rely on the assumption that 

an equal number of measurements are taken for each machine. Thus, the second set of NIST 

measurements was not included in the analysis. Although there are only nine measurements for 

machine #3 for the high energy material, this small deviation in sample size should not 

significantly influence the results of the analysis. The raw data for the eight machines are 

displayed in Figure 1 for low-energy specimens and in Figure 2 for high-energy specimens. 

The plots of the raw data indicate that the measurements for machine #4 are not consistent with 

the remaining data. Table 5 lists summary statistics for each machine and material. The 

deviation is the difference between the individual machine mean and the grand mean for that 

material. The low-energy grand mean is 31.75 kN and the high-energy grand mean is 23.38 kN. 

Consistency statistics for each machine are listed in Table 6. The “k” consistency statistic 

represents the consistency of variation within a laboratory, while the “h” consistency statistic 

summarizes the consistency between laboratories. 

The critical values for h and k were taken from Table 5 in E 691-05 for p = 8 and n =10 . An h 

consistency statistic is considered to be significant if its absolute value is larger than 2.15. A k 

consistency statistic is considered significant if it is larger than 1.55. Plots of the consistency 

statistics and the associated critical values are shown in Figures 8 and 9. 

Figure 8 shows three machines with k values larger than the critical value, indicating that the 

within-machine variation is large compared to the other machines. Machines #2 and #3 have 

large variation for the low-energy material, while machine #6 has large variation for the highenergy material. Since no machine has significant k values for both materials, there is no reason 

to remove machines from the study based on the k statistics. 

 
11 

Table 5. Machine summary statistics. 

Low energy (LL-103) High energy (HH-103) 

Machine Mean 

(kN) 

Standard 

deviation 

(kN) 

Deviation 

 (kN) 

Mean 

(kN) 

Standard 

deviation 

(kN) 

Deviation 

(kN) 

1 33.15 0.17 1.40 23.33 0.06 -0.05 

2 36.47 1.19 4.72 25.03 0.12 1.65 

3 34.56 0.99 2.81 23.64 0.13 0.26 

4 22.90 0.20 -8.85 18.60 0.15 -4.78 

5 32.02 0.28 0.27 24.87 0.22 1.49 

6 31.72 0.61 -0.03 24.06 0.29 0.68 

7 30.24 0.20 -1.51 23.09 0.10 -0.29 

8 32.93 0.55 1.18 24.42 0.11 1.04 

Table 6. Consistency statistics for eight Charpy machines.

Machine Low energy (LL-103) High energy (HH-103) 

h k h k 

1 0.34766 0.26354 -0.0231 0.34751 

2 1.16914 1.86445 0.80543 0.71004 

3 0.69552 1.54991 0.12535 0.80409 

4 -2.19078 0.31448 -2.32847 0.91881 

5 0.06716 0.43727 0.72555 1.36436 

6 -0.00712 0.96304 0.33101 1.79579 

7 -0.37329 0.3097 -0.14263 0.61345 

8 0.29171 0.85946 0.50685 0.64934 

Figure 9 shows that the h consistency statistics are significant for machine #4 for both materials, 

indicating that the measurements for this machine are significantly different from those of the 

remaining machines relative to the between-machine variation. We will remove machine #4 

from the study since the measurements for both low and high energy materials were significantly 

lower than the rest of the measurements. 

Differences in variation between the high and low energy material, are due to differences in the 

characteristic curves for these materials. As shown in Figures 10 and 11, the data for high 

energy material, when fitted with an averaged curve, has a single maximum that defines the 

maximum force. The curve for the low energy material has a maximum point, but this value is 

likely to vary more that the high energy curve due to details of individual fracture events. 

Figures 12 and 13 display the raw data for the seven machines included in the round robin for 

low and high energy materials, respectively. 

The plots of the raw data do not indicate any inconsistencies among machines. Table 7 lists 

deviations of machine means from the grand mean for each material based on seven machines. 

The low-energy grand average is 33.01 kN and the high-energy grand average is 24.06 kN. 
12 

The critical values for h and k in Table 8 are based on 7 p = and n =10. An h consistency 

statistic is considered to be significant if its absolute value is larger than 2.05. A k consistency 

statistic is considered significant if it is larger than 1.54. Figures 14 and 15 display the 

consistency statistics from Table 8 in graphical form along with the critical values. 

Table 8 displays h and k consistency statistics based on seven machines for both low and high 

energy materials. 

Table 7. Deviations for seven machines. 

Machine 

Low 

energy 

deviatio

n (kN) 

High 

energy 

deviatio

n (kN) 

1 0.14 -0.73 

2 3.46 0.97 

3 1.55 -0.43 

5 -0.99 0.81 

6 -1.29 0.00 

7 -2.77 -0.98 

8 -0.09 0.36 

Table 8. Consistency statistics based on seven machines. 

Machine Low energy High energy 

h k h K 

1 0.06905 0.24805 -0.972 0.34371 

2 1.70392 1.75492 1.29185 0.70227 

3 0.76133 1.45886 -0.56638 0.79529 

5 -0.48921 0.41158 1.07358 1.34943 

6 -0.63703 0.90646 -0.00444 1.77614 

7 -1.36577 0.29151 -1.29861 0.60673 

8 -0.0423 0.80896 0.47601 0.64223 
13 

Figure 8. Within-laboratory consistency k statistics for eight Charpy machines. The dashed blue lines 

(left) correspond to the low energy data and the solid red lines (right) represent high energy data. 

Figure 9. Between-laboratory consistency h statistics for eight Charpy machines. The dashed blue lines 

(left) correspond to the low energy data and the solid red lines (right) represent high energy data. 
14 

Figure 10. Low energy curve showing maximum force (peak load). 

 

Figure 11. High energy curve showing maximum force at the maxima of the fitted curve (peak load). 
15 

Figure 12. Maximum force for seven Charpy machines at the low energy level. 

Figure 13. Maximum force for seven Charpy machines at the high energy level. 
16 

 

Figure 14. Within-laboratory consistency k statistics for seven Charpy machines. The dashed blue lines 

(left) correspond to the low energy data and the solid red lines (right) represent high energy data. 

Figure 15. Between-laboratory consistency h statistics for seven Charpy machines. The dashed blue lines 

(left) correspond to the low energy data and the solid red lines (right) represent high energy data. 
17 

Table 9. Precision statistics based on seven machines. 

ID 

Grand 

mean 

(kN) 

Repeatability

standard 

deviation, 

Sr (kN) 

95 % 

repeatability 

limit, 

r (kN) 

Reproducibility

standard 

deviation, 

SR (kN) 

95 % 

reproducibility

limit, 

R (kN) 

HH-108 24.06 0.16 0.45 0.77 2.16 

LL- 108 33.01 0.68 1.90 2.13 5.96 

 

The data in Figures 14 and 15 do not indicate that any machines should be removed from the 

interlaboratory comparison. Significant k statistics for machines #3 and #6 are observed for only 

one material, and there are no significant h statistics. 

Since the data from seven machines are consistent, the precision statistics for each material can 

be computed. Table 9 lists the grand mean, repeatability standard deviation, reproducibility 

standard deviation, the 95 % repeatability limit ( r 2.8S ) and the 95 % reproducibility limit 

( R 2.8S ). 

The grand mean is the unweighted average of the individual machine means and is not the same 

as the certified reference value (which is a weighted mean) discussed earlier. 

4.2. Forces at General Yield 

Forces at general yield (Fgy) are displayed in Figure 16 and 17 for low-energy and high-energy 

specimens, respectively. No results were provided for machine #4. For machine #7, forces at 

general yield were reported only for high-energy specimens; therefore, for low-energy specimens 

we have assumed that Fgy corresponds to Fm. Consequently, values of maximum force have been 

used in the analyses for machine #7 with low-energy specimens. 

The data appear to be fairly consistent among machines with the exception of machine #6, which 

provides test results much lower than the rest of the data for both low and high energies. Data 

from machine #6 are therefore excluded from further analyses. 

4.2.1. Striker Radius 

Figures 18 and 19 display data for general yield forces versus striker radius for low and high 

energies, respectively. 

In order to establish whether striker radius has an effect on force at general yield, we performed 

a t-test to determine if the mean of the data from machines with 8 mm striker is statistically 

different from the mean of data from machines with 2 mm strikers for each energy level. Based 

on the t-test (one tailed distribution, two-sample unequal variance), the 8 mm striker mean is 

statistically different from the 2 mm striker only for high energies (p < 0.0001) but not for low 
18 

Figure 16. Low-energy force at general yield Fgy for seven machines. 

Figure 17. High-energy force at general yield Fgy for seven machines. 

10

15

20

25

30

35

40

0123456789

Machine

Force at general yield (kN)

Striker radius 2 mm Striker radius 8 mm Series7

10

15

20

25

0123456789

Machine

Force at general yield (kN)

Striker radius 2 mm Striker radius 8 mm
19 

Figure 18. General yield force Fgy versus striker radius for low-energy specimens. 

16

18

20

22

24

0 1 2 3 4 5 6 7 8 9 10

Striker radius (mm)

Force at general yield (kN)

Figure 19. General yield force Fgy versus striker radius for high-energy specimens. 

25

27

29

31

33

35

37

39

0 1 2 3 4 5 6 7 8 9 10

Striker radius (mm)

Force at general yield (kN)
20 

Figure 20. Fgy means and associated error bars (twice the standard error of the mean) for both low and 

high energy striker means. 

Table 10. Machine summary statistics. 

Low energy (LL-103) High energy (HH-103) 

Machine 

Mean 

(kN) 

Standard 

deviation 

(kN) 

Deviation 

(kN) 

Mean 

(kN) 

Standard 

deviation 

(kN) 

Deviation 

(kN) 

1 32.82 0.30 4.11 17.68 0.11 -0.80 

2 36.47 1.19 7.76 19.97 0.26 1.49 

3 32.59 0.75 3.88 19.16 1.69 0.69 

5 27.77 0.50 -0.94 20.15 0.51 1.67 

6 13.24 0.20 -15.47 12.58 0.35 -5.90 

7 30.24 0.20 1.53 19.32 0.88 0.84 

8 27.83 1.00 -0.88 20.55 0.28 2.07 

18

19

20

21

22

23

24

25

26

27

28

29

30

31

32

33

012345

Energy Level/Striker Radius (mm)

Force at general yield (kN)

High/2 mm High/8 mm Low/2 mm Low/8 mm
21 

Table 11. Consistency statistics for seven Charpy machines.

Machine Low Energy (LL-103) High Energy (HH-103) 

h k h k 

1 0.54992 0.43836 -0.28914 0.03817 

2 1.03804 1.70618 0.53897 0.09479 

3 0.51876 1.07941 0.24807 0.60973 

5 -0.12555 0.71481 0.60439 0.18529 

6 -2.06867 0.28938 -2.13188 0.12614 

7 0.20490 0.28341 0.30543 0.31760 

8 -0.11740 1.43411 0.74898 0.09975 

energies (p > 0.0001). Figure 20 displays the means of each group along with error bars (twice 

the standard error of the mean, or 2 / s n ). 

The error bars in Figure 20 do not overlap for high energy, also indicating that there is a 

significant difference between 2 mm and 8 mm striker means. On the other hand, they do overlap 

for low energy, thus confirming that there is no significant difference between these means. 

4.2.2. Repeatability and Reproducibility 

The precision of general yield force measurements is evaluated according to the terms of 

repeatability and reproducibility defined in ASTM E691-05. 

For reasons already explained, the second set of NIST measurements was not included in the 

analysis. Moreover, the fact that machine #3 has only 9 measurements instead of 10, like all 

remaining machines, is considered to have negligible influence on the results of the analysis. The 

raw data for the seven machines are displayed in Figure 16 for low-energy specimens and in 

Figure 17 for high-energy specimens. 

The plots of the raw data indicate that the measurements for machine #6 are not consistent with 

the remaining data, most likely due to an incorrect interpretation of the instrumented curves. 

Table 10 lists summary statistics for each machine (including machine #6) and material. The 

low-energy grand mean is 28.71 kN and the high-energy grand mean is 18.48 kN. 

Consistency statistics for each machine are listed in Table 11. 

The critical values for h and k were taken from Table 5 in E 691-05 for p = 7 and n = 10. An h 

consistency statistics is considered significant if its absolute value is larger than 2.05. A k 

consistency statistic is considered significant if it is larger than 1.54. Plots of the consistency 

statistics and the associated critical values are shown in Figures 21 and 22. 
22 

Figure 21. Within-laboratory consistency k statistics for seven Charpy machines. 

Figure 22. Between-laboratory consistency h statistics for seven Charpy machines. 

0

0.25

0.5

0.75

1

1.25

1.5

1.75

1235678

Machine number

k

Low energy

High energy

Critical k

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

1235678

Machine number

h

Low energy

High energy

Critical h

Critical h
23 

One machine (#2) has a k value larger than the critical value for low energy, indicating that its 

within-machine variation is large compared to the other machines. Machine #8 also has a large 

variation for the low-energy material, but its k statistics remains below the critical value. Since 

none of the machines has significant k values for both materials, there is no reason to remove 

any of them from the study based on k statistics. 

The h consistency statistics are significant for machine #6 for both materials, indicating that the 

measurements for this machine are significantly different from those of the remaining machines 

relative to the between-machine variation. We will remove machine #6 from the study since the 

measurements for both low and high energy materials were significantly lower than the rest of 

the measurements. 

Figures 23 and 24 display the raw data for the six machines included in the round-robin for low 

and high energy materials, respectively. 

The plots of the raw data do not indicate any inconsistencies among machines. Table 12 lists 

deviations of machine means from the grand mean for each material based on six machines. The 

low-energy grand mean is 30.84 kN and the high-energy grand average is 19.60 kN. 

Figure 23. Force at general yield Fgy for six Charpy machines at the low energy level. 

25

30

35

40

0123456789

Machine

Force at general yield (kN)
24 

Figure 24. Force at general yield Fgy for six Charpy machines at the high energy level. 

Table 12. Deviations for six machines. 

Machine 

Low 

energy 

deviation 

(kN) 

High 

energy 

deviation 

(kN) 

1 1.98 -1.92 

2 5.63 0.37 

3 1.75 -0.44 

5 -3.07 0.55 

7 -0.60 -0.28 

8 -3.01 0.95 

17

18

19

20

21

22

23

24

0123456789

Machine

Force at general yield (kN)
25 

 

Figure 25. Within-laboratory consistency statistics for six Charpy machines. 

Figure 26. Between-laboratory consistency h statistics for six Charpy machines. 

0

0.25

0.5

0.75

1

1.25

1.5

1.75

2

2.25

123578

Machine number

k

Low energy

High energy

Critical k

-2.5

-2

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

123578

Machine number

h

Low energy

High energy

Critical h

Critical h
26 

Table 13. Consistency statistics based on six machines. 

Low energy High energy 

Machine h k h k 

1 0.59060 0.40829 0.10351 0.12875 

2 1.67808 1.58915 0.25704 0.31972 

3 0.52118 1.00537 1.65342 2.05664 

5 -0.91429 0.66578 0.50246 0.62500 

7 -0.17808 0.26397 0.86123 1.07126 

8 -0.89611 1.33574 0.27050 0.33646 

Table 13 displays h and k consistency statistics based on six machines for both low and high 

energy materials. 

The critical values for h and k in Table 13 are based on p = 6 and n = 10. An h consistency 

statistic is considered to be significant if it is larger than 1.92. A k consistency statistic is 

considered to be significant if it is larger than 1.52. Figures 25 and 26 display the consistency 

statistics from Table 13 in graphical form along with the critical values 

The data in Figure 25 and 26 do not indicate that any machines should be removed from the 

interlaboratory comparison. Significant k statistics for machines #2 and #3 are observed only for 

one material, and there are no significant h statistics. 

Since the general yield data from six machines is consistent, the precision statistics for each 

material can be computed. Table 14 lists the grand mean, repeatability standard deviation, 

reproducibility standard deviation, the 95 % repeatability limit (2.8Sr) and the 95 % 

reproducibility limit (2.8SR). 

Table 14. Precision statistics based on six machines. 

ID 

Grand 

mean 

(kN) 

Repeatability 

standard 

deviation, 

sr (kN) 

95 % 

repeatability 

limit, 

r (kN) 

reproducibility 

standard 

deviation, 

sR (kN) 

95 % 

reproducibility 

limit, 

r (kN) 

HH-103 19.60 0.82 2.30 1.28 3.59 

LL-103 30.84 0.75 2.09 3.43 9.60 
27 

5. References 

[1] F. W. Satterthwaite, An approximate distribution of estimates of variance components, 

Biometrics Bulletin, 2: 110-114; 1948. 

[2] C. M. Wang and H. K. Iyer, Detection of influential observations in the determination of the 

weighted-mean KCRV, Metrologia, 42: 262-265; 2005. 

[3] R. C. Paule and J. Mandel, Consensus values and weighting factors, NIST Journal of 

Research, 87 (5): 303-308; 1982. 

[4] N. A. Heckert and J. J. Filliben, DATAPLOT reference manual, volume I: Commands, 

NIST Handbook 148; 2003. 
28 

Appendix A. Raw Data from Force Verification Round Robin 

Machine Test 

Number 

Fm (kN) 

Low 

Energy 

Fm (kN) 

High Energy 

1 1 33.12 23.39 

1 2 33.14 23.44 

1 3 33.03 23.32 

1 4 33.06 23.31 

1 5 33.31 23.38 

1 6 33.07 23.24 

1 7 32.89 23.30 

1 8 33.11 23.32 

 1 9 33.36 23.30 

1 10 33.44 23.33 

2 1 36.65 25.06 

2 2 37.58 25.16 

2 3 37.00 24.93 

2 4 38.32 24.90 

2 5 35.72 24.96 

2 6 37.17 24.96 

2 7 35.89 25.07 

2 8 34.00 25.00 

2 9 36.05 25.02 

2 10 36.33 25.28 

3 1 34.90 23.60 

3 2 34.81 23.52 

3 3 34.96 23.68 

3 4 34.21 23.68 

3 5 33.60 23.91 

3 6 33.42 23.46 

3 7 35.30 23.64 

3 8 35.01 23.70 

3 9 33.06 23.55 

3 10 36.31 

4 1 22.90 18.50 

4 2 22.70 18.30 

4 3 22.70 18.50 

4 4 23.20 18.60 

4 5 22.70 18.60 

4 6 23.00 18.60 

4 7 22.70 18.60 

4 8 23.00 18.80 

4 9 23.20 18.70 

4 10 22.90 18.80 

5 1 31.70 24.40 

5 2 31.90 24.90 

5 3 32.20 24.70 

5 4 31.90 25.10 

5 5 32.20 24.90 

Machine Test 

Number 

Fm (kN) 

Low 

Energy 

Fm (kN) 

High Energy 

5 6 31.90 25.10 

5 7 32.60 24.90 

5 8 32.20 25.10 

5 9 31.90 24.70 

5 10 31.70 24.90 

6 1 31.90 24.30 

6 2 31.80 24.50 

6 3 32.80 24.50 

6 4 31.40 24.10 

6 5 32.10 23.90 

6 6 31.20 23.80 

6 7 30.70 23.70 

6 8 32.30 23.90 

6 9 31.80 23.80 

6 10 31.20 24.10 

7 1 30.42 23.30 

7 2 30.24 23.10 

7 3 30.09 23.02 

7 4 30.40 23.11 

7 5 30.25 23.03 

7 6 30.57 22.94 

7 7 30.07 23.06 

7 8 30.25 23.19 

7 9 30.25 23.10 

7 10 29.88 23.06 

8a 1 33.35 24.40 

8a 2 33.14 24.43 

8a 3 32.69 24.47 

8a 4 33.40 24.44 

8a 5 33.23 24.50 

8a 6 32.26 24.48 

8a 7 33.53 24.15 

8a 8 33.20 24.50 

8a 9 32.59 24.48 

8a 10 31.88 24.36 

8b 1 32.54 24.23 

8b 2 33.84 24.51 

8b 3 32.82 24.52 

8b 4 32.79 24.41 

8b 5 33.64 24.51 

8b 6 31.75 24.36 

8b 7 33.45 24.40 

8b 8 33.79 24.56 

8b 9 32.26 24.55 

8b 10 33.79 24.44