APMP.M.H-S3 Final Report Comparison on Hardness ... - BIPM

Revision: <strong>Final</strong> <strong>Report</strong>
Date: May 25, 2012
8. Analyzing Method of <strong>Comparison</strong> Results
The measurement results are used to compute the degree of equivalence in <strong>Comparison</strong>
Reference Value (CRV) and En ratio. The calculation is shown in following formulas:
-Calculation of <strong>Comparison</strong> Reference Value (CRV)
Pilot laboratory determined KCRV by calculating the weighted mean of
measurements of all participants (xref).
-The uncertainty of the CRV was calculated by following expression:
Where:
x = The measured value of participating institute i ( i =1,2,…,n)
-Its deviation from CRV
-The uncertainty of this deviation at a 95% level of confidence
Where u(
di
) was given by
And k = 2
Page 19 of 77
Eq. 1
Eq. 2
Eq. 3
Eq. 4
Eq. 5
-Evaluation of Coefficient En
The equivalence between the measurements of participating institutes was expressed
by coefficient E as well.
Where:
x
u
ref
2
1
( x
ref
x
1
u
2
( x ) x
1
2
2
2
1 u ( x ) 1
u ( x ) ... 1
u ( x )
) u
2
1
2
1
( x ) u
1
2
u ( x ) ... x
2
1
( x
i
u( xi
) = The standard uncertainty of i x
n
E
n
d x x
i
i
2
2
2
...
) u
ref
U ( di
) k u(
di
)
2
n
1
( x
2
2
2
u ( d ) u ( x ) u ( x
U
2
i
x x
i
( x ) U
i
ref
2
i
( x
ref
)
ref
2
u ( x )
n
)
)
n
n
Eq. 6