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2.
Measurement Process Characterization
2.3. Calibration 2.3.4. Catalog of calibration designs 2.3.4.1. Mass weights
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CASE 1: CHECK STANDARD = DIFFERENCE BETWEEN FIRST TWO WEIGHTS
OBSERVATIONS 1 1 1 1 1
Y(1) + -
Y(2) + -
Y(3) + -
Y(4) + -
Y(5) + -
Y(6) + -
Y(7) + -
Y(8) + -
Y(9) + -
Y(10) + -
RESTRAINT + +
CHECK STANDARD + -
DEGREES OF FREEDOM = 6
SOLUTION MATRIX
DIVISOR = 10
OBSERVATIONS 1 1 1 1 1
Y(1) 2 -2 0 0 0
Y(2) 1 -1 -3 -1 -1
Y(3) 1 -1 -1 -3 -1
Y(4) 1 -1 -1 -1 -3
Y(5) -1 1 -3 -1 -1
Y(6) -1 1 -1 -3 -1
Y(7) -1 1 -1 -1 -3
Y(8) 0 0 2 -2 0
Y(9) 0 0 2 0 -2
Y(10) 0 0 0 2 -2
R* 5 5 5 5 5
R* = sum of two reference standards
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
K1 1 1 1 1 1
1 0.3162 +
1 0.3162 +
1 0.5477 +
1 0.5477 +
1 0.5477 +
2 0.8944 + +
3 1.2247 + + +
0 0.6325 + -
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT FACTOR
K2 1 1 1 1 1
1 0.7071 +
1 0.7071 +
1 1.2247 +
1 1.2247 +
1 1.2247 +
2 2.0000 + +
3 2.7386 + + +
0 1.4142 + -
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CASE 2: CHECK STANDARD = FOURTH WEIGHT
OBSERVATIONS 1 1 1 1 1
Y(1) + -
Y(2) + -
Y(3) + -
Y(4) + -
Y(5) + -
Y(6) + -
Y(7) + -
Y(8) + -
Y(9) + -
Y(10) + -
RESTRAINT + +
CHECK STANDARD +
DEGREES OF FREEDOM = 6
SOLUTION MATRIX
DIVISOR = 10
OBSERVATIONS 1 1 1 1 1
Y(1) 2 -2 0 0 0
Y(2) 1 -1 -3 -1 -1
Y(3) 1 -1 -1 -3 -1
Y(4) 1 -1 -1 -1 -3
Y(5) -1 1 -3 -1 -1
Y(6) -1 1 -1 -3 -1
Y(7) -1 1 -1 -1 -3
Y(8) 0 0 2 -2 0
Y(9) 0 0 2 0 -2
Y(10) 0 0 0 2 -2
R* 5 5 5 5 5
R* = sum of two reference standards
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
K1 1 1 1 1 1
1 0.3162 +
1 0.3162 +
1 0.5477 +
1 0.5477 +
1 0.5477 +
2 0.8944 + +
3 1.2247 + + +
1 0.5477 +
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT FACTOR
K2 1 1 1 1 1
1 0.7071 +
1 0.7071 +
1 1.2247 +
1 1.2247 +
1 1.2247 +
2 2.0000 + +
3 2.7386 + + +
1 1.2247 +
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