Engineering Statistics Handbook Episode 3 Part 8 pot

2. Measurement Process Characterization
2.3. Calibration
2.3.4. Catalog of calibration designs
2.3.4.1. Mass weights
2.3.4.1.1.Design for 1,1,1
Design 1,1,1
OBSERVATIONS 1 1 1
Y(1) + -
Y(2) + -
Y(3) + -
RESTRAINT +
CHECK STANDARD +
DEGREES OF FREEDOM = 1
SOLUTION MATRIX
DIVISOR = 3
OBSERVATIONS 1 1 1
Y(1) 0 -2 -1
Y(2) 0 -1 -2
Y(3) 0 1 -1
R* 3 3 3
R* = value of reference weight
2.3.4.1.1. Design for 1,1,1
(1 of 2) [5/1/2006 10:11:46 AM]
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
1 1 1
1 0.0000 +
1 0.8165 +
1 0.8165 +
2 1.4142 + +

1 0.8165 +
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT FACTOR
1 1 1
1 0.0000 +
1 1.4142 +
1 1.4142 +
2 2.4495 + +
1 1.4142 +
Explanation of notation and interpretation of tables
2.3.4.1.1. Design for 1,1,1
(2 of 2) [5/1/2006 10:11:46 AM]
Y(6) 0 0 2 -2
R* 4 4 4 4
R* = sum of two reference standards
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
K1 1 1 1 1
1 0.3536 +
1 0.3536 +
1 0.6124 +
1 0.6124 +
0 0.7071 + -

FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT FACTOR
K2 1 1 1 1
1 0.7071 +
1 0.7071 +
1 1.2247 +

1 1.2247 +
0 1.4141 + -
Explanation of notation and interpretation of tables
2.3.4.1.2. Design for 1,1,1,1
(2 of 2) [5/1/2006 10:11:46 AM]
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 +
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 +
2.3.4.1.3. Design for 1,1,1,1,1
(2 of 3) [5/1/2006 10:11:46 AM]
1 1.2247 +
2 2.0000 + +
3 2.7386 + + +
0 1.4142 + -

2 2.0000 + +
3 2.7386 + + +
1 1.2247 +
Explanation of notation and interpretation of tables
2.3.4.1.3. Design for 1,1,1,1,1
(3 of 3) [5/1/2006 10:11:46 AM]
DIVISOR = 8
OBSERVATIONS 1 1 1 1 1 1
Y(1) 1 -1 0 0 0 0
Y(2) 1 0 -1 0 0 0
Y(3) 1 0 0 -1 0 0
Y(4) 1 0 0 0 -1 0

Y(5) 2 1 1 1 1 0
Y(6) 0 1 -1 0 0 0
Y(7) 0 1 0 -1 0 0
Y(8) 0 1 0 0 -1 0
Y(9) 1 2 1 1 1 0
Y(10) 0 0 1 -1 0 0
Y(11) 0 0 1 0 -1 0
Y(12) 1 1 2 1 1 0
Y(13) 0 0 0 1 -1 0
Y(14) 1 1 1 2 1 0
Y(15) 1 1 1 1 2 0
R* 6 6 6 6 6 6
R* = sum of two reference standards
FACTORS FOR COMPUTING REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
1 1 1 1 1 1
1 0.2887 +
1 0.2887 +
1 0.5000 +
1 0.5000 +
1 0.5000 +
1 0.5000 +
2 0.8165 + +
3 1.1180 + + +
4 1.4142 + + + +
1 0.5000 +
FACTORS FOR COMPUTING BETWEEN-DAY STANDARD DEVIATIONS
WT FACTOR
1 1 1 1 1 1
1 0.7071 +

1 0.7071 +
1 1.2247 +
2.3.4.1.4. Design for 1,1,1,1,1,1
(2 of 3) [5/1/2006 10:11:46 AM]
1 1.2247 +
1 1.2247 +
1 1.2247 +
2 2.0000 + +
3 2.7386 + + +
4 3.4641 + + + +
1 1.2247 +
Explanation of notation and interpretation of tables
2.3.4.1.4. Design for 1,1,1,1,1,1
(3 of 3) [5/1/2006 10:11:46 AM]
Y(4) 0 1 0 -1
Y(5) 0 1 -1 0
Y(6) 0 0 1 -1
R* 4 2 2 2
R* = value of the reference standard
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
2 1 1 1
2 0.0000 +
1 0.5000 +
1 0.5000 +
1 0.5000 +
2 0.7071 + +
3 0.8660 + + +
1 0.5000 +
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS

WT FACTOR
2 1 1 1
2 0.0000 +
1 1.1180 +
1 1.1180 +
1 1.1180 +
2 1.7321 + +
3 2.2913 + + +
1 1.1180 +
Explanation of notation and interpretation of tables
2.3.4.1.5. Design for 2,1,1,1
(2 of 2) [5/1/2006 10:11:46 AM]
Y(1) 47 -3 -44 66 11
Y(2) 25 -25 0 -55 55
Y(3) 3 -47 44 -11 -66
Y(4) 25 -25 0 0 0
Y(5) 29 4 -33 -33 22
Y(6) 29 4 -33 22 -33
Y(7) 7 -18 11 -44 -44
Y(8) 4 29 -33 -33 22
Y(9) 4 29 -33 22 -33
Y(10) -18 7 11 -44 -44
R* 110 110 55 55 55
R* = sum of three reference standards
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
2 2 1 1 1
2 0.2710 +
2 0.2710 +
1 0.3347 +

1 0.4382 +
1 0.4382 +
2 0.6066 + +
3 0.5367 + + +
1 0.4382 +
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT FACTOR
2 2 1 1 1
2 0.8246 +
2 0.8246 +
1 0.8485 +
1 1.0583 +
1 1.0583 +
2 1.5748 + +
3 1.6971 + + +
1 1.0583 +
Explanation of notation and interpretation of tables
2.3.4.1.6. Design for 2,2,1,1,1
(2 of 3) [5/1/2006 10:11:47 AM]
2.3.4.1.6. Design for 2,2,1,1,1
(3 of 3) [5/1/2006 10:11:47 AM]
Y(3) -2 2 -6 -1 -1
Y(4) 2 -2 -2 -3 -3
Y(5) -2 2 -2 -3 -3
Y(6) 0 0 4 -2 -2
Y(7) 0 0 0 8 -8
R* 8 8 8 4 4
R* = sum of the two reference standards
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR

2 2 2 1 1
2 0.3536 +
2 0.3536 +
2 0.6124 +
1 0.5863 +
1 0.5863 +
2 0.6124 + +
4 1.0000 + + +
1 0.5863 +
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT FACTOR
2 2 2 1 1
2 0.7071 +
2 0.7071 +
2 1.2247 +
1 1.0607 +
1 1.0607 +
2 1.5811 + +
4 2.2361 + + +
1 1.0607 +
Explanation of notation and interpretation of tables
2.3.4.1.7. Design for 2,2,2,1,1
(2 of 2) [5/1/2006 10:11:47 AM]
Y(2) 15 -8 -8 1 21 1
Y(3) 5 -12 -12 19 -1 -1
Y(4) 0 2 12 -14 -14 -14
Y(5) 0 12 2 -14 -14 -14
Y(6) -5 8 -12 9 -11 -1
Y(7) 5 12 -8 -9 1 11
Y(8) 0 10 -10 0 10 -10

R* 35 14 14 7 7 7
R* = sum of the four reference standards
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
5 2 2 1 1 1
5 0.3273 +
2 0.3854 +
2 0.3854 +
1 0.4326 +
1 0.4645 +
1 0.4645 +
1 0.4645 +
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT FACTOR
5 2 2 1 1 1
5 1.0000 +
2 0.8718 +
2 0.8718 +
1 0.9165 +
1 1.0198 +
1 1.0198 +
1 1.0198 +
Explanation of notation and interpretation of tables
2.3.4.1.8. Design for 5,2,2,1,1,1
(2 of 2) [5/1/2006 10:11:47 AM]
Y(1) 12 0 0 -12 0 0
0
Y(2) 6 -4 -4 2 -12 3
3
Y(3) 6 -4 -4 2 3 -12

3
Y(4) 6 -4 -4 2 3 3
-12
Y(5) -6 28 -32 10 -6 -6
-6
Y(6) -6 -32 28 10 -6 -6
-6
Y(7) 6 8 8 -22 -6 -6
-6
Y(8) 0 0 0 0 15 -15
0
Y(9) 0 0 0 0 15 0
-15
Y(10) 0 0 0 0 0 15
-15
R* 30 12 12 6 6 6
6
R* = sum of the four reference standards
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
5 2 2 1 1 1 1
5 0.3162 +
2 0.7303 +
2 0.7303 +
1 0.4830 +
1 0.4472 +
1 0.4472 +
1 0.4472 +
2 0.5477 + +
3 0.5477 + + +

1 0.4472 +
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
2.3.4.1.9. Design for 5,2,2,1,1,1,1
(2 of 3) [5/1/2006 10:11:47 AM]
WT FACTOR
5 2 2 1 1 1 1
5 1.0000 +
2 0.8718 +
2 0.8718 +
1 0.9165 +
1 1.0198 +
1 1.0198 +
1 1.0198 +
2 1.4697 + +
3 1.8330 + + +
1 1.0198 +
Explanation of notation and interpretation of tables
2.3.4.1.9. Design for 5,2,2,1,1,1,1
(3 of 3) [5/1/2006 10:11:47 AM]
Y(1) 100 -68 -32 119 -111 4
Y(2) 100 -68 -32 4 119 -111
Y(3) 100 -68 -32 -111 4 119
Y(4) 100 -68 -32 4 4 4
Y(5) 60 -4 -56 -108 -108 -108
Y(6) -20 124 -104 128 -102 -102
Y(7) -20 124 -104 -102 128 -102
Y(8) -20 124 -104 -102 -102 128
Y(9) -20 -60 80 -125 -125 -10
Y(10) -20 -60 80 -125 -10 -125
Y(11) -20 -60 80 -10 -125 -125

R* 460 276 184 92 92 92
R* = sum of the three reference standards
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
5 3 2 1 1 1
5 0.2331 +
3 0.2985 +
2 0.2638 +
1 0.3551 +
1 0.3551 +
1 0.3551 +
2 0.5043 + +
3 0.6203 + + +
1 0.3551 +
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT FACTOR
5 3 2 1 1 1
5 0.8660 +
3 0.8185 +
2 0.8485 +
1 1.0149 +
1 1.0149 +
1 1.0149 +
2 1.4560 + +
3 1.8083 + + +
1 1.0149 +
Explanation of notation and interpretation of tables
2.3.4.1.10. Design for 5,3,2,1,1,1
(2 of 3) [5/1/2006 10:11:47 AM]