Measurement Process Characterization_5 pot

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]
2.3.4.1.10. Design for 5,3,2,1,1,1
(3 of 3) [5/1/2006 10:11:47 AM]
2. Measurement Process Characterization
2.3. Calibration
2.3.4. Catalog of calibration designs
2.3.4.1. Mass weights
2.3.4.1.11.Design for 5,3,2,1,1,1,1
Design 5,3,2,1,1,1,1
OBSERVATIONS 5 3 2 1 1 1 1
Y(1) + - -
Y(2) + - - -
Y(3) + - - -
Y(4) + - - - -
Y(5) + - - - -
Y(6) + - - - -
Y(7) + - - - -
Y(8) + - -
Y(9) + - -
Y(10) + - -
Y(11) + - -
RESTRAINT + + +

CHECK STANDARD +
DEGREES OF FREEDOM = 5
SOLUTION MATRIX
DIVISOR = 40
OBSERVATIONS 5 3 2 1 1 1
2.3.4.1.11. Design for 5,3,2,1,1,1,1
(1 of 3) [5/1/2006 10:11:48 AM]
1
Y(1) 20 -4 -16 12 12 12
12
Y(2) 0 -4 4 -8 -8 2
2
Y(3) 0 -4 4 2 2 -8
-8
Y(4) 0 0 0 -5 -5 -10
10
Y(5) 0 0 0 -5 -5 10
-10
Y(6) 0 0 0 -10 10 -5
-5
Y(7) 0 0 0 10 -10 -5
-5
Y(8) 0 4 -4 -12 8 3
3
Y(9) 0 4 -4 8 -12 3
3
Y(10) 0 4 -4 3 3 -12
8
Y(11) 0 4 -4 3 3 8
-12

R* 20 12 8 4 4 4
4
R* = sum of the three reference standards
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
5 3 2 1 1 1 1
5 0.5000 +
3 0.2646 +
2 0.4690 +
1 0.6557 +
1 0.6557 +
1 0.6557 +
1 0.6557 +
2 0.8485 + +
3 1.1705 + + +
4 1.3711 + + + +
2.3.4.1.11. Design for 5,3,2,1,1,1,1
(2 of 3) [5/1/2006 10:11:48 AM]
1 0.6557 +
FACTORS FOR LEVEL-2 STANDARD DEVIATIONS
WT FACTOR
5 3 2 1 1 1 1
5 0.8660 +
3 0.8185 +
2 0.8485 +
1 1.0149 +
1 1.0149 +
1 1.0149 +
1 1.0149 +
2 1.4560 + +

3 1.8083 + + +
4 2.1166 + + + +
1 1.0149 +
Explanation of notation and interpretation of tables
2.3.4.1.11. Design for 5,3,2,1,1,1,1
(3 of 3) [5/1/2006 10:11:48 AM]
2. Measurement Process Characterization
2.3. Calibration
2.3.4. Catalog of calibration designs
2.3.4.1. Mass weights
2.3.4.1.12.Design for 5,3,2,2,1,1,1
OBSERVATIONS 5 3 2 2 1 1 1
Y(1) + - -
Y(2) + - -
Y(3) + - - -
Y(4) + - - -
Y(5) + - - -
Y(6) + - -
Y(7) + - -
Y(8) + - -
Y(9) + - - -
Y(10) + -
Y(11) + -
Y(12) - +
RESTRAINT + + +
CHECK STANDARDS +
DEGREES OF FREEDOM = 6
SOLUTION MATRIX
DIVISOR = 10
OBSERVATIONS 5 3 2 2 1 1

2.3.4.1.12. Design for 5,3,2,2,1,1,1
(1 of 3) [5/1/2006 10:11:58 AM]
1
Y(1) 2 0 -2 2 0 0
0
Y(2) 0 -6 6 -4 -2 -2
-2
Y(3) 1 1 -2 0 -1 1
1
Y(4) 1 1 -2 0 1 -1
1
Y(5) 1 1 -2 0 1 1
-1
Y(6) -1 1 0 -2 -1 1
1
Y(7) -1 1 0 -2 1 -1
1
Y(8) -1 1 0 -2 1 1
-1
Y(9) 0 -2 2 2 -4 -4
-4
Y(10) 0 0 0 0 2 -2
0
Y(11) 0 0 0 0 0 2
-2
Y(12) 0 0 0 0 -2 0
2
R* 5 3 2 2 1 1
1
R* = sum of the three reference standards

FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
5 3 2 2 1 1 1
5 0.3162 +
3 0.6782 +
2 0.7483 +
2 0.6000 +
1 0.5831 +
1 0.5831 +
1 0.5831 +
3 0.8124 + +
4 1.1136 + + +
1 0.5831 +
2.3.4.1.12. Design for 5,3,2,2,1,1,1
(2 of 3) [5/1/2006 10:11:58 AM]
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT FACTOR
5 3 2 2 1 1 1
5 0.8660 +
3 0.8185 +
2 0.8485 +
2 1.0583 +
1 1.0149 +
1 1.0149 +
1 1.0149 +
3 1.5067 + +
4 1.8655 + + +
1 1.0149 +
Explanation of notation and interpretation of tables
2.3.4.1.12. Design for 5,3,2,2,1,1,1

(3 of 3) [5/1/2006 10:11:58 AM]
2. Measurement Process Characterization
2.3. Calibration
2.3.4. Catalog of calibration designs
2.3.4.1. Mass weights
2.3.4.1.13.Design for 5,4,4,3,2,2,1,1
OBSERVATIONS 5 4 4 3 2 2 1 1
Y(1) + + - - - - -
Y(2) + + - - - - -
Y(3) + - -
Y(4) + - -
Y(5) + - -
Y(6) + - -
Y(7) + - - -
Y(8) + - - -
Y(9) + - -
Y(10) + - -
Y(11) + - -
Y(12) + - -
RESTRAINT + +
CHECK STANDARD + -
DEGREES OF FREEDOM = 5
SOLUTION MATRIX
DIVISOR = 916
OBSERVATIONS 5 4 4 3 2 2
1 1
2.3.4.1.13. Design for 5,4,4,3,2,2,1,1
(1 of 3) [5/1/2006 10:11:58 AM]
Y(1) 232 325 123 8 -37 135
-1 1

Y(2) 384 151 401 108 73 105
101 -101
Y(3) 432 84 308 236 168 204
-144 144
Y(4) 608 220 196 400 440 -120
408 -408
Y(5) 280 258 30 136 58 234
-246 246
Y(6) 24 -148 68 64 -296 164
-8 8
Y(7) -104 -122 -142 28 214 -558
-118 118
Y(8) -512 -354 -382 -144 -250 -598
18 -18
Y(9) 76 -87 139 -408 55 443
51 -51
Y(10) -128 26 -210 -36 -406 194
-110 110
Y(11) -76 87 -139 -508 -55 473
-51 51
Y(12) -300 -440 -392 116 36 -676
100 -100
R* 1224 696 720 516 476 120
508 408
R* = sum of the two reference standards (for going-up
calibrations)
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
5 4 4 3 2 2 1 1
5 1.2095 +

4 0.8610 +
4 0.9246 +
3 0.9204 +
2 0.8456 +
2 1.4444 +
1 0.5975 +
1 0.5975 +
4 1.5818 + +
7 1.7620 + + +
2.3.4.1.13. Design for 5,4,4,3,2,2,1,1
(2 of 3) [5/1/2006 10:11:58 AM]
11 2.5981 + + + +
15 3.3153 + + + + +
20 4.4809 + + + + + +
0 1.1950 + -
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT FACTOR
5 4 4 3 2 2 1 1
5 2.1380 +
4 1.4679 +
4 1.4952 +
3 1.2785 +
2 1.2410 +
2 1.0170 +
1 0.7113 +
1 0.7113 +
4 1.6872 + +
7 2.4387 + + +
11 3.4641 + + + +
15 4.4981 + + + + +

20 6.2893 + + + + + +
0 1.4226 + -
Explanation of notation and interpretation of tables
2.3.4.1.13. Design for 5,4,4,3,2,2,1,1
(3 of 3) [5/1/2006 10:11:58 AM]
2. Measurement Process Characterization
2.3. Calibration
2.3.4. Catalog of calibration designs
2.3.4.1. Mass weights
2.3.4.1.14.Design for 5,5,2,2,1,1,1,1
Design 5,5,2,2,1,1,1,1
OBSERVATIONS 5 5 2 2 1 1 1 1
Y(1) + - - -
Y(2) + - - -
Y(3) + - - -
Y(4) + - - -
Y(5) + + - - - -
Y(6) + - -
Y(7) + - -
Y(8) + - -
Y(9) + - -
Y(10) + -
Y(11) + -
RESTRAINT + +
CHECK STANDARD +
DEGREES OF FREEDOM = 4
SOLUTION MATRIX
DIVISOR = 120
OBSERVATIONS 5 5 2 2 1 1
1 1

2.3.4.1.14. Design for 5,5,2,2,1,1,1,1
(1 of 3) [5/1/2006 10:11:58 AM]
Y(1) 30 -30 -12 -12 -22 -10
10 -2
Y(2) -30 30 -12 -12 -10 -22
-2 10
Y(3) 30 -30 -12 -12 10 -2
-22 -10
Y(4) -30 30 -12 -12 -2 10
-10 -22
Y(5) 0 0 6 6 -12 -12
-12 -12
Y(6) -30 30 33 -27 -36 24
-36 24
Y(7) 30 -30 33 -27 24 -36
24 -36
Y(8) 0 0 -27 33 -18 6
6 -18
Y(9) 0 0 -27 33 6 -18
-18 6
Y(10) 0 0 0 0 32 8
-32 -8
Y(11) 0 0 0 0 8 32
-8 -32
R* 60 60 24 24 12 12
12 12
R* = sum of the two reference standards
FACTORS FOR COMPUTING REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
5 5 2 2 1 1 1 1

5 0.6124 +
5 0.6124 +
2 0.5431 +
2 0.5431 +
1 0.5370 +
1 0.5370 +
1 0.5370 +
1 0.5370 +
2 0.6733 + +
4 0.8879 + + +
6 0.8446 + + + +
11 1.0432 + + + + +
16 0.8446 + + + + + +
2.3.4.1.14. Design for 5,5,2,2,1,1,1,1
(2 of 3) [5/1/2006 10:11:58 AM]
1 0.5370 +
FACTORS FOR COMPUTING LEVEL-2 STANDARD DEVIATIONS
WT FACTOR
5 5 2 2 1 1 1 1
5 0.7071 +
5 0.7071 +
2 1.0392 +
2 1.0392 +
1 1.0100 +
1 1.0100 +
1 1.0100 +
1 1.0100 +
2 1.4422 + +
4 1.8221 + + +
6 2.1726 + + + +

11 2.2847 + + + + +
16 2.1726 + + + + + +
1 1.0100 +
Explanation of notation and interpretation of tables
2.3.4.1.14. Design for 5,5,2,2,1,1,1,1
(3 of 3) [5/1/2006 10:11:58 AM]
2. Measurement Process Characterization
2.3. Calibration
2.3.4. Catalog of calibration designs
2.3.4.1. Mass weights
2.3.4.1.15.Design for 5,5,3,2,1,1,1
OBSERVATIONS 5 5 3 2 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 = 4
SOLUTION MATRIX
DIVISOR = 10
OBSERVATIONS 5 5 3 2 1 1
1
Y(1) 1 -1 -2 -3 1 1

2.3.4.1.15. Design for 5,5,3,2,1,1,1
(1 of 3) [5/1/2006 10:11:58 AM]
1
Y(2) -1 1 -2 -3 1 1
1
Y(3) 1 -1 2 -2 -1 -1
-1
Y(4) -1 1 2 -2 -1 -1
-1
Y(5) 1 -1 -1 1 -2 -2
3
Y(6) 1 -1 -1 1 -2 3
-2
Y(7) 1 -1 -1 1 3 -2
-2
Y(8) -1 1 -1 1 -2 -2
3
Y(9) -1 1 -1 1 -2 3
-2
Y(10) -1 1 -1 1 3 -2
-2
R* 5 5 3 2 1 1
1
R* = sum of the two reference standards
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT FACTOR
5 5 3 2 1 1 1
5 0.3162 +
5 0.3162 +
3 0.4690 +

2 0.5657 +
1 0.6164 +
1 0.6164 +
1 0.6164 +
3 0.7874 + +
6 0.8246 + + +
11 0.8832 + + + +
16 0.8246 + + + + +
1 0.6164 +
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT FACTOR
5 5 3 2 1 1 1
2.3.4.1.15. Design for 5,5,3,2,1,1,1
(2 of 3) [5/1/2006 10:11:58 AM]
5 0.7071 +
5 0.7071 +
3 1.0863 +
2 1.0392 +
1 1.0100 +
1 1.0100 +
1 1.0100 +
3 1.4765 + +
6 1.9287 + + +
11 2.0543 + + + +
16 1.9287 + + + + +
1 1.0100 +
Explanation of notation and interpretation of tables
2.3.4.1.15. Design for 5,5,3,2,1,1,1
(3 of 3) [5/1/2006 10:11:58 AM]
2. Measurement Process Characterization

2.3. Calibration
2.3.4. Catalog of calibration designs
2.3.4.1. Mass weights
2.3.4.1.16.Design for 1,1,1,1,1,1,1,1 weights
OBSERVATIONS 1 1 1 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) + -
Y(11) + -
Y(12) + -
RESTRAINT + +
CHECK STANDARD +

DEGREES OF FREEDOM = 5
SOLUTION MATRIX
DIVISOR = 12
OBSERVATIONS 1 1 1 1 1 1
1 1
2.3.4.1.16. Design for 1,1,1,1,1,1,1,1 weights
(1 of 3) [5/1/2006 10:11:59 AM]
Y(1) 1 -1 -6 0 0 0
0 0
Y(2) 1 -1 0 -6 0 0

0 0
Y(3) 1 -1 0 0 -6 0
0 0
Y(4) 1 -1 0 0 0 -6
0 0
Y(5) 1 -1 0 0 0 0
-6 0
Y(6) 1 -1 0 0 0 0
0 -6
Y(7) -1 1 -6 0 0 0
0 0
Y(8) -1 1 0 -6 0 0
0 0
Y(9) -1 1 0 0 -6 0
0 0
Y(10) -1 1 0 0 0 -6
0 0
Y(11) -1 1 0 0 0 0
-6 0
Y(12) -1 1 0 0 0 0
0 -6
R* 6 6 6 6 6 6
6 6
R* = sum of the two reference standards
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT K1 1 1 1 1 1 1 1 1
1 0.2887 +
1 0.2887 +
1 0.7071 +
1 0.7071 +

1 0.7071 +
1 0.7071 +
1 0.7071 +
1 0.7071 +
2 1.0000 + +
3 1.2247 + + +
4 1.4142 + + + +
5 1.5811 + + + + +
6 1.7321 + + + + + +
2.3.4.1.16. Design for 1,1,1,1,1,1,1,1 weights
(2 of 3) [5/1/2006 10:11:59 AM]
1 0.7071 +
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT K2 1 1 1 1 1 1 1 1
1 0.7071 +
1 0.7071 +
1 1.2247 +
1 1.2247 +
1 1.2247 +
1 1.2247 +
1 1.2247 +
1 1.2247 +
2 2.0000 + +
3 2.7386 + + +
4 3.4641 + + + +
5 4.1833 + + + + +
6 4.8990 + + + + + +
1 1.2247 +

Explanation of notation and interpretation of tables

2.3.4.1.16. Design for 1,1,1,1,1,1,1,1 weights
(3 of 3) [5/1/2006 10:11:59 AM]
2. Measurement Process Characterization
2.3. Calibration
2.3.4. Catalog of calibration designs
2.3.4.1. Mass weights
2.3.4.1.17.Design for 3,2,1,1,1 weights
OBSERVATIONS 3 2 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 = 25
OBSERVATIONS 3 2 1 1 1
2.3.4.1.17. Design for 3,2,1,1,1 weights
(1 of 3) [5/1/2006 10:11:59 AM]
Y(1) 3 -3 -4 1 1
Y(2) 3 -3 1 -4 1
Y(3) 3 -3 1 1 -4
Y(4) 1 -1 -3 -3 -3

Y(5) -2 2 -4 -4 1
Y(6) -2 2 -4 1 -4
Y(7) -2 2 1 -4 -4
Y(8) 0 0 5 -5 0
Y(9) 0 0 5 0 -5
Y(10) 0 0 0 5 -5
R* 15 10 5 5 5
R* = sum of the two reference standards
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT K1 3 2 1 1 1
3 0.2530 +
2 0.2530 +
1 0.4195 +
1 0.4195 +
1 0.4195 +
2 0.5514 + +
3 0.6197 + + +
1 0.4195 +
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT K2 3 2 1 1 1
3 0.7211 +
2 0.7211 +
1 1.0392 +
1 1.0392 +
1 1.0392 +
2 1.5232 + +
3 1.9287 + + +
1 1.0392 +

Explanation of notation and interpretation of tables

2.3.4.1.17. Design for 3,2,1,1,1 weights
(2 of 3) [5/1/2006 10:11:59 AM]
2.3.4.1.17. Design for 3,2,1,1,1 weights
(3 of 3) [5/1/2006 10:11:59 AM]
2. Measurement Process Characterization
2.3. Calibration
2.3.4. Catalog of calibration designs
2.3.4.1. Mass weights
2.3.4.1.18.Design for 10-and 20-pound
weights
OBSERVATIONS 1 2 2 1 1
Y(1) + -
Y(2) + -
Y(3) + - +
Y(4) + - +
Y(5) + - +
Y(6) + - +
Y(7) + -

RESTRAINT +
CHECK STANDARD +
DEGREES OF FREEDOM = 3
SOLUTION MATRIX
DIVISOR = 24
OBSERVATIONS 1 2 2 1 1
Y(1) 0 -12 -12 -16 -8
Y(2) 0 -12 -12 -8 -16
2.3.4.1.18. Design for 10-and 20-pound weights
(1 of 2) [5/1/2006 10:11:59 AM]
Y(3) 0 -9 -3 -4 4

Y(4) 0 -3 -9 4 -4
Y(5) 0 -9 -3 4 -4
Y(6) 0 -3 -9 -4 4
Y(7) 0 6 -6 0 0
R* 24 48 48 24 24
R* = Value of the reference standard
FACTORS FOR REPEATABILITY STANDARD DEVIATIONS
WT K1 1 2 2 1 1
2 0.9354 +
2 0.9354 +
1 0.8165 +
1 0.8165 +
4 1.7321 + +
5 2.3805 + + +
6 3.0000 + + + +
1 0.8165 +
FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS
WT K2 1 2 2 1 1
2 2.2361 +
2 2.2361 +
1 1.4142 +
1 1.4142 +
4 4.2426 + +
5 5.2915 + + +
6 6.3246 + + + +
1 1.4142 +
Explanation of notation and interpretation of tables
2.3.4.1.18. Design for 10-and 20-pound weights
(2 of 2) [5/1/2006 10:11:59 AM]