Measurement Process Characterization_5 pot

Measurement Process Characterization2.3.. Catalog of calibration designs 2.3.4.1... Measurement Process Characterization2.3.. Catalog of calibration designs 2.3.4.1... Measurement Proces

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

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2.3.4.1.10 Design for 5,3,2,1,1,1

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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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

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