Engineering Statistics Handbook Episode 3 Part 8 pot

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

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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3411.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3411.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3412.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3413.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3413.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3414.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3414.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3415.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3416.htm (2 of 3) [5/1/2006 10:11:47 AM]

2.3.4.1.6 Design for 2,2,1,1,1

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3416.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3417.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3418.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3419.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3419.htm (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

http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc341a.htm (2 of 3) [5/1/2006 10:11:47 AM]