Engineering Statistics Handbook Episode 3 Part 10 potx

Definition ofmaster block and check standard At the National Institute of Standards and Technology NIST, the first two blocks in the design are NIST masters which are designated R1 and R

Definition of

master block and

check standard

At the National Institute of Standards and Technology (NIST), the first two blocks in the design are NIST masters which are

designated R1 and R2, respectively The R1 block is a steel block, and the R2 block is a chrome-carbide block If the test blocks are steel, the reference is R1; if the test blocks are chrome-carbide, the reference is R2 The check standard is always the difference

between R1 and R2 as estimated from the design and is independent of R1 and R2 The designs are listed in this section of

the catalog as:

Doiron design for 3 gauge blocks - 6 measurements

1

Doiron design for 3 gauge blocks - 9 measurements

2

Doiron design for 4 gauge blocks - 8 measurements

3

Doiron design for 4 gauge blocks - 12 measurements

4

Doiron design for 5 gauge blocks - 10 measurements

5

Doiron design for 6 gauge blocks - 12 measurements

6

Doiron design for 7 gauge blocks - 14 measurements

7

Doiron design for 8 gauge blocks - 16 measurements

8

Doiron design for 9 gauge blocks - 18 measurements

9

Doiron design for 10 gauge blocks - 20 measurements

10

Doiron design for 11 gauge blocks - 22 measurements

11

Properties of

designs that use 2

master blocks

Historical designs for gauge blocks (Cameron and Hailes) work on the assumption that the difference measurements are contaminated

by linear drift This assumption is more restrictive and covers the case of drift in successive measurements but produces fewer designs The Cameron/Hailes designs meeting this criterion allow for:

two reference (master) blocks, R1 and R2

●

check standard = difference between the two master blocks

●

and assign equal uncertainties to values of all test blocks

The designs are listed in this section of the catalog as:

Cameron-Hailes design for 2 masters + 2 test blocks

1

Cameron-Hailes design for 2 masters + 3 test blocks

2

Cameron-Hailes design for 2 masters + 4 test blocks

3

Cameron-Hailes design for 2 masters + 5 test blocks

4

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concept - check

standard

The check standards for the designs in this section are not artifact standards but constructions from the design The value of one master block or the average of two master blocks is the restraint for

the design, and values for the masters, R1 and R2, are estimated

from a set of measurements taken according to the design The

check standard value is the difference between the estimates, R1 and R2 Measurement control is exercised by comparing the current value of the check standard with its historical average

2.3.4.2 Drift-elimination designs for gauge blocks

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Y(4) 0 2 1

Y(5) 0 -1 1

Y(6) 0 -1 -2

R* 6 6 6

R* = Value of the reference standard

FACTORS FOR REPEATABILITY STANDARD DEVIATIONS NOM FACTOR

1 1 1

1 0.0000 +

1 0.5774 +

1 0.5774 +

1 0.5774 +

Explanation of notation and interpretation of tables

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Y(1) 0 -2 -1

Y(2) 0 -1 1

Y(3) 0 -1 -2

Y(4) 0 2 1

Y(5) 0 1 2

Y(6) 0 1 -1

Y(7) 0 2 1

Y(8) 0 -1 1

Y(9) 0 -1 -2

R(1) 9 9 9

FACTORS FOR COMPUTING REPEATABILITY STANDARD DEVIATIONS NOM FACTOR

1 1 1

1 0.0000 +

1 0.4714 +

1 0.4714 +

1 0.4714 +

Explanation of notation and interpretation of tables

2.3.4.2.2 Doiron 3-9 Design

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Y(6) 0 -1 -2 1

Y(7) 0 -1 -2 -3

Y(8) 0 -1 2 1

R* 8 8 8 8

R* = Value of the reference standard FACTORS FOR REPEATABILITY STANDARD DEVIATIONS NOM FACTOR 1 1 1 1 1 0.0000 +

1 0.6124 +

1 0.7071 +

1 0.6124 +

1 0.6124 +

Explanation of notation and interpretation of tables

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Y(2) 0 1 1 2

Y(3) 0 0 1 -1

Y(4) 0 2 1 1

Y(5) 0 1 -1 0

Y(6) 0 -1 0 1

Y(7) 0 -1 -2 -1

Y(8) 0 1 0 -1

Y(9) 0 -1 -1 -2

Y(10) 0 -1 1 0

Y(11) 0 1 2 1

Y(12) 0 0 -1 1

R* 6 6 6 4

R* = Value of the reference standard FACTORS FOR REPEATABILITY STANDARD DEVIATIONS NOM FACTOR 1 1 1 1 1 0.0000 +

1 0.5000 +

1 0.5000 +

1 0.5000 +

1 0.5000 +

Explanation of notation and interpretation of tables

2.3.4.2.4 Doiron 4-12 Design

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Y(4) 0 -20 5 5 15

Y(5) 0 0 -18 18 0

Y(6) 0 -10 -11 -29 -15

Y(7) 0 10 29 11 15

Y(8) 0 -20 14 -4 -30

Y(9) 0 10 11 29 15

Y(10) 0 20 -5 -5 -15

R* 90 90 90 90 90

R* = Value of the reference standard FACTORS FOR REPEATABILITY STANDARD DEVIATIONS NOM FACTOR 1 1 1 1 1 1 0.0000 +

1 0.7454 +

1 0.5676 +

1 0.5676 +

1 0.7071 +

1 0.7454 +

Explanation of notation and interpretation of tables

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Y(2) 0 -4 -24 -79 72 11

Y(3) 0 -20 -120 -35 0 55

Y(4) 0 4 24 -11 -72 79

Y(5) 0 -60 0 75 0 -15

Y(6) 0 20 120 -55 0 35

Y(7) 0 -76 -96 -61 -72 -151 Y(8) 0 64 24 4 -72 4

Y(9) 0 40 -120 -20 0 -20

Y(10) 0 72 72 72 144 72

Y(11) 0 60 0 15 0 -75

Y(12) 0 76 96 151 72 61

R* 360 360 360 360 360 360

R* = Value of the reference standard FACTORS FOR REPEATABILITY STANDARD DEVIATIONS NOM FACTOR 1 1 1 1 1 1 1 0.0000 +

1 0.6146 +

1 0.7746 +

1 0.6476 +

1 0.6325 +

1 0.6476 +

1 0.6146 +

Explanation of notation and interpretation of tables

2.3.4.2.6 Doiron 6-12 Design

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Y(1) 0 -406 -203 -203 -203 -203 -203

Y(2) 0 0 -35 -210 35 210

0 Y(3) 0 0 175 35 -175 -35

0 Y(4) 0 203 -116 29 -116 29

-261 Y(5) 0 -203 -229 -214 -264 -424 -174 Y(6) 0 0 -175 -35 175 35

0 Y(7) 0 203 -61 -221 -26 -11

29 Y(8) 0 0 305 90 130 55

-145 Y(9) 0 0 220 15 360 -160 145 Y(10) 0 203 319 174 319 174

464 Y(11) 0 -203 26 11 61 221

-29 Y(12) 0 0 -360 160 -220 -15

-145 Y(13) 0 203 264 424 229 214

174 Y(14) 0 0 -130 -55 -305 -90

145 R* 1015 1015 1015 1015 1015 1015 1015 R* = Value of the reference standard FACTORS FOR REPEATABILITY STANDARD DEVIATIONS NOM FACTOR 1 1 1 1 1 1 1 1 0.0000 +

1 0.6325 +

1 0.7841 +

1 0.6463 +

1 0.7841 +

1 0.6463 +

1 0.6761 +

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1 0.6325 +

Explanation of notation and interpretation of tables

2.3.4.2.7 Doiron 7-14 Design

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DIVISOR = 2852

OBSERVATIONS 1 1 1 1 1 1

1 1

Y(1) 0 -1392 -620 -472 -516 -976 -824 -916

Y(2) 0 60 248 -78 96 878 -112 -526

Y(3) 0 352 124 -315 278 255

864 289

Y(4) 0 516 992 470 1396 706

748 610

Y(5) 0 -356 620 35 286 -979 -96 -349

Y(6) 0 92 0 23 -138 253 -552 667

Y(7) 0 -148 -992 335 -522 -407 -104 -81

Y(8) 0 -416 372 113 190 995

16 177

Y(9) 0 308 -248 170 -648 134

756 342

Y(10) 0 472 620 955 470 585

640 663

Y(11) 0 476 -124 -191 -94 -117 -128 -703

Y(12) 0 -104 -620 -150 404 -286

4 -134

Y(13) 0 472 620 955 470 585

640 663

Y(14) 0 444 124 -292 140 508

312 956

Y(15) 0 104 620 150 -404 286 -4 134

Y(16) 0 568 -124 -168 -232 136 -680 -36

R* 2852 2852 2852 2852 2852 2852

2852 2852

R* = value of reference block

FACTORS FOR REPEATABILITY STANDARD DEVIATIONS

WT FACTOR

1 1 1 1 1 1 1 1

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1 0.0000 +

1 0.6986 +

1 0.7518 +

1 0.5787 +

1 0.6996 +

1 0.8313 +

1 0.7262 +

1 0.7534 +

1 0.6986 +

Explanation of notation and interpretation of tables

2.3.4.2.8 Doiron 8-16 Design

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SOLUTION MATRIX

DIVISOR = 8247

OBSERVATIONS 1 1 1 1 1 1

1 1 1

Y(1) 0 -3680 -2305 -2084 -1175 -1885 -1350 -1266 -654

Y(2) 0 -696 -1422 -681 -1029 -984 -2586 -849 1203

Y(3) 0 1375 -3139 196 -491 -1279 -1266 -894 -540

Y(4) 0 -909 -222 -1707 1962 -432

675 633 327

Y(5) 0 619 1004 736 -329 2771 -378 -1674 -513

Y(6) 0 -1596 -417 1140 342 303

42 186 57

Y(7) 0 955 2828 496 -401 971 -1689 -411 -525

Y(8) 0 612 966 741 1047 1434

852 2595 -1200

Y(9) 0 1175 1666 1517 3479 1756

2067 2085 1038

Y(10) 0 199 -1276 1036 -239 -3226 -801 -1191 -498

Y(11) 0 654 1194 711 1038 1209

1719 1722 2922

Y(12) 0 91 494 -65 -1394 887

504 2232 684

Y(13) 0 2084 1888 3224 1517 2188

1392 1452 711

Y(14) 0 1596 417 -1140 -342 -303 -42 -186 -57

Y(15) 0 175 950 -125 -1412 437

2238 486 681

Y(16) 0 -654 -1194 -711 -1038 -1209 -1719 -1722 -2922

Y(17) 0 -420 -2280 300 90 2250 -423 483 15

Y(18) 0 84 456 -60 -18 -450

1734 -1746 -3

R* 8247 8247 8247 8247 8247 8247

8247 8247 8247

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R* = Value of the reference standard

FACTORS FOR REPEATABILITY STANDARD DEVIATIONS

NOM FACTOR

1 1 1 1 1 1 1 1 1

1 0.0000 +

1 0.6680 +

1 0.8125 +

1 0.6252 +

1 0.6495 +

1 0.8102 +

1 0.7225 +

1 0.7235 +

1 0.5952 +

1 0.6680 +

Explanation of notation and interpretation of tables

2.3.4.2.9 Doiron 9-18 Design

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