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 measurements1.
Doiron design for 3 gauge blocks - 9 measurements2.
Doiron design for 4 gauge blocks - 8 measurements3.
Doiron design for 4 gauge blocks - 12 measurements4.
Doiron design for 5 gauge blocks - 10 measurements5.
Doiron design for 6 gauge blocks - 12 measurements6.
Doiron design for 7 gauge blocks - 14 measurements7.
Doiron design for 8 gauge blocks - 16 measurements8.
Doiron design for 9 gauge blocks - 18 measurements9.
Doiron design for 10 gauge blocks - 20 measurements10.
Doiron design for 11 gauge blocks - 22 measurements11.
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 blocks1.
Cameron-Hailes design for 2 masters + 3 test blocks2.
Cameron-Hailes design for 2 masters + 4 test blocks3.
Cameron-Hailes design for 2 masters + 5 test blocks4.
2.3.4.2. Drift-elimination designs for gauge blocks
(3 of 4) [5/1/2006 10:12:00 AM]
Important
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
(4 of 4) [5/1/2006 10:12:00 AM]
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
2.3.4.2.1. Doiron 3-6 Design
(2 of 2) [5/1/2006 10:12:00 AM]
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
(2 of 2) [5/1/2006 10:12:00 AM]
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
2.3.4.2.3. Doiron 4-8 Design
(2 of 2) [5/1/2006 10:12:00 AM]
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
(2 of 2) [5/1/2006 10:12:00 AM]
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
2.3.4.2.5. Doiron 5-10 Design
(2 of 2) [5/1/2006 10:12:01 AM]
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
(2 of 2) [5/1/2006 10:12:01 AM]
1
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 +
2.3.4.2.7. Doiron 7-14 Design
(2 of 3) [5/1/2006 10:12:01 AM]
1 0.6325 +

Explanation of notation and interpretation of tables
2.3.4.2.7. Doiron 7-14 Design
(3 of 3) [5/1/2006 10:12:01 AM]
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
2.3.4.2.8. Doiron 8-16 Design
(2 of 3) [5/1/2006 10:12:01 AM]
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
(3 of 3) [5/1/2006 10:12:01 AM]
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
2.3.4.2.9. Doiron 9-18 Design
(2 of 3) [5/1/2006 10:12:02 AM]
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
(3 of 3) [5/1/2006 10:12:02 AM]