Engineering Statistics Handbook Episode 3 Part 10 potx

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 http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc342.htm (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 http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc342.htm (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 http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3421.htm (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 http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3422.htm (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 http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3423.htm (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 http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3424.htm (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 http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3425.htm (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 http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3426.htm (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 http://www.itl.nist.gov/div898/handbook/mpc/section3/mpc3427.htm (2 of 3) [5/1/2006 10:12:01 AM] [...]... 177 Y(9) 0 756 34 2 Y (10) 0 640 6 63 Y(11) 0 -128 -7 03 Y(12) 0 4 - 134 Y( 13) 0 640 6 63 Y(14) 0 31 2 956 Y(15) 0 -4 134 Y(16) 0 -680 -36 R* 2852 2852 2852 - 139 2 -620 -472 -516 -976 60 248 -78 96 878 35 2 124 -31 5 278 255 516 992 470 139 6 706 -35 6 620 35 286 -979 92 0 23 - 138 2 53 -148 -992 33 5 -522 -407 -416 37 2 1 13 190 995 30 8 -248 170 -648 134 472 620 955 470 585 476 -124 -191 -94 -117 -104 -620 -150 404 -286... 0 504 2 232 684 Y( 13) 0 139 2 1452 711 Y(14) 0 -42 -186 -57 Y(15) 0 2 238 486 681 Y(16) 0 -1719 -1722 -2922 Y(17) 0 -4 23 4 83 15 Y(18) 0 1 734 -1746 -3 R* 8247 8247 8247 8247 1 1 1 1 1 -36 80 - 230 5 -2084 -1175 -1885 -696 -1422 -681 -102 9 -984 137 5 -31 39 196 -491 -1279 -909 -222 -1707 1962 - 432 619 100 4 736 -32 9 2771 -1596 -417 1140 34 2 30 3 955 2828 496 -401 971 612 966 741 104 7 1 434 1175 1666 1517 34 79 1756... 1 434 1175 1666 1517 34 79 1756 199 -1276 1 036 - 239 -32 26 654 1194 711 1 038 1209 91 494 -65 - 139 4 887 2084 1888 32 24 1517 2188 1596 417 -1140 -34 2 -30 3 175 950 -125 -1412 437 -654 -1194 -711 -1 038 -1209 -420 -2280 30 0 90 2250 84 456 -60 -18 -450 8247 8247 8247 8247 8247 http://www.itl.nist.gov/div898 /handbook/ mpc/section3/mpc3429.htm (2 of 3) [5/1/2006 10: 12:02 AM] 2 .3. 4.2.9 Doiron 9-18 Design R* = Value... http://www.itl.nist.gov/div898 /handbook/ mpc/section3/mpc3428.htm (3 of 3) [5/1/2006 10: 12:01 AM] 2 .3. 4.2.9 Doiron 9-18 Design SOLUTION MATRIX DIVISOR = 8247 OBSERVATIONS 1 1 1 1 Y(1) 0 - 135 0 -1266 -654 Y(2) 0 -2586 -849 12 03 Y (3) 0 -1266 -894 -540 Y(4) 0 675 633 32 7 Y(5) 0 -37 8 -1674 -5 13 Y(6) 0 42 186 57 Y(7) 0 -1689 -411 -525 Y(8) 0 852 2595 -1200 Y(9) 0 2067 2085 1 038 Y (10) 0 -801 -1191 -498 Y(11)...2 .3. 4.2.7 Doiron 7-14 Design 1 0. 632 5 + Explanation of notation and interpretation of tables http://www.itl.nist.gov/div898 /handbook/ mpc/section3/mpc3427.htm (3 of 3) [5/1/2006 10: 12:01 AM] 2 .3. 4.2.8 Doiron 8-16 Design DIVISOR = 2852 OBSERVATIONS 1 1 1 1 1 1 1 1 Y(1) 0 -824 -916 Y(2) 0 -112 -526 Y (3) 0 864 289 Y(4) 0 748 610 Y(5) 0 -96 -34 9 Y(6) 0 -552 667 Y(7) 0 -104 -81 Y(8) 0 16 177 Y(9) 0 756 34 2... 124 -292 140 508 104 620 150 -404 286 568 -124 -168 - 232 136 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 http://www.itl.nist.gov/div898 /handbook/ mpc/section3/mpc3428.htm (2 of 3) [5/1/2006 10: 12:01 AM] 2 .3. 4.2.8 Doiron 8-16 Design 1 1 1 1 1 1 1 1 1 0.0000 0.6986 0.7518 0.5787 0.6996 0. 831 3 0.7262 0.7 534 0.6986 + + + +... 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 0.7 235 + 1 0.5952 + 1 0.6680 + Explanation of notation and interpretation of tables http://www.itl.nist.gov/div898 /handbook/ mpc/section3/mpc3429.htm (3 of 3) [5/1/2006 10: 12:02 AM] . (2 of 2) [5/1/2006 10: 12:01 AM] 1 Y(1) 0 -406 -2 03 -2 03 -2 03 -2 03 -2 03 Y(2) 0 0 -35 - 210 35 210 0 Y (3) 0 0 175 35 -175 -35 0 Y(4) 0 2 03 -116 29 -116 29 -261 Y(5) 0 -2 03 -229 -214 -264. 1517 34 79 1756 2067 2085 1 038 Y (10) 0 199 -1276 1 036 - 239 -32 26 -801 -1191 -498 Y(11) 0 654 1194 711 1 038 1209 1719 1722 2922 Y(12) 0 91 494 -65 - 139 4 887 504 2 232 684 Y( 13) 0 2084 1888 32 24. 0 92 0 23 - 138 2 53 -552 667 Y(7) 0 -148 -992 33 5 -522 -407 -104 -81 Y(8) 0 -416 37 2 1 13 190 995 16 177 Y(9) 0 30 8 -248 170 -648 134 756 34 2 Y (10) 0 472 620 955 470 585 640 6 63 Y(11)