Engineering Statistics Handbook Episode 3 Part 8 pot

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/div8 98 /handbook/ mpc/section3/mpc3416.htm (3 of 3) [5/1/2006 10:11:47 AM] 2 .3. 4.1.7 Design for 2,2,2,1,1 Y (3) Y(4) Y(5) Y(6) Y(7) R* -2 2 -2 0 0 8 2 -2 2 0 0 8 -6 -2 -2 4 0 8 -1 -3 -3 -2 8 4 R* = sum of the two reference standards -1 -3 -3 -2 -8 4 FACTORS FOR REPEATABILITY WT FACTOR 2 2 2 2 0 .35 36 + 2 0 .35 36 + 2 0.6124 + 1 0. 58 63 1 0. 58 63 2 0.6124... http://www.itl.nist.gov/div8 98 /handbook/ mpc/section3/mpc3419.htm (2 of 3) [5/1/2006 10:11:47 AM] 2 .3. 4.1.9 Design for 5,2,2,1,1,1,1 WT 5 2 2 1 1 1 1 2 3 1 FACTOR 1.0000 0 .87 18 0 .87 18 0.9165 1.01 98 1.01 98 1.01 98 1.4697 1. 83 3 0 1.01 98 5 + 2 2 1 1 1 1 + + + + + + + + + + + + Explanation of notation and interpretation of tables http://www.itl.nist.gov/div8 98 /handbook/ mpc/section3/mpc3419.htm (3 of 3) [5/1/2006 10:11:47 AM] 2 .3. 4.1.10... 3 0.2 985 + 2 0.2 6 38 + 1 0 .35 51 1 0 .35 51 1 0 .35 51 2 0.50 43 3 0.62 03 1 0 .35 51 STANDARD DEVIATIONS 1 1 1 + + + + + + + + + FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS WT FACTOR 5 3 2 1 1 1 5 0 .86 60 + 3 0 .81 85 + 2 0 .84 85 + 1 1.0149 + 1 1.0149 + 1 1.0149 + 2 1.4560 + + 3 1 .80 83 + + + 1 1.0149 + Explanation of notation and interpretation of tables http://www.itl.nist.gov/div8 98 /handbook/ mpc/section3/mpc341a.htm... 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) Y(11) R* 100 100 100 100 60 -20 -20 -20 -20 -20 -20 460 - 68 - 68 - 68 - 68 -4 124 124 124 -60 -60 -60 276 -32 -32 -32 -32 -56 -104 -104 -104 80 80 80 184 119 4 -111 4 -1 08 1 28 -102 -102 -125 -125 -10 92 -111 119 4 4 -1 08 -102 1 28 -102 -125 -10 -125 92 R* = sum of the three reference standards FACTORS FOR REPEATABILITY WT FACTOR 5 3 2 5 0. 233 1... 0 .87 18 + 1 0.9165 + 1 1.01 98 + 1 1.01 98 + 1 1.01 98 + Explanation of notation and interpretation of tables http://www.itl.nist.gov/div8 98 /handbook/ mpc/section3/mpc34 18. htm (2 of 2) [5/1/2006 10:11:47 AM] 1 -1 -14 -14 -1 11 -10 7 2 .3. 4.1.9 Design for 5,2,2,1,1,1,1 Y(1) 12 0 0 -12 0 0 Y(2) 6 -4 -4 2 -12 3 Y (3) 6 -4 -4 2 3 -12 Y(4) 6 -4 -4 2 3 3 Y(5) -6 28 -32 10 -6 -6 Y(6) -6 -32 28 10 -6 -6 Y(7) 6 8 8 -22... Y (8) R* 15 5 0 0 -5 5 0 35 -8 -12 2 12 8 12 10 14 -8 -12 12 2 -12 -8 -10 14 1 19 -14 -14 9 -9 0 7 21 -1 -14 -14 -11 1 10 7 R* = sum of the four reference standards FACTORS FOR REPEATABILITY STANDARD DEVIATIONS WT FACTOR 5 2 2 1 1 1 5 0 .32 73 + 2 0 . 38 54 + 2 0 . 38 54 + 1 0. 432 6 + 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 .87 18 + 2 0 .87 18. .. -6 Y(6) -6 -32 28 10 -6 -6 Y(7) 6 8 8 -22 -6 -6 Y (8) 0 0 0 0 15 -15 Y(9) 0 0 0 0 15 0 Y(10) 0 0 0 0 0 15 30 12 12 6 6 6 0 3 3 -12 -6 -6 -6 0 -15 -15 R* 6 R* = sum of the four reference standards FACTORS FOR REPEATABILITY STANDARD DEVIATIONS WT FACTOR 5 2 2 1 1 1 1 5 0 .31 62 + 2 0. 730 3 + 2 0. 730 3 + 1 0.4 83 0 + 1 0.4472 + 1 0.4472 + 1 0.4472 + 2 0.5477 + + 3 0.5477 + + + 1 0.4472 + FACTORS FOR BETWEEN-DAY... 1 0. 58 63 STANDARD DEVIATIONS 1 1 + + + + + + + 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. 581 1 + + 4 2. 236 1 + + + 1 1.0607 + Explanation of notation and interpretation of tables http://www.itl.nist.gov/div8 98 /handbook/ mpc/section3/mpc3417.htm (2 of 2) [5/1/2006 10:11:47 AM] 2 .3. 4.1 .8 Design for 5,2,2,1,1,1 Y(2) Y (3) Y(4)... 1.0149 + 2 1.4560 + + 3 1 .80 83 + + + 1 1.0149 + Explanation of notation and interpretation of tables http://www.itl.nist.gov/div8 98 /handbook/ mpc/section3/mpc341a.htm (2 of 3) [5/1/2006 10:11:47 AM] 4 -111 119 4 -1 08 -102 -102 1 28 -10 -125 -125 92 . 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* =. 1 0 .33 47 + 1 0. 4 38 2 + 1 0. 4 38 2 + 2 0.6066 + + 3 0. 536 7 + + + 1 0. 4 38 2 + FACTORS FOR BETWEEN-DAY STANDARD DEVIATIONS WT FACTOR 2 2 1 1 1 2 0 .82 46 + 2 0 .82 46 + 1 0 .84 85 + 1 1.05 83 + . 5,2,2,1,1,1,1 http://www.itl.nist.gov/div8 98 /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