1.1...2-1 1.2...2-2 1.3...2-2 2.1...2-3 2.2...2-3 2.3...2-8 3.1...2-11 3.2...2-12 3.3...2-15 3.4...2-16 3.5...2-17 4.1...2-19 4.2...2-19 4.3...2-22 4.4...2-24 4.5...2-26 4.6...2-28 5.1...2-29 5.2...2-32 5.3...2-38
6.1...2-42 6.2...2-45 6.3 ACI...2-47 7.1...2-53 7.2...2-56...2-59...2-60
1.1 ISO 30 30 20 40 10 1 40 40 10% 8 10% 40 720 7 20 8 90 4 1 2 3 2-1
4 4 EXCEL 1.2 4M statistical quality control SQC SQC 1 2 3 4 5 6 1.3 5 1 2 3 4 5 2-2
1 2 3 2.1 100% ( ) ( purposive sampling random sampling 1 2 1 2 (sample size) 3 4 2.2 (random number) 2-3
16 16 0.0010.002 1.000 2.2.1 10 09 [1] 5 3 1.0 9 10 15 5 9 8 3 2 9 0 0 4 6 3 2 1 0 3 2. 3 1000 0.598 0.329 0.004 0.632 0.103 2.2.2 1ASTM D3665 [ ] 0.0010.002 1.0001000 [2] 1 ASTM D3665 5 1 110 10 3 2 3 141 1 2-4
2 14 1 5 0.348 0.311 0.232 0.797 2.2.3 0.0011.000 [3] 5 (1) CASIO fx-991 CASIO fx-3600p INV (RAN#) 5 5 0.887 0.213 0.768 0.533 0.022 (2) CASIO fx-4500p CASIO fx-5500l SHIFT (RAN#) EXE 5 5 0.879 0.229 0.807 0.400 0.681 2-5
1 0 1 2 3 4 5 6 7 8 9 1 0.272 0.519 0.098 0.459 1.000 0.554 0.250 0.246 0.736 0.432 2 0.994 0.978 0.693 0.593 0.690 0.028 0.831 0.319 0.073 0.268 3 0.039 0.449 0.737 0.501 0.960 0.254 0.239 0.474 0.031 0.720 4 0.144 0.695 0.339 0.621 0.128 0.032 0.413 0.617 0.764 0.257 5 0.312 0.138 0.670 0.894 0.682 0.061 0.832 0.765 0.226 0.745 6 0.871 0.838 0.595 0.576 0.096 0.581 0.245 0.786 0.412 0.867 7 0.783 0.874 0.795 0.430 0.265 0.059 0.260 0.563 0.632 0.394 8 0.358 0.424 0.684 0.074 0.019 0.345 0.618 0.176 0.352 0.748 9 0.494 0.839 0.337 0.325 0.669 0.083 0.043 0.809 0.981 0.499 10 0.642 0.514 0.297 0.869 0.744 0.824 0.524 0.656 0.608 0.408 11 0.485 0.240 0.292 0.335 0.088 0.589 0.127 0.396 0.401 0.407 12 0.728 0.819 0.557 0.050 0.152 0.816 0.404 0.079 0.703 0.493 13 0.029 0.262 0.558 0.159 0.767 0.175 0.979 0.521 0.781 0.843 14 0.918 0.348 0.311 0.232 0.797 0.921 0.995 0.225 0.397 0.356 15 0.641 0.013 0.780 0.478 0.529 0.520 0.093 0.426 0.323 0.504 16 0.208 0.468 0.045 0.798 0.065 0.315 0.318 0.742 0.597 0.080 17 0.346 0.429 0.537 0.469 0.697 0.124 0.541 0.525 0.281 0.962 18 0.900 0.206 0.539 0.308 0.480 0.293 0.448 0.010 0.836 0.233 19 0.228 0.369 0.513 0.762 0.952 0.856 0.574 0.158 0.689 0.579 20 0.746 0.170 0.974 0.306 0.145 0.139 0.417 0.195 0.338 0.901 21 0.363 0.103 0.931 0.389 0.199 0.488 0.915 0.067 0.878 0.640 22 0.663 0.942 0.278 0.785 0.638 0.002 0.989 0.462 0.927 0.186 23 0.545 0.185 0.054 0.198 0.717 0.247 0.913 0.975 0.555 0.559 24 0.360 0.349 0.569 0.910 0.420 0.492 0.914 0.115 0.881 0.452 25 0.789 0.815 0.464 0.484 0.020 0.007 0.547 0.941 0.365 0.261 26 0.279 0.609 0.086 0.852 0.890 0.108 0.076 0.089 0.662 0.607 27 0.680 0.235 0.706 0.827 0.572 0.769 0.310 0.036 0.329 0.477 28 0.078 0.444 0.178 0.651 0.423 0.672 0.571 0.660 0.657 0.972 29 0.676 0.830 0.531 0.888 0.305 0.421 0.307 0.502 0.112 0.808 30 0.861 0.899 0.643 0.771 0.037 0.241 0.582 0.578 0.634 0.077 31 0.111 0.364 0.970 0.669 0.548 0.687 0.639 0.510 0.105 0.549 32 0.289 0.857 0.948 0.980 0.132 0.094 0.298 0.870 0.309 0.441 33 0.961 0.893 0.392 0.377 0.864 0.472 0.009 0.946 0.766 0.287 34 0.637 0.986 0.753 0.566 0.213 0.807 0.017 0.460 0.515 0.630 35 0.834 0.121 0.255 0.453 0.376 0.583 0.422 0.371 0.399 0.366 36 0.284 0.490 0.402 0.151 0.044 0.436 0.747 0.694 0.136 0.585 37 0.038 0.814 0.594 0.911 0.324 0.322 0.895 0.411 0.160 0.367 38 0.351 0.283 0.027 0.220 0.685 0.527 0.943 0.556 0.853 0.612 39 0.143 0.384 0.645 0.479 0.489 0.052 0.187 0.990 0.912 0.750 40 0.512 0.056 0.018 0.122 0.303 0.803 0.553 0.729 0.205 0.925 41 0.296 0.705 0.156 0.616 0.534 0.168 0.564 0.866 0.739 0.850 42 0.451 0.536 0.768 0.513 0.481 0.880 0.835 0.734 0.427 0.847 43 0.837 0.405 0.591 0.370 0.104 0.848 0.004 0.414 0.354 0.707 44 0.724 0.153 0.841 0.829 0.470 0.391 0.388 0.163 0.817 0.790 45 0.665 0.825 0.671 0.623 0.770 0.400 0.068 0.440 0.019 0.944 46 0.573 0.716 0.266 0.456 0.434 0.467 0.603 0.169 0.721 0.779 47 0.332 0.702 0.300 0.570 0.945 0.968 0.649 0.097 0.118 0.242 48 0.755 0.951 0.937 0.550 0.879 0.162 0.791 0.810 0.625 0.674 49 0.439 0.491 0.855 0.446 0.773 0.542 0.416 0.350 0.957 0.419 50 0.700 0.877 0.442 0.286 0.526 0.071 0.154 0.988 0.333 0.626 2-6 ASTM D3665
1 0 1 2 3 4 5 6 7 8 9 51 0.523 0.613 0.752 0.733 0.528 0.072 0.820 0.929 0.777 0.461 52 0.905 0.182 0.567 0.249 0.227 0.229 0.604 0.304 0.217 0.142 53 0.373 0.120 0.602 0.793 0.692 0.863 0.954 0.873 0.107 0.675 54 0.057 0.953 0.041 0.090 0.223 0.508 0.806 0.438 0.203 0.586 55 0.967 0.040 0.708 0.271 0.189 0.342 0.740 0.801 0.985 0.263 56 0.917 0.715 0.758 0.005 0.666 0.599 0.934 0.100 0.987 0.085 57 0.131 0.646 0.659 0.047 0.051 0.562 0.435 0.731 0.362 0.317 58 0.326 0.605 0.443 0.601 0.386 0.560 0.378 0.172 0.445 0.636 59 0.299 0.106 0.237 0.732 0.796 0.476 0.099 0.804 0.735 0.950 60 0.101 0.055 0.776 0.686 0.171 0.533 0.936 0.095 0.982 0.211 61 0.267 0.598 0.754 0.658 0.274 0.215 0.177 0.218 0.330 0.628 62 0.471 0.102 0.454 0.568 0.963 0.357 0.882 0.507 0.157 0.580 63 0.535 0.881 0.014 0.966 0.958 0.190 0.180 0.759 0.433 0.355 64 0.277 0.458 0.295 0.196 0.772 0.148 0.466 0.291 0.688 0.046 65 0.719 0.167 0.181 0.653 0.328 0.070 0.015 0.155 0.631 0.063 66 0.385 0.858 0.713 0.883 0.916 0.084 0.561 0.999 0.379 0.668 67 0.862 0.928 0.822 0.812 0.977 0.395 0.788 0.920 0.673 0.698 68 0.486 0.938 0.757 0.749 0.991 0.219 0.264 0.932 0.898 0.006 69 0.091 0.872 0.959 0.922 0.727 0.811 0.075 0.374 0.133 0.730 70 0.146 0.482 0.930 0.611 0.179 0.011 0.248 0.886 0.344 0.926 71 0.709 0.184 0.390 0.409 0.191 0.117 0.860 0.135 0.406 0.134 72 0.996 0.896 0.760 0.347 0.053 0.372 0.193 0.756 0.565 0.914 73 0.971 0.859 0.147 0.114 0.418 0.889 0.792 0.064 0.652 0.288 74 0.202 0.538 0.026 0.949 0.696 0.008 0.846 0.259 0.415 0.425 75 0.212 0.321 0.778 0.940 0.496 0.231 0.664 0.903 0.473 0.909 76 0.207 0.799 0.487 0.022 0.813 0.891 0.500 0.368 0.725 0.437 77 0.818 0.503 0.906 0.224 0.904 0.892 0.455 0.343 0.924 0.197 78 0.701 0.984 0.174 0.141 0.704 0.908 0.048 0.828 0.997 0.058 79 0.035 0.380 0.001 0.381 0.251 0.497 0.214 0.794 0.552 0.588 80 0.221 0.200 0.587 0.353 0.584 0.270 0.885 0.110 0.956 0.711 81 0.647 0.403 0.530 0.738 0.280 0.457 0.650 0.276 0.661 0.973 82 0.667 0.722 0.327 0.723 0.410 0.635 0.012 0.907 0.316 0.677 83 0.644 0.590 0.021 0.269 0.042 0.062 0.387 0.183 0.964 0.544 84 0.302 0.123 0.116 0.282 0.851 0.256 0.648 0.845 0.782 0.993 85 0.633 0.933 0.331 0.546 0.842 0.016 0.236 0.164 0.923 0.976 86 0.060 0.681 0.683 0.755 0.624 0.955 0.126 0.655 0.919 0.113 87 0.165 0.532 0.431 0.341 0.092 0.244 0.222 0.336 0.034 0.216 88 0.875 0.691 0.383 0.382 0.596 0.301 0.275 0.188 0.868 0.805 89 0.726 0.902 0.252 0.130 0.238 0.398 0.763 0.463 0.615 0.140 90 0.273 0.393 0.285 0.161 0.619 0.865 0.551 0.030 0.571 0.258 91 0.253 0.821 0.600 0.023 0.606 0.849 0.610 0.577 0.082 0.774 92 0.340 0.654 0.173 0.495 0.498 0.992 0.192 0.506 0.751 0.129 93 0.194 0.290 0.592 0.983 0.509 0.998 0.522 0.627 0.741 0.540 94 0.166 0.450 0.210 0.204 0.840 0.826 0.833 0.516 0.965 0.375 95 0.712 0.314 0.033 0.823 0.629 0.939 0.887 0.066 0.743 0.081 96 0.622 0.800 0.710 0.575 0.678 0.465 0.802 0.969 0.150 0.784 97 0.313 0.294 0.897 0.718 0.614 0.876 0.025 0.049 0.620 0.125 98 0.137 0.087 0.003 0.483 0.201 0.209 0.320 0.935 0.447 0.787 99 0.243 0.679 0.844 0.069 0.024 0.543 0.714 0.234 0.505 0.428 100 0.361 0.359 0.230 0.761 0.334 0.149 0.511 0.475 0.854 0.119 2-7 ASTM D3665
2.3 sample unit 320m 3 80 320m 3 3 2.3.1 (simple random sampling) 2.2 [4] 320m 3 4 80 1 1 4 [2] 0.348 0.311 0.232 0.797 2 80 2 2 (1) (2) (3) (4) No. (1) (2) 1 80 0.348 27.8 28 2 80 0.311 24.8 25 3 80 0.232 18.5 19 4 80 0.797 63.7 64 2.3.2 2-8
stratified random sampling sublot [5] 320m 3 4 80 1 4 80/420 2 1 4 ( [2] ) 0.348 0.311 0.232 0.797 3 3 3 (1) (2) (3) (4) (5) No. (1) (2) (3)+(4) 1 20 0.348 6.9 0 7 2 20 0.311 6.2 20 27 3 20 0.232 4.6 40 45 4 20 0.797 15.9 60 76 2.3.3 (systematic random sampling) [6] 320m 3 4 80 1 2-9
80/420 2 1 0.348 3 20 0.1366.97 4 20 4 4 No. 1 20 0.348 7 2 720 27 3 2720 47 4 4720 67 3 1 1 3 ( ) 2-10
3.1 ( ) 5 28 fc 210 kgf/cm 2 2 28 CNS 3090[ ] 2 test result 5 312No.17 173No.9 30 173~312 2-11
5 (kgf/cm 2 ) (1) (2) (3) (4) (5) (6) No. 1 2 1 95.7.1 P5-1 260 249 255 2 95.7.1 P5-2 246 260 253 3 95.7.2 P7-1 255 272 264 4 95.7.2 P7-2 305 290 298 5 95.7.3 P3-1 294 275 285 6 95.7.3 P3-2 266 278 272 7 95.7.4 P4-1 224 242 233 8 95.7.4 P4-1 225 204 215 9 95.7.5 P6-1 177 169 173 10 95.7.5 P6-2 198 210 204 11 95.7.6 P1-1 209 231 220 12 95.7.6 P1-2 236 214 225 13 95.7.7 C1-1 257 243 250 14 95.7.7 C1-2 260 280 270 15 95.7.8 C1-3 226 252 239 16 95.7.8 P8-1 286 271 279 17 95.7.8 P8-2 313 310 312 18 95.7.9 P8-3 274 273 274 19 95.7.9 S3-1 243 248 246 20 95.7.10 S3-2 184 201 193 21 95.7.10 S3-3 230 207 219 22 95.7.11 S3-4 209 190 200 23 95.7.11 S3-5 241 257 249 24 95.7.13 C3-1 286 296 291 25 95.7.13 C3-2 271 246 259 26 95.7.14 W3-1 220 236 228 27 95.7.14 G6-1 272 281 277 28 95.7.14 G6-2 307 300 304 29 95.7.15 G6-3 266 258 262 30 95.7.15 G6-4 248 272 260 3.2 [7] 2-12
[7] 5 6 1 312173139 2 Sturges k13.32 log(n) 1 k n n k = 2 n30 k1+3.32 log(30)5.9 6 3 / 139/623.2 25 4 /2 1731/2172.5 5 2-13
172.525197.5 6 /2 172.5197.5/2185 7 25 25 25 6 13 8 5 6 6 4 1~3 255253264 247.5272.5 4 298 297.5322.5 5 30 1 2 3 4 5 2 9 / 100 2/30 100 6.7 2 5/30 100 16.7 2-14
6 3.3 6 3 5 18522105 (histogram) 3 3 1 2 kgf/cm 2 3 250 2-15
250 kgf/cm 2 4 210 210 kgf/cm 2 16 % 3 3.4 6 2 7 197.56.7222.523.4 XY 4 4 1 S 2 90 192309 kgf/cm 2 3 255 kgf/cm 2 4 210 kgf/cm 2 2-16
95 3.5 4 Microsoft EXCEL 5 14 27 3 EXCEL 4 XY EXCEL 3 1 EXCEL A B 1 160 0 2 185 2 3 210 5 4 235 5 5 260 10 6 285 5 7 310 3 8 335 0 2 3 B1B8 X A1A8 2-17
4 X,kgf/cm 2 Y 5 6 0 5EXCEL 1. 2-18
4.1 3 6 55 5 271 Kgf\cm 2 6 4.2 (mean) (arithmetic mean) x x,..., n 1, 2 x n 2-19
x = 1 ( x n 1 + x 2 + + 1 x ) = n n x i n i= 1 3 x = 1 x i = i1n n ( ) ( x x bar) (mu) 4 N 3 N 1 1 µ = ( x1 + x2 + + xn ) = x i N 4 N i= 1 100% () 10 10 450 N/mm 2 450 N/mm 2 [8] 5 5 255,253,264,298,285 kgf/cm 2 x (255+253+264+298+285)/5271.0 kgf/cm 2 CNS 8905[ ] x S L +1.6σ 5, x 2-20
S L A S L 40 kgf/cm 2 B S L 60 kgf/cm 2 C S L 80 kgf/cm 2 x m 255253264 2982855 3 x i 255 253 264 298 285 xm 257.3 271.6 282.3 255+253+264/3257.3 253+264+298/3271.6 264+298+285/3282.3 7 AB C 10 10 100 3 8 A B C 7 7 ABC No. A B C 1 101 96 104 2 99 98 100 3 100 100 100 4 99 99 101 5 103 101 100 6 98 99 99 7 100 102 100 8 103 99 101 9 98 103 97 10 99 103 98 100 100 100 2-21
8 A B C 1 101 96 104 2 99 98 100 3 100 100.0 100 98.0 100 101.3 4 99 99.3 99 99.0 101 100.3 5 103 100.7 101 100.0 100 100.3 6 98 100.0 99 99.7 99 100.0 7 100 100.3 102 100.7 100 99.7 8 103 100.3 99 100.0 101 100.0 9 98 100.3 103 101.3 97 99.3 10 99 100.0 103 101.7 98 98.7 100 100 100 7 4.3 (standard deviation) n x 1, x 2,..., x n n 2 ( xi x) i= 1 s = n 1 6 s 12 2-22
x i i1n x n ( ) (s) ( sigma) N 2 ( xi µ) i= 1 σ = 7 N x i i1n N 100% () s () 32 30 kgf/cm 2 30 kgf/cm 2 [ ]CNS 2579[ ] standard deviation CNS [9] 5 5 255,253,264,298,285 kgf/cm 2 x = 271 s = = 2 2 2 2 ( 255 271) + ( 253 271) + ( 264 271) + ( 298 271) + ( 285 271) 1554 4 = 388.5 = 19.7kgf/cm 2 5 1 2 2-23
9 x i x i x 2 ( x i x ) 255-16 256 253-18 324 264-7 49 298 27 729 285 14 196 1554 1554/(5-1) 388.5 388.5 = 19.7 kgf/cm 2 4.4 coefficient of variation s s V = = 100% 8 x x V s x [10] 5 5 s19.7x 271 V 19.7 = = 0.073 = 7.3% 271 10ACI 214R-02 2-24
5 1 overall variation 5 2 within-test variation precision CNS 3090 2 25 6 11 [12] 10ACI 214R-02 overall variation psi (kgf/cm 2 ) Excellent Very Good Good Fair Poor <400 400-500 500-600 600-700 >700 (<28.1) (28.1-35.2) (35.2-42.2) (42.2-49.2) (>49.2) <200 200-250 250-300 300-350 >350 (<14.1) (14.1-17.6) (17.6-21.1) (21.1-24.6) (>24.6) within-test variation % Excellent Very Good Good Fair Poor <3.0 3.0-4.0 4.0-5.0 5.0-6.0 >6.0 <2.0 2.0-3.0 3.0-4.0 4.0-5.0 >5.0 10 402-94 6530 34.2 kgf/cm 2 10 2-25
4.5 (range) R = x max x min R x max x min 9 [11] 5 x i 2 255,253, 264, 298, 285 kgf/cm xmax = 298 x = min 253 R29825345 kgf/cm 2 n10 R n10 R k Ri i= R = 1 k 10 R s = d 2 11 R i i k k10 s d 2 d 2 (n) 11 n 2-26
11 d 2 (n) d 2 2 1.128 3 1.693 4 2.059 5 2.326 6 2.534 7 2.704 8 2.847 9 2.970 10 3.078 [12] 5 10 12 x 1 x 2 R 1 260 249 11 2 246 260 14 3 255 272 17 4 305 290 15 5 294 275 19 6 266 278 12 7 224 242 18 8 225 204 21 9 177 169 8 10 198 210 12 R 147 R 147/10 14.7 d 2 11 n2 1.128 s 1 14.7/1.128 13 x 10 245 V 13/245 100% 5.3% 1 10 V 1 5.3% 5.06.0% 2-27
4.6 1 2 3 4 5 [13] 5 5 255,253,264,298,285 kgf/cm 2 CASIO fx-991 13 INV MODE SD 255 M+(x) 255 253 M+(x) 253 264 M+(x) 264 298 M+(x) 298 285 M+(x) 285 INV 6(n) 5 5 INV 7( x ) 271 INV 9(σ n 1 ) 19.71 INV 8(σ n ) 17.62 EXCEL 1 EXCEL A1A5 2 A6 AVERAGE(A1:A5)271 3 A7 STDEV(A1:A5) 19.71 EXCEL 2-28
A 1 255 2 253 3 264 4 298 5 285 6 271 AVERAGE(A1:A5) 7 19.71 STDEV(A1:A5) 5.1 3 8 normal distribution curve 8 (12) 1 x µ 1 ( ) 2 σ ( x) = e 2 f - x 2πσ 12 x e2.718281828( ) 2-29
X XN (, 2 ) 13 X 250.3 kgf/cm 2 34.2 kgf/cm 2 XN (250.3,34.2 2 ) (1) () (2) x () 9 σ σ µ 9 XN(300,20 2 ) (3) - + (4) () () a. () 10 2-30
XN(300,20 2 ) XN(320,20 2 ) 10 XN(300,20 2 )XN(320,20 2 ) b. () 11 XN(300,20 2 ) XN(300,30 2 ) 11 XN(300,20 2 )XN(300,30 2 ) (5) - + 1 x x a b Px Xx 12 a b P[260X320] 12 XN(300,20 2 ) X260320 P[260X320] 2-31
2 (6) X ~ N( µ, σ ) Z ~ N(0,1) 0 1 13 P[260X320] P[-2Z1] 13 5.2 PWL X n ( x ) (s) x P[ x X x ] b a 1 ( x ) () 2 (s) () x a b 2-32
3 x b x a 4 a b x x () x µ z = a a σ 14 x µ z = b b σ 15 5 14 -- z a z b P[ Z za ] z z a P Z z ] z [ b z b 6 P [ xa b b a X x ] = P[ Z z ] P[ Z z ] 16 P[ Z za ] (15) P [ Z z a ] = F ( z a ) = z a 1 2 π e 1 2 t 2 dt 17 F(z a ) - z a (z 0 )z<0 -z a F( za) za 1 F z ) (16) ( a a ( a F z ) = 1 F( z ) 18 2-33
F ( z ) = z 1 14 2 π e 1 2 t 2 z 0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.0 0.5000 0.5040 0.5080 0.5120 0.5160 0.5199 0.5239 0.5279 0.5319 0.5359 0.1 0.5398 0.5438 0.5478 0.5517 0.5557 0.5596 0.5636 0.5675 0.5714 0.5753 0.2 0.5793 0.5832 0.5871 0.5910 0.5948 0.5987 0.6026 0.6064 0.6103 0.6141 0.3 0.6179 0.6217 0.6255 0.6293 0.6311 0.6368 0.6406 0.6443 0.6480 0.6517 0.4 0.6554 0.6591 0.6628 0.6664 0.6700 0.6736 0.6772 0.6808 0.6844 0.6879 0.5 0.6915 0.6950 0.6985 0.7019 0.7054 0.7088 0.7123 0.7157 0.7190 0.7224 0.6 0.7257 0.7291 0.7324 0.7357 0.7389 0.7422 0.7454 0.7486 0.7517 0.7549 0.7 0.7580 0.7611 0.7642 0.7673 0.7703 0.7734 0.7764 0.7794 0.7823 0.7852 0.8 0.7881 0.7910 0.7939 0.7967 0.7995 0.8023 0.8051 0.8078 0.8106 0.8133 0.9 0.8159 0.8186 0.8212 0.8238 0.8264 0.8289 0.8315 0.8340 0.8365 0.8389 1.0 0.8413 0.8438 0.8461 0.8485 0.8508 0.8531 0.8554 0.8577 0.8599 0.8621 1.1 0.8643 0.8665 0.8686 0.8708 0.8729 0.8749 0.8770 0.8790 0.8810 0.8830 1.2 0.8849 0.8869 0.8888 0.8907 0.8925 0.8944 0.8962 0.8980 0.8997 0.9015 1.3 0.9032 0.9049 0.9066 0.9082 0.9099 0.9115 0.9131 0.9147 0.9162 0.9177 1.4 0.9192 0.9207 0.9222 0.9236 0.9251 0.9265 0.9279 0.9292 0.9306 0.9319 1.5 0.9332 0.9345 0.9357 0.9370 0.9382 0.9394 0.9406 0.9418 0.9429 0.9441 1.6 0.9452 0.9463 0.9474 0.9484 0.9495 0.9505 0.9515 0.9525 0.9535 0.9545 1.7 0.9554 0.9564 0.9573 0.9582 0.9591 0.9599 0.9608 0.9616 0.9625 0.9633 1.8 0.9641 0.9649 0.9656 0.9664 0.9671 0.9678 0.9686 0.9693 0.9699 0.9706 1.9 0.9713 0.9719 0.9726 0.9732 0.9738 0.9744 0.9750 0.9756 0.9761 0.9767 2.0 0.9772 0.9778 0.9783 0.9788 0.9793 0.9798 0.9803 0.9808 0.9812 0.9817 2.1 0.9821 0.9826 0.9830 0.9834 0.9838 0.9842 0.9846 0.9850 0.9854 0.9857 2.2 0.9861 0.9864 0.9868 0.9871 0.9875 0.9878 0.9881 0.9884 0.9887 0.9890 2.3 0.9893 0.9896 0.9898 0.9901 0.9904 0.9906 0.9909 0.9911 0.9913 0.9916 2.4 0.9918 0.9920 0.9922 0.9925 0.9927 0.9929 0.9931 0.9932 0.9934 0.9936 2.5 0.9938 0.9940 0.9941 0.9943 0.9945 0.9946 0.9948 0.9949 0.9951 0.9952 2.6 0.9953 0.9955 0.9956 0.9957 0.9959 0.9960 0.9961 0.9962 0.9963 0.9964 2.7 0.9965 0.9966 0.9967 0.9968 0.9969 0.9970 0.9971 0.9972 0.9973 0.9974 2.8 0.9974 0.9975 0.9976 0.9977 0.9977 0.9978 0.9979 0.9979 0.9980 0.9981 2.9 0.9981 0.9982 0.9982 0.9983 0.9984 0.9984 0.9985 0.9985 0.9986 0.9986 3.0 0.9987 0.9987 0.9987 0.9988 0.9988 0.9989 0.9989 0.9989 0.9990 0.9990 3.1 0.9990 0.9991 0.9991 0.9991 0.9992 0.9992 0.9992 0.9992 0.9993 0.9993 3.2 0.9993 0.9993 0.9994 0.9994 0.9994 0.9994 0.9994 0.9995 0.9995 0.9995 3.3 0.9995 0.9995 0.9995 0.9996 0.9996 0.9996 0.9996 0.9996 0.9996 0.9997 dt F(z) 0 z Z 2-34
[14] 30 5 250.3 kgf/cm 2 34.2 kgf/cm 2 x (1)Px300 (2)Px210 210 (3)P210x300 300 1 ()250.3 kgf/cm 2 ()34.2 kgf/cm 2 2 Px300 14 z(300250.3)/34.21.45 Px300 PZ1.45 14( ) Pz1.45 0.926592.65 % P[x 300] 14 P[x 300]( kgf/cm 2 ) 3 Px210 15 z(210250.3)/34.2 1.18 Px210 Pz 1.18 Pz 1.18 Pz1.18 2-35
1 Pz1.18 1Pz1.18 14( ) Pz1.18 0.8810 Pz 1.18 10.88100.119011.90 % P[x 210] 15 P[x 210]( kgf/cm 2 ) 4 P210x300 16 P210x300 Px300 Px210 0.92650.11900.807580.75 % P[210 x 300] 16 P[210 x 300]( 210 300 kgf/cm 2 ) EXCEL NORMDISTx,,, 1 x F(x)[14] NORMDIST300,250.3,34.2,1 2-36
NORMDIST210,250.3,34.2,1 NORMDIST300,250.3,34.2,1 NORMDIST210,250.3,34.2,1 0 x f(x) x150 NORMDIST150,250.3,34.2,0 EXCEL x100400x 1416 10 Y XY XY 15 14x100200 15 X x Y f(x) EXCEL 4 EXCEL 23 13 17 1 1 ( ) P[ x ] P[-1z1]20.8413-0.5 0.68260.6868 2 2 ( ) P[ 2 x 2] 2-37
P[-2z2]20.9772-0.5 0.95440.9595 3 ( ) P[ 3 x 3] P[-3z3]20.9987-0.5 0.99740.9999 0.6826 0.9544 0.9974 17 3 natural tolerance limit 99% 2 1 95%68 [15] X 2.0mm 3 tolerance limit 3 3 3 3(2.0) 6.0mm X 5000 mm 5,000 6.0mm 5.3 n x x 18 (19)(20) 2-38
µ = µ x 19 σ σ = 20 x n µ x σ x 2 X ~ N( µ, σ ) 21 σ 2 X ~ N( µ,( ) ) n 22 n σ x ( x ) 4 x x 30 2 2 X ~ N(300,( ) ) X ~ N(300,30 ) 4 2 30 2 18 X ~ N(300,30 ) 4 X ~ N(300,( ) ) 4 3 [16] 6.0mm 4 σ 2.0 ± 3 σ = ± 3 = ± 3 = ± 3. mm x n 4 0 4 3.0mm 19[15][16] 4 2-39
20 3 ±6.0 ±3.0 19 [15] [16]4 [17]CNS 3090[ ] fc -35 kgf/cm 2 3 fc fc 210 kgf/cm 2 () 30 kgf/cm 2 CNS 3090 (fcr ) 1 1% 2 (14) 0.99 z2.33 2.33( 20) 1-0.010.99Pz 2.33 0.99010.99 z2.33 z2.326 CNS 12891[ ] z2.33 3 ( 20) fcr fc -35+2.33 23 2-40
fcr 210-35+(2.33)(30)244.9245 kgf/cm 2 2.33 fcr 245 S L 175 20 S L 175, fcr 245 kgf/cm 2 4 (20) 3 σ σ = x 3 24 5 21 σ fcr fc +2.33σ x fc +2.33 fc +1.34 25 3 fcr 210+(1.34)(30)250.2250 kgf/cm 2 6 (23)(25) fcr 250 kgf/cm 2 S L 210 2.33σ x fcr 250 21 3 S L 210, fcr 250 kgf/cm 2 (23)(25) CNS 12891[ ] CNS 3090[ ] 2-41
(23)(25) 3 1 (23) fc -35(25) fc σ 2 (23) (25) x CNS 12891 30 3 (23)(25) 1%2.33 6.1 1924 Dr. Shewhart Chart 1 process control chart 6.2 CL UCL LCL 2 acceptance control chart 6.3 ACI 1 control chart for variable 6.26.3 5 2 control chart for attribute 2-42
7.2 100 (1) random causes (2) assignable causes CL 3 CL 3 ( 99%) CL 2 1% 3 22 (1) (2) (3) 2-43
UCL CL LCL UCL CL LCL UCL CL LCL 22 3 2-44
6.2 - x R Chart x R Chart n210 [18] [18] - 1 1010 2 16 2 16 16 x R No.,% x 1 x 2 x R 1 5.63 5.33 5.480 0.30 2 5.60 5.85 5.725 0.25 3 5.18 5.58 5.380 0.40 4 5.65 5.40 5.525 0.25 5 5.55 5.61 5.580 0.06 6 5.38 5.49 5.435 0.11 7 6.05 5.69 5.870 0.36 8 5.12 5.54 5.330 0.42 9 5.58 5.47 5.525 0.11 10 5.90 5.60 5.750 0.30 55.600 2.56 ( )/ 2 x = x 1 + x 2 x R max min = x 3 ( x ) (R 2-45
k 1 x = xi = 55.600 /10 = 5.56 26 k i= 1 k 1 R = R i = 2.56/10 = 0.256 27 k i= 1 k 4 56 CL = x = 5. 28 UCL = x + A R = 5.56 + ( 1.880)( 0.256) 6. 04 29 2 = LCL = x A2 R = 5.56 ( 1.880)( 0.256) = 5. 08 30 5 256 CL = R = 0. 31 UCL = D ( )( ) 4 R = = 84 32 LCL = D R ( 0)( 0.256) 0. 3 = = 33 6 23 7 22 (28)(33) A 2 D 3 D 4 17 3 17 n A 2 D 3 D 4 2 1.880 0 3.267 3 1.023 0 2.575 4 0.729 0 2.282 5 0.577 0 2.115 6 0.483 0 2.004 7 0.419 0.076 1.924 8 0.373 0.136 1.864 9 0.337 0.184 1.816 10 0.308 0.223 1.777 2-46
UCL=6.04 CL=5.56 CL=5.08 UCL=0.84 CL=0.256 23 x R 6.3 ACI ACI 214 ACI 3 [19] ACI ACI 214 CNS 3090 402-94 1 x Chart 2-47
ACI 214 fc fcr CNS 3090 fc -35 kgf/cm 2 2 x m Chart ACI 214 5 CNS 3090 3 ACI 214 fcr CNS 3090 3 fc 3 3 R m Chart 10 ACI 214 10 5% 10 Max. R m = σ 1 d 2 = ( V1 fcr') d 2 = V1 d 2 fcr' (34) m Max. R 1 fcr V 1 d 2 (n) 11 2 n2d 2 1.128 Max. R m = V1 ( 1.128) fcr' (35) V 1 10 3456% [19] 5 ACI (1) fc 210 kgf/cm 2 (2) fcr 250 kgf/cm 2 [17] 1 18 2 ACI 24 2-48
a. fc 210 kgf/cm 2 fcr 250 kgf/cm 2 S L fc 35 kgf/cm 2 175kgf/cm 2 b. fcr 250 kgf/cm 2 S L fc 210 kgf/cm 2 c. Max. R m = V1 ( 1.128) fcr' 10 fcr 250 Max. R m = V1 ( 1.128) fcr' = V1 ( 1.128)( 250) = 282 V1 V 1 V 1 Max. R m 0.03 8.5 0.04 11.3 0.05 14.1 0.06 16.9 3 18 (1)(2) 4 (3) 24 (260+249)/2255 4 5 5 2 (5) 260-24911 6 3 3 (4) 24 (255+253+264)/3257.3 710 10 (6) 24 (14+11+17+15+19+12+18+21+8+12)/1014.7 EXCEL 81 2-49
a. 1 fc -35kgf/cm 2 402-94 b. 4 fc 402-94 c. 17 1827 2-50
18ACI (1) (2) (3) (4) (5) (6) 3 10 No. x 1 x 2 x x m R R m 1 260 249 255 11 2 246 260 253 14 3 255 272 264 257.3 17 4 305 290 298 271.7 15 5 294 275 285 282.3 19 6 266 278 272 285 12 7 224 242 233 263.3 18 8 225 204 215 240 21 9 177 169 173 207 8 10 198 210 204 197.3 12 14.7 11 209 231 220 199 22 15.8 12 236 214 225 216.3 22 16.6 13 257 243 250 231.7 14 16.3 14 260 280 270 248.3 20 16.8 15 226 252 239 253 26 17.5 16 286 271 279 262.7 15 17.8 17 313 310 312 276.7 3 16.3 18 274 273 274 288.3 1 14.3 19 243 248 246 277.3 5 14.0 20 184 201 193 237.7 17 14.5 21 230 207 219 219.3 23 14.6 22 209 190 200 204 19 14.3 23 241 257 249 222.7 16 14.5 24 286 296 291 246.7 10 13.5 25 271 246 259 266.3 25 13.4 26 220 236 228 259.3 16 13.5 27 272 281 277 254.7 9 14.1 28 307 300 304 269.7 7 14.7 29 266 258 262 281 8 15.0 30 248 272 260 275.3 24 15.7 2-51
fc =210 fcr =250 fc -35=175 fc =210 fcr =250 V 1 >6% V 1 56% V 1 45% V 1 34% V 1 <3% 24ACI 2-52
7.1 7.1.1 30.0 0.1mm 2 2 gono go gauge 25 30.1mm, 29.9mm D=30.1 D=29.9 25 2-53
19 3 1 19 36 95.12.1 1 1 2 15 3 6 4 8 5 4 6 4 7 2 1 1 7.1.2 26 19 X 2727 80 3 EXCEL 28 26 2-54
27 28 7.1.3 1 n 2 d 2-55
d 3 p = 36 n 4 k n 1,n 2, n k d 1,d 2, d k p d + d +... + d 1 2 k i= 1 = = k n1 + n2... + nk ( 1 p) k i= 1 d n i i 37 p σ p = 38 n 38 7.2 p chart pn chart c chart [20][21] 1 2 [20]20 400 2-56
n d p 1 400 1 0.0025 2 400 3 0.0075 3 400 0 0 4 400 7 0.0175 5 400 2 0.005 6 400 0 0 7 400 1 0.0025 8 400 0 0 9 400 8 0.02 10 400 5 0.0125 11 400 2 0.005 12 400 0 0 13 400 1 0.0025 14 400 0 0 15 400 3 0.0075 6000 33 0.0825 1 p=d/n 2 CL 33 CL = p = = 0.0055 39 6000 0.0825 CL = p = = 0. 0055 40 15 3 UCL ( 1 p) 0.0055( 1 0.0055) p UCL = p + 3 = 0.0055 + 3 n = 0.0055 + 0.0111= 0.0166 400 41 LCL 2-57
( 1 p) 0.0055( 1 0.0055) p LCL = p 3 = 0.0055 3 n = 0.0055 0.0111= 0.0056 = 0 400 42 0 4 29 549 13 29 [21]20 400 1 CL n = 400 CL = pn = 33 15 = 2.2 43 2 UCL 2-58
p = 2.2 400 = 0.0055 UCL = pn + 3 = 2.2 + 4.4 = 6.6 pn ( 1 p) = 0.0055 + 3 2.2( 1 0.0055) 44 LCL UCL = pn 3 pn p = 2.2 4.4 = 2.2 = 0 ( 1 ) = 0.0055 3 2.2( 1 0.0055) 45 3 30 449 13 30 1. 2. 2-59
3. 4. 5. [1],2005," ", [2]," ", [3],2006," ", [4],"EXCEL ", [5],2005," ", 402-94 [6],1988," ", [7]CNS 3090," " [8]CNS 9042," " [9]CNS 12891," " [10]D.C.Montgomery,G.C.Runger and N.F. Hubele,2004,"Engineering Statistics " [11]ACI 214-02,2002,"Recommended Practice for Evaluation of Strength Test Results of Concrete" [12]ACI 318-2005,"Building Code Requirement for Reinforced Concrete" [13]ASTM D3665,"Standard Practice for Random Sampling of Construction Materials" 2-60