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[教学]统计分析方法与应用


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市场部
2009.10.30

郭海发


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2-1

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2-2

¨D§tBMI°]A¤w¤¤\~kCCA§Q-p¤èkA §@BzCH-p¤èk°°ò~ §N°u-p~v] statistical quality control ASQC^C -p¤Rkbsy~¤w¨\Ai°êab¤@¤u{¤]¤TB |¤Q~H¤WúvA °ê¤~¨¤]í-M¨As{¤§¤¤°ê°êa ] CNS^M¤u{I¤uWd¤wv¤J-p¤èkA¤u{v-n-p¤§°ò ¤~àFC 1.3 -p¤Rb¤@¤u{~¤W¤§ ¤@¤u{M¨SxPsy~¤PA¨°ò{§¤MOüA¤@ ¤u{]A]-pBiBI¤uB¤¨¤-¤j¨BJA]¤@¤u{¤§-±~ ] Total Quality Control A TQC^Msy~¤@]A¤-¤j¨A¨C¤@q¤§~è ¨§i¨Aí-p¤èkA-zp¤UG ] 1^ ]-p¨G-qw~èB]w§÷PI¤u¤tB¤u{iaפRC ] 2^i¨GH÷B¨s§@C ] 3^ s{¨G-qws{BH÷BG¤RB¨s§@C ] 4^¨G]-p-peBC ] 5^@¨G]°jk¤RBwú@÷B¤u{iaפRC U~è¨q¤§S¤PA±¤§-p¤èkt§A-ó I¤uq¤§~AH¤i¨Ps{¨¨§@~±` ¨ì¤§-p¤èk° DC ¤GBH÷ 2.1 H÷§-z ¤u{ê°¤WA]°¨}ag¤W¤§--¨A¤à§@ 100% (G )AM± (G )C¤N] purposive sampling^PH÷] random sampling^¨A¨UuIC ] 1^NGbé (population)¤¤D[wNí ] sample A§tA§K|]¤§D[D¨¤§° ^ tAb-p~¤Wq±`¤NC ] 2^H÷GHH÷¤èé[w ¤èkA¤@¤§u ¨Mwv§Y°¤@H÷A-pü¤§\üH÷C{N ¤u{I¤uWd±`WwHH÷wCY¨Sí±piठH÷A¨pV¤gcy¤§p¤Aq±`g¤§¤u{v
2-3

w¨NíBw¤§ìmp¨úC H÷¨H¤USG (1) 餤¨C¤@-ìQ¤¤÷vPC (2) i¤j¤p (sample size)±±¨~tFUh~tU¤pA¨Yi -p¤íC (3) -pqiH¤°-pé°C ùG ¤°-p (unbiased estimate)ü-p-¤u-°°P°§C¤§÷| C (4) L{[¤-AG¨A¤OC 2.2 H÷ H÷(random number)¤SuvAUWq°¤@D±`A¨ì¤ óWh±§AB¨¤¤¨C¤@-rX{÷vC¨pGsò§Y¤@ §¤¤-±¤lA±NX{ 1¨ì6IH÷A]°¨C§YX{I±C LóWhA1¨ì6¤§X{÷vU°¤¤¤§¤@C ¤u{ê°¤WA§QH÷¨iH÷C¤u{~¤§q¤@¤¤jA ±` 0.001B0.002B… 1.000@-p¤@¤d-¨¤§¤TìH÷C 2.2.1 sH÷ ¤Q-PêyBw d¤ùAU¤§O¤W0¨ì9¤Q-rA±N ry¤J¤@eAR¤¤AH÷X¤@-n¨¤WrAAm^eA- e-z¨BJò±oq°¤C [¨ 1] Hrd¤ùs¤--¤TìH÷C G ¨BJ 1.H 0 ¨ì 9 @¤Q-r¤§srd¤ùH÷±o5 --A 1 ±o§±Cp¤U G 598329004632103 ¨BJ 2.¨§¨C¤T¨¤@H÷A¨H¤pí G 0.598 0.329 0.004 0.632 0.103 ùGU¤@-A±±óáA¨ú¨C 2.2.2 dH÷í -p¤U¤¤u{Wd±`H÷íAi¨±Cí 1 Y ASTM D3665 [ ¤u{§÷H÷k ][21]H÷íA° 0.001 0.002 … 1.0001000 B B -¨A¤@¤u{~q¤¤jAí¤w¨¨]t§ó¤jH÷
2-4

íi¨¤jq¤§Ap CNS 9042[15]40-¤§H÷í^C¨AH AíH÷¤èkw¤@°_IAMᨧ¨úX-¤§H÷]q±`k ¨ú^C [¨ 2] Hí1.¤§ ASTM D3665 H÷íd¨ú¤--H÷C G ] 1^H 2.2.1 `¤èkAHrd ¤ùHm^kH÷X¤T-§@ °°_IüA°]°u368 AHe¤GNíCA¤TN v íC368 Ní¨úH÷°_I¤§y° C8 C 36 ùG-YH÷° 00ANí C0 C 0 100 ] 2^ 36 C8 °_sòd¨ú¤--H÷p¤U G 0.136 0.585 0.038 0.814 0.594 2.2.3 H-p÷H÷ x¤W¤u{-p÷¤jh¨H÷\àAi H÷A¤u{~¤W¤Q¤êC [¨ 3] H¤u{x¤W-p÷¤--H÷C G ¤PtPP÷¤§-p÷±`¤P¤èkA\-p÷ú CH¤U°X÷¤§d¨G (1) CASIO fx-991 ¤ CASIO fx-3600PG ¨C INV ¤¤pI E (RAN#)¤@i¤@-H÷A 0.001¨ì1.000¤§

-¤-±oH¤U¤--H÷ G 0.887 0.213 0.768 0.533 0.022 (2) CASIO fx-4500P ¤ CASIO fx-5500LG SHIFT ¤¤pI E (RAN#)±°H÷\àAA¨C

¤@EXE i±o¤@-H÷A-¤-±oH¤U¤--H÷ G 0.879 0.229 0.807 0.400 0.681

2-5

í 1 H÷í
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 0 0.272 0.994 0.039 0.144 0.312 0.871 0.783 0.358 0.494 0.642 0.485 0.728 0.029 0.918 0.641 0.208 0.346 0.900 0.228 0.746 0.363 0.663 0.545 0.360 0.789 0.279 0.680 0.078 0.676 0.861 0.111 0.289 0.961 0.637 0.834 0.284 0.038 0.351 0.143 0.512 0.296 0.451 0.837 0.724 0.665 0.573 0.332 0.755 0.439 0.700 1 0.519 0.978 0.449 0.695 0.138 0.838 0.874 0.424 0.839 0.514 0.240 0.819 0.262 0.348 0.013 0.468 0.429 0.206 0.369 0.170 0.103 0.942 0.185 0.349 0.815 0.609 0.235 0.444 0.830 0.899 0.364 0.857 0.893 0.986 0.121 0.490 0.814 0.283 0.384 0.056 0.705 0.536 0.405 0.153 0.825 0.716 0.702 0.951 0.491 0.877 2 0.098 0.693 0.737 0.339 0.670 0.595 0.795 0.684 0.337 0.297 0.292 0.557 0.558 0.311 0.780 0.045 0.537 0.539 0.513 0.974 0.931 0.278 0.054 0.569 0.464 0.086 0.706 0.178 0.531 0.643 0.970 0.948 0.392 0.753 0.255 0.402 0.594 0.027 0.645 0.018 0.156 0.768 0.591 0.841 0.671 0.266 0.300 0.937 0.855 0.442 3 0.459 0.593 0.501 0.621 0.894 0.576 0.430 0.074 0.325 0.869 0.335 0.050 0.159 0.232 0.478 0.798 0.469 0.308 0.762 0.306 0.389 0.785 0.198 0.910 0.484 0.852 0.827 0.651 0.888 0.771 0.669 0.980 0.377 0.566 0.453 0.151 0.911 0.220 0.479 0.122 0.616 0.513 0.370 0.829 0.623 0.456 0.570 0.550 0.446 0.286 4 1.000 0.690 0.960 0.128 0.682 0.096 0.265 0.019 0.669 0.744 0.088 0.152 0.767 0.797 0.529 0.065 0.697 0.480 0.952 0.145 0.199 0.638 0.717 0.420 0.020 0.890 0.572 0.423 0.305 0.037 0.548 0.132 0.864 0.213 0.376 0.044 0.324 0.685 0.489 0.303 0.534 0.481 0.104 0.470 0.770 0.434 0.945 0.879 0.773 0.526 5 0.554 0.028 0.254 0.032 0.061 0.581 0.059 0.345 0.083 0.824 0.589 0.816 0.175 0.921 0.520 0.315 0.124 0.293 0.856 0.139 0.488 0.002 0.247 0.492 0.007 0.108 0.769 0.672 0.421 0.241 0.687 0.094 0.472 0.807 0.583 0.436 0.322 0.527 0.052 0.803 0.168 0.880 0.848 0.391 0.400 0.467 0.968 0.162 0.542 0.071 6 0.250 0.831 0.239 0.413 0.832 0.245 0.260 0.618 0.043 0.524 0.127 0.404 0.979 0.995 0.093 0.318 0.541 0.448 0.574 0.417 0.915 0.989 0.913 0.914 0.547 0.076 0.310 0.571 0.307 0.582 0.639 0.298 0.009 0.017 0.422 0.747 0.895 0.943 0.187 0.553 0.564 0.835 0.004 0.388 0.068 0.603 0.649 0.791 0.416 0.154 7 0.246 0.319 0.474 0.617 0.765 0.786 0.563 0.176 0.809 0.656 0.396 0.079 0.521 0.225 0.426 0.742 0.525 0.010 0.158 0.195 0.067 0.462 0.975 0.115 0.941 0.089 0.036 0.660 0.502 0.578 0.510 0.870 0.946 0.460 0.371 0.694 0.411 0.556 0.990 0.729 0.866 0.734 0.414 0.163 0.440 0.169 0.097 0.810 0.350 0.988 8 0.736 0.073 0.031 0.764 0.226 0.412 0.632 0.352 0.981 0.608 0.401 0.703 0.781 0.397 0.323 0.597 0.281 0.836 0.689 0.338 0.878 0.927 0.555 0.881 0.365 0.662 0.329 0.657 0.112 0.634 0.105 0.309 0.766 0.515 0.399 0.136 0.160 0.853 0.912 0.205 0.739 0.427 0.354 0.817 0.019 0.721 0.118 0.625 0.957 0.333 9 0.432 0.268 0.720 0.257 0.745 0.867 0.394 0.748 0.499 0.408 0.407 0.493 0.843 0.356 0.504 0.080 0.962 0.233 0.579 0.901 0.640 0.186 0.559 0.452 0.261 0.607 0.477 0.972 0.808 0.077 0.549 0.441 0.287 0.630 0.366 0.585 0.367 0.612 0.750 0.925 0.850 0.847 0.707 0.790 0.944 0.779 0.242 0.674 0.419 0.626

KASTM D3665[21]

2-6

í 1 H÷í]ò^
51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 0 0.523 0.905 0.373 0.057 0.967 0.917 0.131 0.326 0.299 0.101 0.267 0.471 0.535 0.277 0.719 0.385 0.862 0.486 0.091 0.146 0.709 0.996 0.971 0.202 0.212 0.207 0.818 0.701 0.035 0.221 0.647 0.667 0.644 0.302 0.633 0.060 0.165 0.875 0.726 0.273 0.253 0.340 0.194 0.166 0.712 0.622 0.313 0.137 0.243 0.361 1 0.613 0.182 0.120 0.953 0.040 0.715 0.646 0.605 0.106 0.055 0.598 0.102 0.881 0.458 0.167 0.858 0.928 0.938 0.872 0.482 0.184 0.896 0.859 0.538 0.321 0.799 0.503 0.984 0.380 0.200 0.403 0.722 0.590 0.123 0.933 0.681 0.532 0.691 0.902 0.393 0.821 0.654 0.290 0.450 0.314 0.800 0.294 0.087 0.679 0.359 2 0.752 0.567 0.602 0.041 0.708 0.758 0.659 0.443 0.237 0.776 0.754 0.454 0.014 0.295 0.181 0.713 0.822 0.757 0.959 0.930 0.390 0.760 0.147 0.026 0.778 0.487 0.906 0.174 0.001 0.587 0.530 0.327 0.021 0.116 0.331 0.683 0.431 0.383 0.252 0.285 0.600 0.173 0.592 0.210 0.033 0.710 0.897 0.003 0.844 0.230 3 0.733 0.249 0.793 0.090 0.271 0.005 0.047 0.601 0.732 0.686 0.658 0.568 0.966 0.196 0.653 0.883 0.812 0.749 0.922 0.611 0.409 0.347 0.114 0.949 0.940 0.022 0.224 0.141 0.381 0.353 0.738 0.723 0.269 0.282 0.546 0.755 0.341 0.382 0.130 0.161 0.023 0.495 0.983 0.204 0.823 0.575 0.718 0.483 0.069 0.761 4 0.528 0.227 0.692 0.223 0.189 0.666 0.051 0.386 0.796 0.171 0.274 0.963 0.958 0.772 0.328 0.916 0.977 0.991 0.727 0.179 0.191 0.053 0.418 0.696 0.496 0.813 0.904 0.704 0.251 0.584 0.280 0.410 0.042 0.851 0.842 0.624 0.092 0.596 0.238 0.619 0.606 0.498 0.509 0.840 0.629 0.678 0.614 0.201 0.024 0.334 5 0.072 0.229 0.863 0.508 0.342 0.599 0.562 0.560 0.476 0.533 0.215 0.357 0.190 0.148 0.070 0.084 0.395 0.219 0.811 0.011 0.117 0.372 0.889 0.008 0.231 0.891 0.892 0.908 0.497 0.270 0.457 0.635 0.062 0.256 0.016 0.955 0.244 0.301 0.398 0.865 0.849 0.992 0.998 0.826 0.939 0.465 0.876 0.209 0.543 0.149 6 0.820 0.604 0.954 0.806 0.740 0.934 0.435 0.378 0.099 0.936 0.177 0.882 0.180 0.466 0.015 0.561 0.788 0.264 0.075 0.248 0.860 0.193 0.792 0.846 0.664 0.500 0.455 0.048 0.214 0.885 0.650 0.012 0.387 0.648 0.236 0.126 0.222 0.275 0.763 0.551 0.610 0.192 0.522 0.833 0.887 0.802 0.025 0.320 0.714 0.511 7 0.929 0.304 0.873 0.438 0.801 0.100 0.731 0.172 0.804 0.095 0.218 0.507 0.759 0.291 0.155 0.999 0.920 0.932 0.374 0.886 0.135 0.756 0.064 0.259 0.903 0.368 0.343 0.828 0.794 0.110 0.276 0.907 0.183 0.845 0.164 0.655 0.336 0.188 0.463 0.030 0.577 0.506 0.627 0.516 0.066 0.969 0.049 0.935 0.234 0.475 8 0.777 0.217 0.107 0.203 0.985 0.987 0.362 0.445 0.735 0.982 0.330 0.157 0.433 0.688 0.631 0.379 0.673 0.898 0.133 0.344 0.406 0.565 0.652 0.415 0.473 0.725 0.924 0.997 0.552 0.956 0.661 0.316 0.964 0.782 0.923 0.919 0.034 0.868 0.615 0.571 0.082 0.751 0.741 0.965 0.743 0.150 0.620 0.447 0.505 0.854 9 0.461 0.142 0.675 0.586 0.263 0.085 0.317 0.636 0.950 0.211 0.628 0.580 0.355 0.046 0.063 0.668 0.698 0.006 0.730 0.926 0.134 0.914 0.288 0.425 0.909 0.437 0.197 0.058 0.588 0.711 0.973 0.677 0.544 0.993 0.976 0.113 0.216 0.805 0.140 0.258 0.774 0.129 0.540 0.375 0.081 0.784 0.125 0.787 0.428 0.119

KASTM D3665[21]

2-7

2.3 H÷§N ieA±Né ] population^¨Aíì ]sample unit^C ¤ ¨pY¤@¤±Ns320 m3 V¤gA¤¨ 80¨°eè¤uaAh 320 m3 V
¤ NC@@°@ìCiy g°éAi ¨ ¤ ¨§ ¤ - ± ± - ¨ ¤ ¤ ¤ ¤ ± ¤ § púìmCHUTu{`§H÷NC

ùG ¤W±Né§@§] lot^ 2.3.1 H÷ H÷ (simple random sampling)uH÷vAY±Né ¤¤¤§¨C¤@줧Os ]ê°¤W¨Du¤WXAu-nà¤@w§§ ¨ì¤@Níì§Yi ^A§Q2.2`-z¤èk- H÷AX¨C¤@H÷ìsA§YiH¨úC [¨ 4] °]YwCV¤g-±¤u{AWwH °¤@§A 1000m ¤-I¤§p×AY§°_I°10K+000CH ÷kwìm¤§C G ¨BJ 1.í 1 d±o¤--H÷]¤[¨ 2]G ^ G 0.136 0.585 0.038 0.814 0.594 ¨BJ 2.±N` 1000m ¤§O-HUH÷A§Y±oUIP°_I¤§ Z÷AA¤§O[¤W°_I§Y°¨úIA-ppí 2 C H÷°°ò¤èkAq¤j§@~¤KAìm| §°¤¤AyqקK±C í 2 H÷k-p No. 1 2 3 4 5 (1) `× 1000 1000 1000 1000 1000 (2) H÷ 0.136 0.585 0.038 0.814 0.594 (3) ÷°_IZ÷ × (1)2) ( 136 585 38 814 594 (4) ¨úI × 10K+000+(3) 10K+136 10K+585 10K+038 10K+814 10K+594

2-8

2.3.2 ¤h ¤h ]straitified sampling^Y±Néww¤j¤p¤°-Y¤zh] ¤W§@¤p§sublot^AMá±q¨C¤@h¤¤AHH÷kUX¤@ó C [¨ 5] °]YwCV¤g-±¤u{AWwH °¤@§A 1000m ¤-I¤§p×AY§°_I°10K+000C¤h kwìm¤§ C G ¨BJ 1.±N§§¤°¤-¤p§A¨C¤p§ G 1000/5=200 U¤p§°_I¤§O°10K+000 B10K+200B… B10K+800 ¨BJ 2.í 1.d±o¤--H÷p¤U (¤[¨ 2]G )G 0.136 0.585 0.038 0.814 0.594 ¨BJ 3.H¤p§-UH÷A-p±o¨úIApí 3 G í 3 ¤hk-p No. 1 2 3 4 5 (1) ¤p§× 200 200 200 200 200 (2) H÷ 0.136 0.585 0.038 0.814 0.594 (3) Z÷ =(1)2) ( 27 117 8 163 119 (4) ¤p§°_I 10K+000 10K+200 10K+400 10K+600 10K+800 (5) ¨ú =(3)+(4) 10K+027 10K+317 10K+408 10K+763 10K+919

¤hk-pAiTO¤¨ìéUhAeQ±¨üA bq¤hy±C 2.3.3 ¨t ¨t (systematic sampling)uZvAY±Né¤j ¤p§ ¤AMá±q¤@¤¤¤AHH÷kX¤@óAMá¨CjP¤P B¨ú¤@óC

2-9

[¨ 6] °]YwCV¤g-±¤u{AWwH °¤@§A 1000m ¤-I¤§p×AY§°_I°10K+000C¨t kwìm¤§C G ¨BJ 1.-p¤@¤G 1000/5=200 ¨BJ 2.í 1.d±o¤@-H÷° G 0.136 ¨BJ 3.-p¤@Iìm G 10K+000 + 200×0.136 = 10K+027 ¨BJ 4.-pU¨úIpí4G í 4 ¨tk-p No. 1 2 3 4 5 -p 10K+027+200 10K+227+200 10K+427+200 10K+627+200 ¨ú 10K+027 10K+227 10K+427 10K+627 10K+827

¨tkAóq¤j¤§±pC-Yé¨g¤AB¤ gê°Z-A|oY-°tA¤i±Cs{¨¤W× §K±AH§K§@~¤w¨ú÷w§@AvT¤§NíC H¤W¤TG¤§p 1C

2-10

3

1

2

5

4

10K+000 1 10K+000 2

(a)H÷k 3 4 10K+800

11K+000 5 11K+000

10K+200

10K+400

10K+600

(b)¤hk 1

1
10K+000 10K+200

2

3

4

5

2

3
(c)¨tk

4

5
11K+000

1

¤TH÷G¤§

e¤T¨-pX ìm¤§]ay^Aó_-±¤W¤§ìm] y^AtHH÷¨MwA°]-±e×° 15mAtd±o¤--H÷° 0.530B 0.738B 0.280B 0.457B 0.650A±N¨¤§O-H 15mAò±o¤--y 7.95B 11.07B4.20B6.86B9.75mA§Ybe¤T¨¤¤±o¤§ìm¤§IAZ° ¤W-z_-±Z÷B¨ú]ùGó°q°_i¨ùwApk°^C H [¨5]¤hk±oA°tXH¤W-p±o¤§yAi±oìm p¤U]°¨ 2^G í5 _-±H÷k-p ¨úIs 1 2 3 4 5 10K+027 10K+317 10K+408 10K+763 10K+919 Z]m^ 7.95 11.07 4.20 6.86 9.75

2-11

15 _ -±@ 12 9 6 3 0 0
10K+000

100 200

300 400

500

600 700

800 900 1000
11K+000

a _ -±@ 2 êìm

¤TBz

~§@~¤¤±Nò±o\h~è (p ) Ag¤u{vMiH
±q-§OX¤@¨-AgL¤@w{§zA¤RMkA¤~à XépAw¨oiU¤]GYCó§ AqM~¤§¤PA¨z¤R¤èk±`§AH¤U¤¤u{~ ±`°òzkC 3.1 ¤@í z¤§¤@¨B°±N~-nAí¤ (pG¤u{§OB§OB §OB§O¤ )A±N--n¨§n°Os¨u¤@ ívCí 6°YwV¤gt¤§ 28¤¤§êW駱j× ]Ww±j× fc’=210 kgf/cm2^CwV¤gt¨C±¤GuéAWwi v 28¤¨ú¨§±j×C CNS 3090[wV¤g][14]WwH¤Gu é±jפ§-§-§@°¤§G] test result^C ùG¨CNS 3090¤§wqA¨C¤@G°¤@-§O-A¨¨°P¤@ ¨ú°UêWé±jפ§-§-C ¤@íY±N-ìlí¤¤¤§P÷°¤¤b¤@°_Ai¤èK\A¨K ó§@i¤@¨B¤RCí6¤¤±oG¤§¤j-° 312] No.17^A¤p-° 173] No.9^A G¤T¤Q¤§§±jרó 173~312¤§C

2-12

í 6 V¤g§±jפ@í (1) No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 (2) ¨ú¤é 85.7.1 85.7.1 85.7. 2 85.7. 2 85.7. 3 85.7. 3 85.7. 4 85.7. 4 85.7. 5 85.7. 5 85.7. 6 85.7. 6 85.7. 7 85.7. 7 85.7. 8 85.7. 8 85.7. 8 85.7. 9 85.7. 9 85.7. 10 85.7. 10 85.7. 11 85.7. 11 85.7. 13 85.7. 13 85.7. 14 85.7. 14 85.7. 14 85.7. 15 85.7. 15 (3) ~N P5-1 P5-2 P7-1 P7-2 P3-1 P3-2 P4-1 P4-1 P6-1 P6-2 P1-1 P1-2 C1-1 C1-2 C1-3 P8-1 P8-2 P8-3 S3-1 S3-2 S3-3 S3-4 S3-5 C3-1 C3-2 W3-1 G6-1 G6-2 G6-3 G6-4 §±j× (kgf/cm2) (4) (5) (6) é 1 é 2 G 260 249 255 246 260 253 255 272 264 305 290 298 294 275 285 266 278 272 224 242 233 225 204 215 177 169 173] ¤p ^ 198 210 204 209 231 220 236 214 225 257 243 250 260 280 270 226 252 239 286 271 279 313 310 312]¤j^ 274 273 274 243 248 246 184 201 193 230 207 219 209 190 200 241 257 249 286 296 291 271 246 259 220 236 228 272 281 277 307 300 304 266 258 262 248 272 260

2-13

3.2 ¤°tí -ìlqe¤jAi-¤j¤pAí[H¤s§@u¤°tívA HKì¨BA¨¤°tpA¨ii¤@¨B¨su¤èv-p¤§A ¤°tís§@¨BJp¤UG [¨ 7] Hí6 s§@¤°tí]°¨í 7 ^ C G ¨BJ 1.-p¤§ZC Z=¤j-¤p-=312 173=139 ¨BJ 2.-pC q±`¨g-pA¨H¤U`¤è§O¤O§_ êíC-YL󰤤¤Aí¤¤i°uW[F ¤¤§ALó¤A¨CX{¤Aí¤ hi°u¤C-YL¨°÷gAiH¤U¤T¤èk-p C ]¤èk¤@^vSN] Sturges^ [3]g¤G k=1 3.32×log(n) ¤¤A k=¤A n=- ]¤èk¤G^g¤G
k= n

] 1^

] 2^

]¤èk¤T^gí[3]G n k 50~100 6~10 100~250 7~11 250 H¤W 10~14

¨± ¤èk¤@ n=30Ahk=1+3.32×log(30)=5.9Ai¤ 6C G ùG¤¨¤@ì-Aê±|{¨¤§¤èK¤ §e{ ¤§¤°tpC ¨BJ 3.-pZC Z=Z/=139/6=23.2
2-14

q-p¤s¤èKA±`¨ú5 ¤§-C qU¤¤-|A±`¨ú_]_°H2 |¤-ì ¤Uh¤@ìA°¨¨BJ 6.ᤧù C ^ ¨gH¤W{AZw 25C ¨BJ 4.-p¤@¤§¤¤IC ¤@¤§¤¤I¤p-Z /2=173 25/2=185.5 q-p¤èKA±`¨ú ¤§-C¨± 180C 5 ¨BJ 5.-p¨lU¤§¤¤IC U¤§¤¤I=e¤@¤§¤¤IZ ¨G 180 25=205A205 25=230A… C ¨BJ 6.-pU¤§--]dò ^ C ¤U-=¤¤IZ/2 ¤W--¤¤IZ/2 = ¨¤@G¤U-=180 25/2=167.5 ¤W-- 180 25/2=192.5 = ¤GG¤U-=205 25/2=192.5 ¤W-- 205 25/2=217.5 = ùG¤@¤W--P¤G¤U--P° A]-ì°O 192.5 -ìA¤| 192.5 X{AG¤G¤|-|C ¨BJ 7.n°O¤-pC ±Ní6 ¤§(6)uGv¨dòn°Oóí 7 ¤§(4)A¨§g¨r]p¤§}§@~ An§ ^ ¨áAA-p U (p 5 )¨-p`C¨¤@ 253Aìó242.5-267.5 AGó¤¤I° ¤§¤@ 255 §A¨l±C¨`°30C ùG°Oi¨°ê¤HDgur¨è¨uUv ¨ v ü r¤§|u¤¤@±×u]°¨ 3 A±§÷]A¤ ^ qr¤§qA]4^Hxí§eA ¨ê¤g§íC

1

2

3

4

5

3 è°O

2-15

¨BJ 8.-pU`¤§¤¤C U`¤§¤¤ =U /` 00 1 ¨¤@¤¤ 1/30 00=3.3 = 1 ¤G¤¤ =4/30 00=13.3 1 ¨¤°tíiH¤j-PXG (1) ¤j÷-¨ó 180 305 ¤§C (2) ¤¤I× 255 ¤W¤U¤§A-p-§-ù° 255C í 7 ¤°tí (2) (3) (4) ¤U-¤W-- °O 167.5 192.5 ¤@ 192.5 217.5 ¤ 217.5 242.5 ¤@ 242.5 267.5 ¤ 267.5 292.5 ¤B 292.5 317.5 ¤U

(1) ¤¤I 180 205 230 255 280 305 X-p

(5) (6) ¤¤ 1 3.3 4 13.3 6 20 9 30 7 23.4 3 10 30 100

2-16

3.3 ¤è Hí7¤§ (1)u¤¤Iv°yA (5)uv (6)u¤¤v °ayAH¨ê]p 1801B2054A1803.3%B20513.3% ^H¤è§íA¨¤è (histogram)] 4^C ¤è±`óì¨B¤RꤧA¤èiH§tX¤ °tpC¨p 4iì¨Bp¤UG ] 1^¤è§e{kù¤¤s§Aü±`A¤°t¤§§Ai§Pw§ §÷±`¤C ] 2^-±n¤§ k¤¤¤y]ù 255 Ai-p§V¤g¤§-§§ ^ 2 ±j×ù° 255kgf/cm C ] 3^¤pó 210¤§-±n]±×u¤^ù`-±n¤C¤¤§¤@A-p§±j פpó 210kgf/cm2¤§¤¤ù° 15%C

10 8 6 4 2 0 155 180 205 230 255 280 305 330 §±j× gf/cm2 4 V¤g§±j×¤è °H¤W¤¤§-p¤§~A|\h-pi°tX¤Rí{-n±` Q±A¨pH Microsoft ExceliH 5 CU-pA¨C i¤¤G¤C-Aih[C 4¤èYH±sA¤` ¤§U¨h XY§GsC 210 255

2-17

÷HMicrosoft Excels 4¤è°¨ú°ò¨BJp¤UG ] 1^±° Microsoft ExcelAb¤u§@í¤Jp¤UG
1 2 3 4 5 6 7 8 A 155 180 205 230 255 280 305 330 B 0 1 4 6 9 7 3 0

] 2^¤u§@Cu¤JAuíAu± v v AIu¤U¤@¨B v C v ] 3^uC AusW v AIu-v±Aì-íu v I±CIu§O Xbv±Aì-íu ±AIu ¤U¤@¨B C v ] 4^uDAbu§O Xbv¤è¤Ju§±j× v Ybv¤è¤Ju AIu¤U¤@¨B v C v B1B8 v A A1A8AI v

,kgf/cm2bu- v A

] 5^Iu¤u§@í¤¤óAIu§¨ChX{±A¤¤U± v v AòH¤U¨BJ°¤§C ] 6^IN¤@±AkAIuêCAIu v A v u §OZv-×° 0AIuTwCp§Yi¤èA-n¤i v i-קCBC

2-18

16 14 12 10 8 6 4 2 0 123 1.±4 5 6

2. ±

3. §éu

4. ê§

5.XY§G

10 5 0 6. °°ì

7. °é

8. pF

S 1 9. ±-±

15 10 5 0 4 10. ww

S2 S1 11. 12. êW 13. ê@

S2 S1 14. ÷r

5 Microsoft Excel Fs-p

| B°¤¤P÷ {×
4.1 °¤¤P÷{ק-z P¤@餧~èS¤j÷|X{bY¤@¤¤¤-A÷}¤¤¤-V AX{÷vV¤Ap 4¤§¤è¨p¤s§Ao{Hu°¤¤vA ¤u{~¤W±`-§]-§-^í¤¤¤-C ¤u{~è-Y¤z{פ§¤§¤]p 6í 6e¤--G- ¤§¤§Gp^AH-§°¤¤¤A¤W¤U¤A¨¤§eu÷{×vC ~èV¤§¤A÷{×VúA¤u{~¤W±`HtB§YBZ¨ í÷{×C
2-19

305 300 295 290 285 280 275 270 265 260 255 250 0

2 §±j×kgf/cm §±j× Kgf\cm2

¤j-×298

298

285 -§×271 264 ¤p-×253 2 3 s s 6 ~褧÷ 4 5 Z

255 1

253 6

4.2 -§ -p¤W-§Aq±`S§OüúA-§ (arithmetic mean)A-§°-§-C °]¤@é¨ú n-A¨-§O-¤§O°
-pp¤UG

(mean)YüN-§

x1 , x 2 ,..., xn A¨-§

1 1 n x = ( x1 + x2 + + x n ) = ∑ xi n n i =1

(3)

¤¤A = -§ x i=1 n n=¤j¤p(-) -§ ( x A°áx bar)Y¨D±oA°u-§vA¤@ u-§vC餤-§¤§ué-§vHg A-p-§] (°ámu)íC (g)C ¤u{ê°¤WA¤§@100%Aé-§ (g)Lk±oA±
x ^AA§Q-§] x ^-pé-§ x i = -§O-A

2-20

[¨ 8] -pí 6 e¤-V¤g§±j×G¤§-§G x i =255,253,264, 298,285 kgf/cm2 G
x =(255+253+264+298+285)/5=271

kgf/cm2

§-g±`H-§í¤@s¤Tw-¤§¤¤-A¨p-§¨-°B-§ B-§±j×C¤u{Wd¤¤±`H-§í¤u{~è¤AWw¨C§ -Y¤zóA¨-§¤±o¤póY¤@w-C¨pA CNS 1178[V¤g¤jk ][12] 3.3`WwG u_-±§±j×G¤wt±¤T-A¤t±¤C -V¤g¤jiA¨¤UC¤A§°Xv

x ≥ S L + 1.6σ (4) ¤¤, x =-§- SL=W¤U---] CNS 8905[V¤g¤j]WwA jG A 2 2 SL=40 kgf/cm A B jGSL=60 kgf/c m A C jGSL=80 kgf/cm2^ m =ét (¤tHt s -p¤§A 4.3 ` )
¤u{~¤W¤]±`¨úsò-Y¤z¤§°-§]
x m ^AH~褧°

C×u°-§vY°_I}lAsò¨úüw--§O-¤§-§A Máv ¤U±i¤@A¨Cei¤@P±óá¤@C¨pH¤U¤-- ] 255,253,264,298,285^¤§¤T°-§p¤UG

xi =

255

253

264

298

285 282.3

xm =

257.3 271.6

ú 255+253+264^ /3=257.3 G ] ] 253+264+298^ /3=271.6 ] 264+298+285^ /3=282.3 4.3 t t (standard deviation)óíꤧ÷{×A-Y餤¨ú A¨-¤§O° x1 , x 2 ,..., x n A¨t-pp¤UG
2-21

n-

s=

∑ (x

i

x )2

n 1

(5)

¤¤A =t s x i =-§O-A i=1 n x =-§ n =¤j¤p(-) t (s)Y¨D±oA°utv A ¤@utvC -Yú±o餤 ¤§¨C¤@-é-AhiH-pét (mA°á sigma)p¤UG
σ=

∑( x

i

) 2

N

(6)

¤¤Am =ét x i =-§O-A i=1 N g=é-§ N=餤¤§-é]§q^ ¤u{ê°¤WA¤§@ 100%Aét (m )Lk±oA± A-pt] s^AA§Qt-pét (m )C tHí¤@s¤§÷{×AtU¤jíU ¤t§ U¤jF-Y°~èSAtU¤jí~èU¤§¤C±¨|¤ [-p Wü]¤CNS 2579[~è¨üJ ]§±Nstandard deviation °utvA ÷¤g¤ìv CNS¤|¤H¤hh¨¤éyu°tvC [¨ 9] -pí 6 ¤§e¤-V¤g§±j×G¤§tC x i =255,253,264, 298,285 kgf/c m2 G 8]±o x =271A÷H [¨ (5)í-pp¤U G í 8 t-pí
xi
xi x

( x i x) 2

255 253 264 298 285

-16 -18 -7 27 14

X-p 1554/(5-1)=
388.5 =

256 324 49 729 196 1554 388.5 19.7

2-22

4.4 §Y §Y] coefficient of variation^°t-§¤§¤-A-p¤ ¤UG
s V = ( ×100)% x

p

(7)

¤¤A V=§Y]i¤pí^ s=t x =-§ [¨ 10]-pí 6 ¤§e¤-V¤g§±j×G¤§§YC G ] 1^[¨ 8]¤ [¨ 9]-p±oG s=19.7Ax =271 ] 2^N¤J] 7^A±oG
V= 19.7 = 0.073 = 7.3% 271

¤u{~¤W±`Ht §Yí¤u{~褧¤§¤A¨-U¤j íU¤§¤Có±t§YíA¤§±p¤Uó à¤~è¤w]°¨í 9ê¨^Cti°÷{פ§-A §Yh°÷{×-§¤§-A-Y§YOù¤@wA-§¤j ¨¤§t¤jC í9°ACI 214[19]HV¤g¨¤¤§hAúp¤UG ] 1 - ^±§] overall variation G°UG¤§t§AHtíA ^ óV¤g~褧§¤AtU¤jAíV¤g~èU¤§ ¤A¨¤UtC -±§¤§tHU¤§GH] 5^ -p±o¤§C ] 2^¤§] within-test variation G°¤@¤¤Ué±jפ§t§A ^ H§YíA󤧱K×] precisionC¨§Yó ^ U餧s§@Biv¤t§¤°_A¤§P§@¤ -wAPV¤g~èLC¤§Y-p ¤¤§tA]¤@餧q¤hA¤y] 5^-ptA H] 9^-p¤§] [¨12] C ^

2-23

í 9 ACI 214V¤g¨¤h -±§]overall variation^ tApsi (kgf/cm2) n iH |i Very Good Good Fair 400-500 500-600 600-700 (28.1-35.2) (35.2-42.2) (42.2-49.2) 200-250 250-300 300-350 (14.1-17.6) (17.6-21.1) (21.1-24.6) ¤§]within-test variation^ §YA % n iH |i Very Good Good Fair 3.0-4.0 2.0-3.0 4.0-5.0 3.0-4.0 5.0-6.0 4.0-5.0

§@~ ¤ua

¨ Excellent <400 (<28.1) <200 (<14.1)

¤¨} Poor >700 (>49.2) >350 (>24.6)

§@~ ¤ua

¨ Excellent <3.0 <2.0

¤¨} Poor >6.0 >5.0

-p¤Riò±o[A§@~hà¤H°¨wA¨¨w {à¤O¤ON×A§°ê| L¤§V¤g¨¤hAí 9§@~¤§¤¤¤Y¤¤g¤ì¤§Q|¤§V¤g¤u{I¤uWd 3.7`¤§ ]¤g¤ì 402-88^[10]C÷H] 5^-p±oí 6¤§30G¤§t° 34.2 kgf/cm2Aí 9i§Pw¤u{¤§I¤u¤unvC 4.5 Z Z(range)°¤¤¤j-P¤p-¤§tA¨-p¤p¤UG

R = xmax xmin
¤¤A =Z R

(8)

x max =¤j-

x min =¤p-
[¨ 11] -p¤UC¤-V¤g§±j×G¤§ZC

x i = 255,253, 264, 298, 285 kgf/cm2

2-24

G

xmax = 298 A xmin = 253 R= 298 253 = 45 kgf/c m2 Zóí¤§÷{×A¨-peA¤é±`¤~ê°¤W±` Hí~褧 ÷{×C tM-§Z] R ^í¨}n-pYAb¤¤§±p¤UA ±`¤§-§Z] R ^-pétA¤p¤U G
σ=
R=

∑R
k

R d2

(9)
i

(10)

¤¤Am =ét k= Aq±`-n¨D k 10A¨±G°zQ R i= i ¤§Z d 2 =-pYAM¨C¤§¤j¤p (n)Apí10 í 10 d 2 Y ¤j¤p (n) 2 3 4 5 6 7 8 9 10

d2

1.128 1.693 2.059 2.326 2.534 2.704 2.847 2.970 3.078

[¨ 12] Hí6e 10¤§V¤g§±j×-p¤§¤§t¤ §YC G

2-25

í 11 H-§Z-pt §O 1 2 3 4 5 6 7 8 9 10

∑R
R d2

x1 260 246 255 305 294 266 224 225 177 198

x2 249 260 272 290 275 278 242 204 169 210

R
11 14 17 15 19 12 18 21 8 12 147 14.7 1.128 13 245 5.3%

s1
x V1

147/10= dí 10A n=2 C±o 14.7/1.128= -p¤Q¤§-§ 13/245×100%=

ùGACI 214Hs1 ¤ V1¤§Oí¤§¤§t¤
§YC

í 9±o¤§] V1=5.3%^ u|i¤v] 5.0-6.0%^Aí P¤@¤§¨é±j×t|¤jA-n°Q§@~¤§-wPWi ±K×C 4.6 -p÷¤§-p-p\à e¤u{¤§q¤l-p÷¤jh¨°ò-p-p\àAq¤¤jA¤Q ¤êA¨D-n§@¨BJp¤UG (1)}÷C (2)à¤J-p\àC (3)¤JC (4)d¤§-pqC UtP¤-p÷¤§§@¤èk±`U¤PA°\U-p÷ ¤§§@¤UCH¤UH¤@±`¨-p÷°¨ú¤§C

2-26

[¨ 13] H-p÷-pH¤U¤§-§PtC

xi =255,253,264, 298,285 kgf/c m2
G÷H CASIO fx-991 -p÷°¨ú¤§C í 12 -p÷¤§-pB INV MODE E 255 M+ (x) 253 M+ (x) 264 M+ (x) 298 M+ (x) 285 M+ (x) INV 6(n) INV 7( x ) INV 9( σ n 1 ) INV 8( σ n ) SD 255 253 264 298 285 5 271 19.71 17.62 ú i¤J-p\à ¤J ¤J ¤J ¤J ¤J G¤w¤J¤-- G-§ Gt Gét

ùG]^¤¤°-p÷¤W¤è¤§rC pGqe¤jg±`¤RAiq{¤RA÷H 13]úp¤UG ] 1^}± EXCELAb-¤Jp¤UG EXCEL-p [¨

A 1 255 2 253 3 264 4 298 5 285 ] 2^b A6¤Ju =AVERAGE(A1:A5)AuTwA¤¤X{ 271A§Y v v °-§C ] 3^b A7¤Ju =STDEV(A1:A5)AuTwA¤¤X{ 19.71A§Y° v v tC EXCELGp¤UG

2-27

1 2 3 4 5 6 7

A 255 253 264 298 285 271 19.71

¤-B±`A¤°t
5.1 ±`A¤°t§-z s¤è] 4^ApG-vW[Ah¤iW[A hZv¤pA¤§¤è±Nvó-±uAí-óL --hA h~èS¤§¤°t±u±`§ek¤§§±u]p 7^A °±`A¤°t±u] normal distribution curve^A¨i (11)¤§±`A¤°t¤§÷ v±KרíG
1 x 2 ( ) 1 f ( x) = e 2 σ 2π σ

-x

(11)

¤¤A x= g=é-§ m =ét

e=2.718281828(M )

f(x;,σ )=f(x;250.3,34.225)

10 8 6 4 2 0
100 150 200 250 300 350 400

0.012 0.008 0.004 0.000
xA§±j× (kgf/cm2) 7 ¤èP±`A¤°t±u
2-28

¤u{~èꤰtp°¤H¤OLkò Aê°¤W±`±N¨°]°±`A¤ °tAH°]°°òA§-iH]w¤t¤j¤pBwws{Bs§@¨B -peBs{à¤OA~sxC ±`A¤°t±uH¤USèG (1) ±`A¤°t±u°pAp¤§¤-y-°é-§ (g)C (2) ±`A¤°t±u°kó x=g¤§bA¨°U¤@-¤±IAU ¤±IP-§¤§¤-Z÷°¤@-ét (m ]p 8 ) C ^

1m 1m
-4s -3s -2s -1s

+1s +2s

+3s

+4s

8 ±`A¤°t±u (3) ¨°H¤-b°uA[\dò° - +C (4) ±`A¤°t¨-°A¤§O°-§ (g)Mt (m )A±u§ ¨°¨MwG a. -§ (g)¨Mw±`A¤°t±u¤¤¤u¤§¤-ìmG -§¤jA¤¤¤uk-F¤¤§A-§¤pA¤¤¤u] 9.a C ^ b. t (m )¨Mw±u¤eG t¤jA±u-wA¤eF¤¤§At¤pA±uyUA¤ U] 9.b C ^

g 1 s1 s2

g 2

(a)tTwA-§§

(b)-§TwAt§ 9 ±`A¤°t±u¤ 2-29

(5) ±`A¤°t±u`\-±n]¤-y - +^°-¤§X{÷ vA]w° 1C¤-b¤Wó¨yI] x a ¤ x b ^§¨±u-±nA° ¨-¤ y§X{÷v Pe x a xCbf x
P[xa xxb]

xa

xb

x

10 ¨yI§¨±u-±n

(6) -§ =gAt =m¤§±`A¤°t] [ N ( ,σ 2 ) ]íAm 2°t¤§ ¤ - ià°g - è A p W ü ° u §^v =0 B m=1¤§±`A¤°t] [ N (0,1) ]í Càeᤧ¨yI§¨±u-±n¨`-±n¤§ ^ ¤vPA±`A¤°t¤§-±nidí¨ú±oC

N(,σ2)

xa

xb

x

N (0,1)

(1)±`A¤ °t za
0

zb

z

(2)±`A¤°t

11 ±`A¤°t਱`A¤°t

2-30

5.2 H±`A¤°t -p÷v ¤u{~¤W±`°]~èS°±`A¤°tA§-iH-pY¤@wdò¤ ÷v]MvB§v^ApXv]~èSbW--¤¤§÷v^B ¤Xv]~èSWXW--¤§÷v^C °]Y~èSH xíAB¨§e{±`A¤°tAg n¨-p±o -§ ( x )¤t (s)A¤±-p~èSX{b x a ¤ x b ¤§÷vA Pe x a x x b fC-p¤èkp¤U G (1)H-§ (x )-pé-§ (g)C (2)Ht (s)-pét (m )C (3)Tw¨D-¤§¤W¤U--dòGx a ¤ x b C (4)¤§O-p x a M x b P-§ (g)¤§tZAHt (m )íG
xa σ x zb = b σ za =

(12) (13)
G

(5)d±`A¤°tí]í 13A¤§O¨D±o -¨ì za P zb ¤§n÷v ^ Pe z Gaf z b za H¤U¤§n÷v z Pe z Gbf z b zb H¤U¤§n÷v z (6)¤Gn÷vA§Yi±o G Pe x a x x b f =Pe z zb f Pe z za f Pez za f°±`A¤°t¤§n÷vAi ¤WAYdí [±`A¤°tí ] ±o¤§C 13
P[ z ≤ za ] = F (za ) =

(14)

(15)-pA¤H¤u§@ ~ê°
1 t 2
2



za ∞

1 e 2π

dt

(15)

¤¤A a)Ní±`A¤°t-¨ì za ¤§n÷vC F(z ±`A¤°t±u°kA±`A¤°tíq±`Ckb÷z ( 0 ÷)Az<0 ÷A]°±`A¤°tb-za H¤U÷¤§-±n F (za ) ∝∞ H¤W÷¤§-±n 1 F(za ) Α←Γ∞ι∞∈ za (16)C

F (za ) = 1 F (za )

(16)

2-31

í 13 ±`A¤°tí f(z)
F (z ) =
1 e 2π 1 t 2



z ∞

2

dt

-
z 0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3.0 0.00 0.5000 0.5398 0.5793 0.6179 0.6554 0.6915 0.7257 0.7580 0.7881 0.8159 0.8413 0.8643 0.8849 0.9032 0.9192 0.9332 0.9452 0.9554 0.9641 0.9713 0.9772 0.9821 0.9861 0.9893 0.9918 0.9938 0.9953 0.9965 0.9974 0.9981 0.9987 0.01 0.5040 0.5438 0.5832 0.6217 0.6591 0.6950 0.7291 0.7611 0.7910 0.8186 0.8438 0.8665 0.8869 0.9049 0.9207 0.9345 0.9463 0.9564 0.9649 0.9719 0.9778 0.9826 0.9864 0.9896 0.9920 0.9940 0.9955 0.9966 0.9975 0.9982 0.9987 0.02 0.5080 0.5478 0.5871 0.6255 0.6628 0.6985 0.7324 0.7642 0.7939 0.8212 0.8461 0.8686 0.8888 0.9066 0.9222 0.9357 0.9474 0.9573 0.9656 0.9726 0.9783 0.9830 0.9868 0.9898 0.9922 0.9941 0.9956 0.9967 0.9976 0.9982 0.9987 0.03 0.5120 0.5517 0.5910 0.6293 0.6664 0.7019 0.7357 0.7673 0.7967 0.8238 0.8485 0.8708 0.8907 0.9082 0.9236 0.9370 0.9484 0.9582 0.9664 0.9732 0.9788 0.9834 0.9871 0.9901 0.9925 0.9943 0.9957 0.9968 0.9977 0.9983 0.9988 0.04 0.5160 0.5557 0.5948 0.6311 0.6700 0.7054 0.7389 0.7703 0.7995 0.8264 0.8508 0.8729 0.8925 0.9099 0.9251 0.9382 0.9495 0.9591 0.9671 0.9738 0.9793 0.9838 0.9875 0.9904 0.9927 0.9945 0.9959 0.9969 0.9977 0.9984 0.9988 0.05 0.5199 0.5596 0.5987 0.6368 0.6736 0.7088 0.7422 0.7734 0.8023 0.8289 0.8531 0.8749 0.8944 0.9115 0.9265 0.9394 0.9505 0.9599 0.9678 0.9744 0.9798 0.9842 0.9878 0.9906 0.9929 0.9946 0.9960 0.9970 0.9978 0.9984 0.9989 0.06 0.5239 0.5636 0.6026 0.6406 0.6772 0.7123 0.7454 0.7764 0.8051 0.8315 0.8554 0.8770 0.8962 0.9131 0.9279 0.9406 0.9515 0.9608 0.9686 0.9750 0.9803 0.9846 0.9881 0.9909 0.9931 0.9948 0.9961 0.9971 0.9979 0.9985 0.9989 0.07 0.5279 0.5675 0.6064 0.6443 0.6808 0.7157 0.7486 0.7794 0.8078 0.8340 0.8577 0.8790 0.8980 0.9147 0.9292 0.9418 0.9525 0.9616 0.9693 0.9756 0.9808 0.9850 0.9884 0.9911 0.9932 0.9949 0.9962 0.9972 0.9979 0.9985 0.9989

0

z=za
0.08 0.5319 0.5714 0.6103 0.6480 0.6844 0.7190 0.7517 0.7823 0.8106 0.8365 0.8599 0.8810 0.8997 0.9162 0.9306 0.9429 0.9535 0.9625 0.9699 0.9761 0.9812 0.9854 0.9887 0.9913 0.9934 0.9951 0.9963 0.9973 0.9980 0.9986 0.9990



0.09 0.5359 0.5753 0.6141 0.6517 0.6879 0.7224 0.7549 0.7852 0.8133 0.8389 0.8621 0.8830 0.9015 0.9177 0.9319 0.9441 0.9545 0.9633 0.9706 0.9767 0.9817 0.9857 0.9890 0.9916 0.9936 0.9952 0.9964 0.9974 0.9981 0.9986 0.9990

2-32

[¨ 14] YV¤g¤u{gsò¤T¤Q¤§§±j×AGpí 6 A-p±o-§- )=250.3 kgf/c m2 A t (s)=34.2 (x 2 kgf/cm A°]V¤g¤§§±jקe±`A¤°tA-pH¤U÷ v] x NíV¤g¤§§±j×^ G (1) Pe x 300 G±j×b 300 H¤U¤§÷vC f (2) Pe x 210 G±j×b 210 H¤U¤§÷vC f (3) Pe 210 x 300 G±jפó 210 300 ¤§÷vC f G (1) H-§ ( x )¤t (s)¤§O-p±oé-§-¤ét p¤UG é-§- (g)=250.3 kgf/cm2 ét (m )=34.2 kgf/cm2 (2) -p Pex300f ]°¨ 12^ G zb=(300250.3)/34.2 =1.45 Pex300f =PeZ1.45f dí 13.(±`A¤°tí )G Pez1.45f =0.9265=92.65% ùG-Y300°W¤W--Ah 92.65%°XvCê¤WV¤g¤§§±j ×Wq±`u]¤U---A¨h]¤W---Ap÷¤l§tqC
0.016 0.012 0.008 0.004 0.000 150 200 250 300 350 f(x, ,σ)=f(x,250.3,34.2)

I = 0.9265

(±jפpó 300 kgf/cm2 ¤§÷v

)

12 ±`A¤°t-p P[x ≤ 300] (3)-p Pex210f ]°¨ 13^ G za=(210250.3)/34.2=1.18
2-33

Pex210f =Pez 1.18f ]°±`A¤°t°kAG Pez 1.18f× Pez1.18f ]°±`A¤°t¤U¤§`-±n× 1AG Pez1.18f =1Pez1.18f dí 13.(±`A¤°tí )G Pez1.18f =0.8810 Pez 1.18f =10.8810=0.1190=11.90% ùG-Y210°W¤U--Ah11.90%°¤XvC
0.016 0.012 0.008 0.004 0.000 150 200 250 300 350 f(x, ,σ)=f(x,250.3,34.2)

I = 0.1190

(±jפpó 210 kgf/cm2 ¤§÷v

)

13 ±`A¤°t-p -p P[x ≤ 210] (3)-pPe210x300f ]°¨ 14^ G Pe210x300f =Pex300f Pex210f = 0.92650.1190 = 0.8075=80.75% ùG-Y300¤210¤§O°W¤W¤U--Ah0.75%°XvC 8
0.016 0.012 0.008 0.004 0.000 150 200 250 300 350 f(x, ,σ)=f(x,250.3,34.2)

I = 0.8075

(±jפó 210P 300 kgf/cm2 ¤§ ) 14 ±`A¤°t-p P[210 ≤ x ≤ 300]
2-34

HP¤èki¨D±o±`A¤°t-§¤W¤U¤@-t¤T-t¤§[\ ÷vp¤U]°¨ 15^G ] 1^-§¤W¤U¤@-t (g )G m P[gm xgm] = p[-1z1] = 2] 0.8413-0.5^= 0.6826 ] 2^-§¤W¤U¤G-t (g )G 2m P[g 2mxg 2m = p[-2z2] = 2] 0.9772-0.5^= 0.9544 ] ] 3^-§¤W¤U¤T-t (g )G 3m P[g 3mxg 3m = p[-3z3] = 2] 0.9987-0.5^= 0.9974 ] H¤W¤T-±`Q¤A¤u{D¤W±`¨úüw- m§@°¤tA-Yé°±` 3 A¤°tA¨[\÷vù° 99.74%A ¤u{--nAii¤@¨B{± 2m§@°¤tA¨[\÷v° 95.44%C
0.5 0.4

0.39894 0.6826

f(z)

0.3 0.2

0.9544
0.1

0.9974
0.0 -5 -4 -3 -2 -1 0 1 2 3 4

z
5

±`A- z 15 ±`±`A¤°t§t§v [¨ 15] Y¤u{WdWw X §÷¤§×¤ gdH±`s{ tA ê¤R±oפ§t° 2.0mmAwX §÷פ§ -§O-¤t--]tolerance limit ^ C G ÷¤u{D¨ú-t¤T-t] ^ § @ 3 m °M¤t-] natural tolerance limit^ AGiwX §÷פtp¤UG m=(2.0)= .0mm 3 3 6 -Y X§÷¤§]-p×° 5000mmAh]-pi×° 5000.0mm 6 5.3 -§¤§¤°t ¤@§e{±`A¤°t¤§é [ N ( ,σ 2 ) ]¤¤H÷¨ú nóA-p¨-§
x Ah x §e{±`A¤°t

[N ( , (

σ 2 ) ) ] ] 16 ¨ -§MtAp (17)(18) ^A n 2-35

¨C nU¤jA σ x U¤pAG±`A¤°t±uUyUC¤u{~±`H-§ °~èüA-§]
x = σx = σ n
x ^¤°tP-§O-]

(x )§@ x^¤°t¤§t¤PA¤àVC (17) (18)

¤¤Gg =-§O-¤°t¤§-§ x =-§¤°t¤§-§ m =-§O-¤°t¤§t σ x =-§¤°t¤§t -§-¤°tG
N (, ( σ 2 ) ) n

-§O-¤°tG
N ( , σ 2 )

x =
16 -§¤§±`A¤°t b[¨15]¤¤Y±-§O-¤§¤t° 6.0mmA°]I¤u¤¤i §-¤§¤th°G
± 3σ x = ±3 σ n = ±3 2. 0 4 = ±3.0mm

4¤A¨-

bP÷v¤§±ó¤UA-§¤t--¤-§O-¤t--UAW dA¤±-§§@§P_AS§O`N] 18^¤§YA¨-M¤ PA]§±-t¤T-t§@°¤t--A±NùP¤§XvC [¨ 16]CNS 3090[wV¤g ]WwV¤g¤§±j×G¨ ¤UC¨-n¨DG ±ó¤ ó¤@±jפ§G¤±o§Có @G fc’-35 kgf/cm2 C
2-36

±ó¤GGósò¤T±j×G¤§-§-¤±o¤póW w±j× fc’C -YY¤u{¤§Ww±j×fc’ ] ^° 210 kgf/c m2A
Hü¤u{¤§ê-pV¤g§±jפ§ t (m)° 30 kgf/cm2C°F¨ì

CNS 3090 ¤§¨ -n¨DAV¤g¤§-n¨D-§±j×]°t¤ ±j×^ (fcr’)AH§@°°t¤]-p¤I¤u±±¨¤§ C G (1) °]¤\o¤X¤W-z¨±ó¤§÷v§° 1%C ]ùG°ê¤V¤gWd¤jh¤ü°êV¤g|] ACI^WdA ACI-318V¤g]-pWd [20]]we-z÷v° 1%^ (2) ±`A¤°tí (í13)AHn÷v 0.99¤d±o¤§ z=2.33A§Y ¨-§-¤¤U---° 2.33m (°\ 17)C ùG1-0.01=0.99A Pez2.33f=0.9901A°± 0.99AG±z=2.33A -Y-n§óT-i¤tk¨D¤§Ai±o z=2.326C¨¨ CNS 12891[V ¤g°t¤]-ph ][16]¤§Ww± z=2.33C (3) ±`A¤°t±o-nX±ó¤@ A-n¨D-§±j×° (°¨ 17.a)G fcr’=fc’ -35+2.33m (19) N¤J-±oG fcr’=210-35+(2.33)(30)=244.9245 kgf/cm2 (4) (18)Aósò¤T-§±jפ§t°G
σx = σ 3

(20) ¨ 17.b G ^ (21)
σ 3

(5) ±`A¤°t±o-nX±ó¤GA¤§-n¨D-§±j×°]° fcr’=fc’+2.33 σ
x

=fc’+2.33

=fc’+1.34m

N¤J-±oG fcr’=210+(1.34)(30)=250.2250 kgf/cm2 (6) °òów{A¨ú (19)P(21)¨G¤§-¤jA§Y G fcr’=250 kgf/cm2 (19)P(21)¨§¤J CNS 12891[V¤g°t¤]-ph ][16]B ¤g¤ì¤§Q |V¤g¤u{I¤uWd [10]¤CNS 3090[wV¤g][14]Wd¤¤C (19)P(21)¨iXA]w~è{¤T]A¤Cp¤UG a. W--Gp(19)¤§ fc’-35P(21)¤§ fc’ -q±`¤u{Wd]wC C
2-37

b. s{à¤OGp (19)¤§mP(21)¤§ σ
¨ MwA

x C -q±`¨t°¤§¤u{à¤O

CNS 12891WwHLhìü¤u{¤§sò¤T¤QH¤W¤§ GtCC c. i§¨ü¤§±vGp (19)P(21)¨§± 1%A§Y°2.33-tC -q±`¤u{Wd¨¤u{¤§--n ¨MwA--nV°i§¨ü¤§±v V§CC
0.016 0.012 0.008 0.004 0.000 150
Ι=1%

2.326σ
35 175 210

σ=30

f'cr = ? 300 350

200 250 f 'c (kgf/cm2)

(a) -§O-¤§±`A¤°t

0.024 0.020 0.016 0.012 0.008 0.004 0.000 150
Ι=1% 210

f'cr = ? 300 350

200 250 f'c (kgf /cm2)

(b) -§-¤§±`A¤°t 17 V¤g-n¨D¤§-§§±j×
2-38

¤B¨ 6.1 ¨§-z ~è¨ó 1924~ Dr. ShewhartXAG¤SShewhart ChartC¤u{I ¤ug±`ú¤[A±NP¤@~èS¤§¨CG¨§b¤@y ¤WAiHs¨¤@°§C°_¤§§éuAú~è¤pAtH-p-ì z] m¤W¤U¨--¤¤¤¤uA§Y§¨~è¨Aí§±`HAiH§Y± ¨ú±IC~è¨S§OAó¤jq¤sòs¤§§÷I¤uC vT~褤§]hAH¨o÷v¤vT{×i¤°¨¤j G

(1) H÷-ì]]÷J-ì]A random causesGp§÷b¤tdò¤¤ ^ \¤B¤t§B¨ú¤H÷~tC¨¨hA ~èvTLA-n§°¤gA¤@¤¤°l¨sC¤u{Wd q±`|{H÷-ì]¤°_¤§~è¤A¤\-Y¤z¤tC (2) §±`-ì]]i¨s-ì]A assignable causesGp ù§÷B§÷°t¤è ^ ù~B÷±±±B§@ù~B¨ú¤èk¤C¨o÷|¤ hAU¤@o~èvTY-A§Y°l¨s-ì]¨§@§C ~訤§~bó°úO§_u§±`-ì]vsbA¨~§P_¤§ ¨C q±`H¤¤¤u] CL^¤§¤W¤UU¤T-t] CLm^°¨-- ([\÷ 3 vù 99.74%)A±-ni]m¨--° CLmAH°¤F±×A 2 ¤]|W[ò±i× (]°¨I§óeWX¨--Aià±NH÷-ì]¤§¤ ~§P°§±`-ì]¤§¤A~o°T¤°_¤u§@¤H-ò±i )C ¨¤§§PY±-pw-ìzAH÷v ±ís{°±`AY{ H¤§X{÷|§C]q±`]w°¤pó 1%^ApGX{{HA§-N§Pws {§±`¤FC¤@í¤UC¤T{H¤§¤@Ai§Pw§±`-ì]sbA°l¨s§ ]°¨ 18^ (1) ó¤@I¨b¨--H~ (± CLm°¨--As{±`A 3 ¨X{÷v¤pó 1%)C (2) sò¤CIX{b¤¤¤u¤§¤W¤UC (3) sò¤CIX{ùò¤W¤ùò¤U-°C ùGBC|°§PWhA¨¨¤@¤u{¨A§ó§P Wh°\~±MAp°¤m [3]C ¤i¨¨ìA±Wh§Y iGAígiAi¤@¨B{± §ó§PWhC

2-39

60 55 50 45 40 35 30 25 20 0 60 55 50 45 40 35 30 25 20 0

UCL CL LCL

2

4

6

8

10

12

14

16

(a)¤@I¨ó¨--H~ UCL CL LCL

2

4

6

8

10

12

14

16

(b)sò¤CI¨ó 60 55 50 UCL 45 CL 40 35 LCL 30 25 20 0 2

CL ¤§¤W¤U

4

6

8

10

12

14

16

(c)sò¤CIùò¤W¤ùò¤U-°

18 ¨§±`{H¨

2-40

6.2 -§- -Z¨ -§-Z¨] x R Chart^AY-§-¨] x Chart^P Z¨] R Chart^¨X¨Aq±`Aó 1n10±pC-§-¨ó ¨~褧°¤¤AZ¨ó¨~褧÷{×Cs{¨y¨ s{-w]Z¨^AA¨D-§-ùzQ]-§-¨^A pvA--n¨Dx¤ ¤g-nA¨uI±oH°¤¤AMá¤~ ù¨uIR¤¤v¤C ¨úU--§¤§-§ (x )P¨úU-Z¤§§Z ( R )UCLB CLBLCL¤T±¨uA x P R ¨Dkp¨ 17C [¨ 17] ÷HYwC-±¤u{¤§wC§tqG°¨ s§@-§- M -Z¨C G (1) `°H±`s{êA¤ 10C¨ ±e¤Q¤éê°¨A Hsò¤G-G°¤@Apí 14C ùGbsy~¤Ws§@¨Aq±`-n¨D 25H¤WA¤@¤u{ò ±o¨°A±`H¤-q¨--A¨~§Pv°Ayb nhá-s°Q¨--C (2) -pU-§MZ]pí 14 C ^ í 14 x R ≡≠…∨ No. 1 2 3 4 5 6 7 8 9 10 wC§tq,% R x x1 x2 =(x 1+x 2)/2 =|x1 -x2 | 5.63 5.33 5.480 0.30 5.60 5.85 5.725 0.25 5.18 5.58 5.380 0.40 5.65 5.40 5.525 0.25 5.55 5.61 5.580 0.06 5.38 5.49 5.435 0.11 6.05 5.69 5.870 0.36 5.12 5.54 5.330 0.42 5.58 5.47 5.525 0.11 5.90 5.60 5.750 0.30 X-p 55.600 2.56
1 n x i = ∑ ( xi ) r n r =1

Ri=(xi)max-(xi)min n=¨C (xi)1,(xi)2,K i)3 ,(x = i¤§ n - (xi)max,(xi)min = i¤§ n - ¤¤¤§ ¤j-P¤p- Ri= i-Z

2-41

(3)¤§O-p-§¤§-§ ( x )¤-§Z ( R )G
1 k x = ∑ x i = 55 .600 / 10 = 5.56 k i =1
R= 1 k ∑ Ri =2.56/10=0.256 k i=1

k= (4)-p-§¨¤§¨-¤¤¤uGCL = x = 5.56

G (22) (23) (24) (25) (26)

LCL ¨¤U--G = x A2 R = 5.56 (1.880)(0.256) = 5.08 (5)-pZ ¨¤§¨-- G ¤¤¤uGCL = R = 0.256
UCL ¨¤W--G = D 4 R = (3.267 )(0.256 ) = 0.84

¨¤W--G = x + A2 R = 5.56 + (1.880 )(0.256) = 6.04 UCL

LCL ¨¤U--G = D3 R = (0 )(0.256) = 0. (27) (6)s¨] 19 A¨UI§L 18¤§§±`±§As{¤w§e^ wAiTw¨--AHá¨CW[¤@ê§Y¤¤JA¨H°Q ¤§@-n¤§-×C

ùG(22) (27)¤¤¤§ A2B D3B D4 °¨YAidí 15 ±o¤§C H¤W¨YOH-p-ìzoA ¨D± ¨¨uP¤¤¤uZ ¤T-t¤§YC í 15 -pq-¨Y ¨C n 2 3 4 5 6 7 8 9 10 A2 1.880 1.023 0.729 0.577 0.483 0.419 0.373 0.337 0.308 ¨Y D3 D4 0 3.267 0 2.575 0 2.282 0 2.115 0 0.076 0.136 0.184 0.223 2.004 1.924 1.864 1.816 1.777

2-42

-§- ( x )

6.20 UCL=6.04 6.00 5.80 5.60 CL=5.56 5.40 5.20 LCL=5.08 5.00 0 1 2 0.9 0.8 UCL=0.84 0.7 0.6 0.5 0.4 0.3 0.2 CL=0.256 0.1 LCL=0. 0 0 1 2

3

4

5

6

7

8

9

10

11

12

ZR) (

3

4

5

6 7 §

8

9

10

11

12

19 wC§tq x R ≡≠

6.3 -§O--°Z¨ -Y¨úWv§CAB¨Càò±o¤@- n=1 ±p G]§Y A ^ i±-§O- X°Z¨]x Rm Chart A¨-§O-]x^°U ^ ¤§GA°Z] m ^°eá¤GG¤§t-C R [¨ 18] ÷Hí 6 ¤§e¤Q-ú-§O- X°Z¨¤§s §@C G (1) -pUIêpí 16C

2-43

í 16 x Rm ≡≠…∨ No. 1 2 3 4 5 6 7 8 9 10
X-p

G-§O- x 255 253 264 298 285 272 233 215 173 204 2452 Rm Chart G ^

¤GI°Z Rm


2 11 34 13 13 39 18 42 31 203

(2) -p°Z¨]

¤¤¤uGCL = R = 203 / 9 = 22. 6

LCL ¨¤U--G = D3 R = (0 )(22.6) = 0. (30) ùG¤W¤¤°¨Y ¤ D4Aí 15 ¤§ n=2 Cd±oC D3 (3) -p-§O- ¨] x Chart G ^ q±`¨--±u CLmvA]°-§O-¨¤±P]ùG¤± 3 Püs{¤wo¤A¨|LX{§^AG±`±u CLmv§@° 2 ¨--AH°±P×A-pp¤UG

UCL ¨¤W--G = D 4 R = (3.267)(22.6 ) = 73.8

(28) (29)

¤¤¤uG CL = x = 2452 / 10 = 245.2 ¨¤W--G = x + 2σ = x + UCL ¨¤U--G = x 2σ = x LCL d2Aí
2R 2(22.6 ) = 245.2 + = 285.3 d2 1.128

] 31^ (32) (33)

2R 2(22.6) = 245.2 = 205.1 d2 1.128

10 ¤§ n=2 Cd±oC

(4) s¨Ap 20A-§O-¨i¨¤TIWX ¨--A s{|¤-wAyA[±j¨As{-wá¤~Tw¨ --C
2-44

310 290 UCL=285.3 270 250 230 CL=245.2 210 190 LCL=205.1 170 150 0 1 2 3 100

-§O-]x)

4

5

6

7

8

9

10 11 12

°Z] Rm ^

80 60

UCL=73.8

40 CL=22.6 20 LCL=0. 0 0 1 2

3

4

5

6

7

8

9

10

11

12

s 20 V¤g§±j× x Rm ¨

2-45

6.4 ACI V¤g§±jר °°¤u{~¤§-nA|ioiUA ¤§Sí¨Apü°êV ¤g| ACI 214e-| [19]§Y°tXACIV¤g]-p¤I¤uWdoiX¤@Sí ¨A-§O-¨] x Chart^B°-§-¨] x m Chart^¤° -§Z¨] R m Chart^¤T-X¨AH¤U±NH[¨19]úACIV ¤g§±jר] 21^¤§s§@CUúp¤UG (1) -§O-¨] x Chart G ^ ¤¤¤§êI°é±j×AsUG]P¤G餧-§-^ ¨§éuAHG¤§°§C¤A¤¤Ww±j×] fc’ ^¤-n -§±j×]°t¤±j×^] fcr’ ^C (2) °-§-¨] x m Chart G ^ ¤¤UI°esò¤-G¤§°-§A¨pH¤@¤- G¤§-§AIX¤@-°-§±j×FH¤G¤G ¤§-§AIX¤G-°-§±j×FH¤U±Ci±jפ¨ Bg¤Có¨úsòX¤§°-§Ai-×-nwC ¤¤-n-§±j×]°t¤±j×^] fcr’ ^C (3) °-§Z¨]
R m Chart G ^

¤¤UI°esò¤Qé±jפ§°-§ZA¨pH¤@ ¤Q¤§-§ZAIX¤@-°-§ZFH¤G¤Q¤@¤§-§ ZAIX¤G-°-§ZFH¤U±Ci±K×A §@°§P_¤§¤¤§C¤¤êuYHí 9¤§¤§ uiHv ° ¤W-5%] V=0.05^A¨-pp¤U G
Max.R m = σ 1 d 2 = ( fcr 'V1 ) d 2

(34)

¤¤A R m ×°-§Z¤§\i¤j- Max. m1פt fcr’ =-n-§±j×]°t¤±j×^ V1=¤§YAB]w°.05 0 d2=-pYA¨¤@餧- (n)¨Mw]dí 10^ -Y¨C¨-éA n=2Ad2=1.128 Max.R m × (0.05)(1.128)fcr’ =0.05640Dfcr’ (35) -Y¨C¤T-éA n=3Ad2=1.693 Max.R m × (0.05)(1.693)fcr’ =0.08465Dfcr’ (36)

2-46

[¨ 19] ÷Hí6 ¤§V¤g§±j× êús§@ACI V¤g§ ±jר¤§L{C ¤wI¤u-n¨D±óp¤UG (1)Ww§±j×G fc’ = 210 kgf/cm2 (2)¨D-§§±j×G fcr’= 250 kgf/c m2]°¨ [¨ 16]^ G ¨BJ 1.-píApí 17C ¨BJ 2. ACI V¤g§±jרAp 21AU °up¤UG (1) -§O-¨G Ww§±j× fc’= 210 kgf/cm2 ¨D-§§±j× fcr’= 250 kgf/c m2 (2) °-§¨G -n-§§±j× fcr’= 250 kgf/cm2 (3) °-§Z¨G
Max.R m =0.05640fcr’= (0.05640)(250)=14.1 kgf/c m2

¨BJ 3.¨Cò±o§iáA§Y±Né±jפJí ¤§ (1)(2) 17 ¨C ¨BJ 4.-pU¤§G]-§PUé±j× A¤J(3)¤ ^ 21C pG (260+249)/2=255]±|±¤-¤J^ ¨BJ 5.-pU¤Gué±jפ§ZA¤J (5)C pG 260-249=11 ¨BJ 6.nF¤-}lAv-pe¤-G¤§°§±j×A¤J(4)¤ 21C pG (255+253+264+298+285)/5=271.0 ¨BJ 7.nF¤Q}lAv-pe¤Q¤§°-§ Z¤J(6)¤ 21C pG (14+11+17+15+19+12+18+21+8+12)/10=14.7 ùGH¤WYH¤¤u-p¤úL{Aê°¤Wy±qB¤ AH°vA¨§± EXCEL -p¤ C¨¤§B±j§YA±¨úêH¨ìH¤ ¤èA-Y§±`§Y§C¤iH¨áw°¤¤sAà C
2-47

í 17 ACI¨-pí]¤-I°-§ (1) No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 (2) (4) ¤-I° G -§±j× x xm 255 253 264 298 285 271.0 272 274.4 233 270.4 215 260.6 173 235.6 204 219.4 220 209.0 225 207.4 250 214.4 270 233.8 239 240.8 279 252.6 312 270.0 274 274.8 246 270.0 193 260.8 219 248.8 200 226.4 249 221.4 291 230.4 259 243.6 228 245.4 277 260.8 304 271.8 262 266.0 260 266.2 (3)

±j×^ (5) Z R 11 14 17 15 19 12 18 21 8 12 22 22 14 20 26 15 3 1 5 17 23 19 16 10 25 16 9 7 8 24 (6) ¤QI° -§Z
Rm

é±j× x1 260 246 255 305 294 266 224 225 177 198 209 236 257 260 226 286 313 274 243 184 230 209 241 286 271 220 272 307 266 248 x2 249 260 272 290 275 278 242 204 169 210 231 214 243 280 252 271 310 273 248 201 207 190 257 296 246 236 281 300 258 272

14.7 15.8 16.6 16.3 16.8 17.5 17.8 16.3 14.3 14.0 14.5 14.6 14.3 14.5 13.5 13.4 13.5 14.1 14.7 15.0 15.7

2-48

-§O-¨ -§O-¨ 2 §±j×]kgf/cm ) §±j× (kgf\cm2) 350 300 250 200 150 0 fc’=210 5 10 15 20 25 30 fcr’=250

¤-I°-§¨ ¤-I°-§¨ §±j×]kgf/cm ) §±j× (kgf\cm2) 2 350 300 250 200 150 0 fcr’=250

°-§Z]kgf/cm ) §-§¤Z 2 (kgf\cm )

5

10

15

20

25

30

¤QI°-§Z¨ ¤QI°-§Z¨ 19 18 17 16 15 V1=5% R m = 14.1 14 13 12 11 10 0 5 10

2

15 s s

20

25

30

21 ACIV¤g¨ (¤-I°-§- )

2-49

¨i°tX¤u{-×-n[H-×Aí 18¤22°°tX CNS 3090[14] ¤V¤gI¤uWd]¤g¤ì 402-88^[10]ACIV¤g¨§@¤§-×C¤§O úp¤UG (1) -§O-¨] x Chart]¨ 3±±±¨u ^ G ^ -§O-¨WCfc’-35°uA¤¤¤@I§Có fc’-35kgf/cm2A V¤gI¤uWd]¤g¤ì 402-88^[10]¤v§NWh[11]¤§-n¨DAìz p¤HT{¨iC (2) °-§-¨ ] x m Chart]¨ 2±±±¨u ^ G ^ °-§-¨§°¨úsò¤TI¤§°-§-A¤¤WC fc’ ° uA¤¤|I§Có fc’ AV¤gI¤uWd]¤g¤ì 402-88^[10]¤§-n¨D °Q-ì]¤°áò±j×C (3) °-§Z¨]
R m Chart ]¨ ^

4±±±¨u G ^

°-§Z¨¤§OCXíó¤§Y° 3B4B5M 6% ]°¨í 9^¤§°uA¨-¤§O° 8.5 11.3 14.1¤16.9 B B A-pL{p¤UG ] fcr’=250AGG Max.R m × fcr’(V 1)(d 2 )=(250)(V1 )(1.128)= 282(V1) HU¤--¤§ 1 N¤J¤WA¨D±o V Max.R m p¤UG V1 0.03 0.04 0.05 0.06
Max.R m

(36)

8.5 11.3 14.1 16.9

22¤¤i¨ 17IHe¤§¤§°u|ivu¤¨}v¤AM ±Kפ¨Cg§iáA 1827Ió-wAu|iv uiHv¤ A¨á¤S°°A-n[±j`NC

2-50

í 18 ACI¨-pí]¤TI°-§±j×^ (1) No. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 (2) (4) ¤TI° G -§±j× x xm 255 253 264 257.3 298 271.7 285 282.3 272 285 233 263.3 215 240 173 207 204 197.3 220 199 225 216.3 250 231.7 270 248.3 239 253 279 262.7 312 276.7 274 288.3 246 277.3 193 237.7 219 219.3 200 204 249 222.7 291 246.7 259 266.3 228 259.3 277 254.7 304 269.7 262 281 260 275.3 (3) (5) Z R 11 14 17 15 19 12 18 21 8 12 22 22 14 20 26 15 3 1 5 17 23 19 16 10 25 16 9 7 8 24 (6) ¤QI° -§Z
Rm

é±j× x1 260 246 255 305 294 266 224 225 177 198 209 236 257 260 226 286 313 274 243 184 230 209 241 286 271 220 272 307 266 248 x2 249 260 272 290 275 278 242 204 169 210 231 214 243 280 252 271 310 273 248 201 207 190 257 296 246 236 281 300 258 272

14.7 15.8 16.6 16.3 16.8 17.5 17.8 16.3 14.3 14.0 14.5 14.6 14.3 14.5 13.5 13.4 13.5 14.1 14.7 15.0 15.7

2-51

§±j× 22 (kgf\cm ) §±j×,kgf/cm

-§O-¨

-§O-¨

350 330 310 290 270 fcr’=250 250 230 fc’=210 210 190 fc’-35=175 170 150 0 5 10
¤TI°-§¨

15

20

25

30

2 (kgf\cm2) §±j×,kgf/cm

¤TI°-§¨

350 300 250 200 fc’=210 150 0 5 10 15 20 25 30
fcr’=250

§±j×

¤QI°-§Z¨ ¤QI°-§Z¨

§-§Z 2) 2 (kgf\cm °-§Z,kgf/cm

19 ¤¨} 1>6% V 17 15 |i V1=5~6% 13 iH V1=4~5% 11 9 n V1=3~4% 7 ¨ V1<3% 5 0 5

16.9 14.1 11.3 8.5

10

15 s s

20

25

30

22 ACIV¤g¨ (¤TI°-§- )

2-52

¤CBy

-p¤èkYH`°B¤R¤¤jq-ꤧ¤èkAOA -p¤èk¨DUàA°ò¤WH¤U--¨ A ¨`NG
1. -p¤èkAóiq¤¤§êC 2. -p¤èkMY[¤èkA-p¤RG¤§¤¤u{±M~-IA ¤u{~¤H-¨¤u§@¤§¤u{±M~°òA¤~àT§P-p¤R GC 3. zL-p¤Ri¤u{~èpAT]-pPI¤u¨ê° ¤~àTO¤u{~èC 4. ±-p¤R Tia¤§A§Y~gT¨ú¤ òB¤èks¨éB¨HWw¤èkA±o¤§gT¤§ -p¤R¤~¨êNqC -p¤èkb¤u{~¤§sA{¤¤@¤@¤u{±`÷A ~¤H-yH¤h[A§N¤~àùòiPmA-±¤W\h -p~yi¨Cy±N§YI¤§êA}liA ígAiAs§N¤@hC

2-53

°¤m [1] ¤[,1995,"-p§P¤èk",¤T§ ,x_ [2] M ,1981,"~訤§-p¤èk",¤¤°ê~è| [3] M ,1986,"~è¨",¤¤°ê~è| [4] ±iG°s,1989, "-p",¤-|ì¤j¨ ,xW°°§ ,x _ [5] xPH~-ì ,qW ,1979,"¤u{Mv,¤¤°ê¤g¤ì¤§Q " ¤u{| ,x_ [6] ±ièM ,1986,"¤°òO-p ",X ,x_ [7] ±ièM ,1986,"¤°òO-p¤R ",X ,x_ [8] ,1988,"-p¤èkb¤u{~¤W¤§ ",x_F±B¤u {§ [9] ¤¤¤¤,1997,"EXCEL óê¤RP-pB ",¤q,x_ [10] ¤¤°ê¤g¤ì¤§Q¤u{|1999,"V¤g¤u{I¤uWd , ",¤g¤ì 402-88 [11] ¤F,1989,"v§NWh " [12] CNS 1178-1987,"V¤g¤jk" [13] CNS 2580-1987,"L{¤¤¨~褧¨k " [14] CNS 3090-1994,"wV¤g " [15] CNS 9042-1982,"H÷k " [16] CNS 12891-1991,"V¤g°t¤]-ph" [17] Miller,I.and Engineers " Freund,J.E.,1984,"Probability and Statistics Statistics for for

[18]Walpole,R.and Myers,R.H.,1972,"Probability and Engineers and Scientists", Macmillan Publishing Co.

[19]ACI 214-77 ] Reapproved 1997 ^ ,"Recommended Practice for Evaluation of Strength Test Results of Concrete", ACI Manual of Concrete Practice 1998 Part 2 [20] ACI 318-1995,"Building Code Requirement for Reinforced Concrete" [21]ASTM D3665-1994,"Standard Practice for Random Sampling of Construction Materials",1998 Annual Book of ASTM Standards Vol.04.03

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