This standard gives a method to determine the lower confidence limit RL of the probability R that the characteristic value X of a product that follows a normal distribution (mean and standard deviation are unknown) falls within a given limit (L, U). GB/T 14438-1993 Lower confidence limit of normal probability within a given limit GB/T14438-1993 Standard download decompression password: www.bzxz.net
This standard gives a method to determine the lower confidence limit RL of the probability R that the characteristic value X of a product that follows a normal distribution (mean and standard deviation are unknown) falls within a given limit (L, U).

National Standard of the People's Republic of China
Lower confidence limit of normalprobahility within specified limitgQuestion content and scope of application
GB/T 14438 -- 93
This standard gives a method to determine the lower confidence limit R of the probability R (see figure) that the product characteristic value X that obeys the normal distribution (mean and standard deviation) falls within the specified limit (L,). The distribution density function of X is: f(r) =
2Reference standard
a+ x
Schematic diagram of the normal probability R within the specified limit ()
GB 3358
Statistical terms and symbols
3Symbols
—population mean, x
—-population standard deviation.a0;
·A sample mean:
s——sample standard deviation+
1-lower specification limit;
upper specification limit;
The probability of a stopping state within the limit (1.), sometimes also called the lower confidence limit of performance reliability: R:
Xiao Confidence level, i.e. the probability of 1 falling within (x) #
The rate of X falling within (x):
Approved by the State Administration of Technical Supervision on June 10, 1993. (1)
Implemented on January 1, 1994
) Upper confidence limit:
pu ()——Confidence upper limit of ():
The force quantile of the standard normal distribution,
——Bilateral penetration coefficient.
4 Determination of the lower confidence limit of normal probability within the specified limit GB/T1443893
This standard provides two methods for determining R:, the table lookup method and the piece count method. The table lookup method is simple and easy to use. When the parameter exceeds the range of the table or in order to avoid the error of the value caused by the table, the calculation method should be adopted. 4.1 Negative table method
4.1.1 Steps
Calculate the coefficients and
according to the given sum. Calculate the text.
(3)
c. The given and calculated and are respectively checked in the table of normal distribution two-sided allowable limit coefficients in Appendix A of the standard to obtain () and (
The calculated lower limit Rt
R = 1 - (pc() + pt(U)
4.1.2 Example
Under certain production conditions: The mandrel diameter under the condition follows normal distribution, and the design requirement for the mandrel diameter is 20. Fifteen pieces are randomly selected from a batch of products for measurement. According to the measurement results, the sample mean and standard deviation are obtained: X -19.980
Given a confidence level of 0.80, calculate the confidence lower limit R1 of the energy reliability R that meets the design requirements and sum t:
t -- X - 1 - 19. 980 - (20 - 0. 05)s
— 2.000 00
ku = /-X_ (20 + 0, 03) - 19. 980 =3.33333
According to ? is 0.80 and is 15, use αt and αt to look up the table in Appendix A, and through linear interpolation, we get: Wrury
1. 415 83
— 2. 520 59
Use u and αt to look up the quantile table of standard normal distribution, and through linear interpolation, we get: GB/T 14438—93
Pu(L) = 0. 078 414
Pu(U) - 0. 005 867
The lower confidence limit of K for the core shaft diameter at a confidence level of 0.80 is: Ri=1-(Pu(L))+u(0)1-(0.078414+0.005867)-0.915719 0.916
4.2 Calculation method
The steps for determining the lower confidence limit of the probability mask of the stop state within the limit by calculation method are as follows: Calculate X according to (2) and (3), 5:
Calculate iu according to (4) and (5)!
Take and respectively solve the following nonlinear equations to get () and)ot
P(F/2)20 2/2L
Wu Zhong:(u)=
r=(8-a)/(/ /f-/ / )
fn—l
dCalculate the confidence lower limit RL of R according to formula (6).
Appendix B of this standard gives a BASIC program for solving RL suitable for IBM-PC i computers and compatible computers. (7)
A1 Parameter range and table distance
GB/T 14438—93
Appendix A
Table of two-sided allowable limit coefficients of normal distribution
(supplement)
Y0.50.0.60.0.70,0.75.0.80.0.85,0.90.0.95.0.991p-0.15,0.125,0.10(-0.01)0.01(-0.001)0.001,.0005.0.0001.0.00001:n=2(1)50(10)120.
The table gives the quantiles of the standard normal distribution. First, according to the calculated coefficient (or ratio), use the number table to linearly drag and get u (or uu), and then use the standard normal distribution quantile table to interpolate and get u(T) (or: (U)). Interpolation through intermediate variables can improve the interpolation accuracy compared to direct interpolation. A3 Normal distribution double allowable limit coefficient table
.150 00
1. 036 43
127.707 11
15.322 09
7. 61-1 44
1- 331 06
3. 430 95
3. 311 17
2. 170 85
2. 308 15
2.243 -15
2. 186 90
2. 136 96
2. 092 49
2. 052 58
1. y83 78
1. 426 40|| tt | 67
1. 64% 32
1. 639 26
1. 636 56
1. 622 21
1. 599 02
1. 584 53
1. 327 02
1 380 31
0. 125 00
1. 150 35
136.796 11
16.431 63
8, 204 65
5. 776 66
4. 655 25
4. 012 96
3. 302 59
2. 914 30
2. 778 32
2. 573 CO
2. 183 02
2. 14B 23| |tt||2. 116 46
2- 087 31
2. 012 55
1- 991 68
1- 971 [2
1. 917 09
1. 902 33
1. 887 53 |
1. 664 57
1. 618 91
1. 583 19
1.554 31
GB/T 14438---93
Normal distribution effective side penetration limit coefficient meter
0. 100 00
117.26:31
1.3-10 47
3. 892 17
3. 576 80
3. 342 03
#-013 98
2. 894 21
2. 634 66
2. 570 24
2. 518 89
2、46281
2. 376 51
2-334 33
2. 305 40
2. 194 46
2. 171 57
2. 093 65
1. 982 01
1. 960 24| |tt||1. 950 01
1. 9340 88
1. 901 82
1. 77> 61
1. 707 17
1. 631 21
1. 641 91
0. 090 00
151.98796
9- :17 15
6. 4-18 09
4. 4H9 G5
4. 026 55
3. 459 16
8-271 36|| tt | 48
2, 461 34
2. 126 67
2. 25: 48
2. 281 49
3. 173 36
2. the 30
2. 185 99
3. 124 6-1|| tt | 67 | |tt | 0 97 | 77
2. 745 39
2. 6h1 68
2. 520 62
2. 484 6H
2. 451 61
2. 367 03
2. 342 75 138 35
2. 097 91
2. 078 45
2. n69 28
2. 051 95
1. 925 11
1. 924 03| | tt | 05
19.618 26
5. 503 04
4. 825 54.
-1. 334 55
3. 986 57
3-526 95
3. 231 1 1
3-030 13
2-919 95
2. 815 86
2. 665 69
2. 621 53
2. 522 23
2. 441 22
2. 395 92 | |tt | .58415
. #64 1h
0. 060 00
169. cka 51
20. 354 47
10. 213 41
4- 154 24
3. 885 52
3. 677 19
3. 510 47
3-373 70
3- 259 21
3. 161 79
3. C04 36
2. 939 66|| tt||2. 741 81
2. 703 29
2. 635 4.
2. 577 60
2. 551 55
2. 527 32
2. 50-1 61 | t||2. 159 21
2. 104 78
2. 062 28
2. 027 97
1. 975 63
1..951 89
1. 611 85
176.25199
21.280 77
10.663 88
5- 258 36
4. 722 58
3. 312 ±8
2. 967 84| |tt||2. 875 55
2. 798 78
2. 764 67
2 G77 77
2. 652 60
2. 629 04
2. 566 52
2. 518 00
2. 530 47
2. 198 06
2. 183 05
2. 468 74
2. 442 06
2. 395 21
2. 355 32
2.213 95
2. 169 88
2. 134 31
2. 104 86
2. 079 97
2. 058 59||tt ||0. 040 00
-1. 750 69
184.t95 02
22.323 32
11.194 16
7. 909 67|| tt||6. 394 42
5. 527 98
4. 966 61
1. 279 00
1- 051 77
3-870 00
3-720 95
3. 318 74
3. 248 35
2. 091 34||tt| |2. 952 97
2. 917 65
2. 854 72
2. 775 64
2. 752 55
2. 608 29
2. 594 05
2. 551 97
2. b31 56
2609 96
2. 499 76
2. 489 95
2. 401 41
2. 206 60
2. 228 86
2. 202 04
2. 180 68||tt ||195.07587
23.606 59
11. 847 40
8. 376 73
6. 775 76
5. 267 601||tt| |4. 301 74
3. 952 74
3. 709 28
3. 227 65
3. 183 55
3. 143 17
3. 071 60
3. 039 72
3. 010 06
2. 956 47||tt| |2. 932 17
2. 909 31
2. 887 77
2. 867 42
2. 829 91
2. 796 09
2- 780 38
2. 751 09
2. 711 74
2. 699 69
2. 688 11
2. 676 97
2. 666 26
2. 655 93
2. 645 98
2 452 79
2. 381 67
2. 354 46
0. 020 00
208-87540
25. 314 77
12- 717 67|| tt||7- 284 26
6. 303 96
4. 262 02
4. 121 34
4. c01 72
3. 898 57
3. 808 60
3. 658 85
8. 695 72
3. 638 81||tt| |3. 140 09
3. 396 94
3. 357 23
3. 171 77
3. 147 39
3. 124 41
3. 102 71
3. 082 17
3. 044 22
3. 026 64
2. 978 68
2. 964 09
2. 936 71
2. 923 89
2. 911 55
2. 899 69||tt| |2. 888 27
2. 619 57
2. 585 31
GB/T14438-:93
2. 326 35
230.625 21
14.092 83
8. 088 59
7. 005 62
6. 304 48
5. 163 45
1. 937 11
4. 751 63
4. 596 51
4. 464 66
4. 251 86||tt| |3. 96± 74
3. 897 89
3. 734 50
3. 711 53
3. 677 11
3. 642 30
3. 699 82
3. 579 43
3. 524 12
3. 475 01
3. 131 05
3. 410 74
3. 322 71
3. 292 68
3-118·62
3. 016 39||tt ||2. 944 72
2. 907 18
2. 875 49
233.75846
28.400 12
14. 291 23||tt| |10. 125 74
7. 106 93
6. 396 23
5. 897 32
5. 010 31
4,665 14
4- 531 51
1. 315 87
4-227 36
1. 014 79
3 . 904 70
3. 812 32
3. 733 51
3. 631 55
3. 605 67
3. 578 51|| tt||3. 552 92
3. 528 76
3. 444 09
3. 344 06
3. 829 77
3-316 05
3-30285
3- 290 16
3- 277 93
3. 167 76
3. 094 60
2. 953 63
2-921 53
2-893 98
0,00800
237.213 03||tt| |28.828 90
14.510 04
10-282 44
7. 218 68
5. 951 14
5. 615 04
5. 323 84
4. 900 34
4. 740 84
4. 386 49
4. 216 92||tt ||4. 145 46
4. 081 05
4. 022 69
3. 969 37
3. 920 57
3. 875 67
3. 834 19
3. 795 73
3. 759 95
3. 726 58
3. 695 35
3 638 52
3.612 56
3- 522 03
3-502 19
3-483 29
3-46527
3. 448 06||tt| |3. 431 60
3-415 84
3:372 33
3. 358 95
3. 346 C8
3. 335 68
3. 321 72
8. 221 97
3. 147 79
3. 089 99
3. 043 -0
2. 972 32
241.070 57
29,307 80
14. 754 47
10. 457 50
8. 475 87
7. 343 54
6. 610 51
6. 095 97
5. 181 30
4. 825 43||tt ||4. 687 68
4. 568 91
4. 374 17
4-09571
4-G41 63
3-992 06
3-946 45
3- 964 31
3. 865 24
3. 828 90||tt| |3. 795 00
3. 654 31
3. 630 76
3. 608 44
3. 119 35
3. 421 63
3- 395 96
3. 282 52
3-20720
3. 148 51
0. 006 09
2. 512 15
215-149 36
23. 841 55
15.032 04
7. 185 34
6 . 738 94
6. 215 01
5. 283 80
4. 921 51
4-660 41
4. 555 01|| tt||4+ 12 16
1. 379 Gf
4. 305 77
4-239 18
4. 178 77
4. 123 71
4. 673 26
. 526 84
3. 944 20
3. 872 72
8. 844 44
3. 810 17
3. 781 70
3. 729 55
3. 705 59
3. 661 31| |tt||3. 640 81
3. 621 28
3. 602 66
3. 567 87
3. 551 69
3. 535 98
3. 521 (1
3. 506 63
3. 492 81
3. 479 51||tt ||3. 466 70
3. 454 34
3. 351 29
3. 271 67
3. 214 96
3. 166 87
3. 127 07
3. 093 47
3. 064 63
2-575 83
250.530 61
30482 69
1535427
10.887 13
7. 650 00
6. 888 08
5- 648 58|| tt||5. 402 81
5. 201 45
5. 033 08
1. 889 98
4. 766 64
4. 659 08
4. 561 34
4. 480 16
4. 404 77
4. 336 82
4. 219 01
4. 167 54
4. 076 44
4. 035 88
3. 998 15||tt| |3. 562 96
3. 899 15
3. 870 12
3. 816 92
3. 769 31
3. 747 32
3. 726 41
3. 706 49
3. 687 49
3. 652 01
3. 635 11
3. 604 22
3. 589 56
3. 431 14
3. #53 01
3. 292 14||tt ||3. 243 09
3. 202 51
3. 168 26
3. 138 86
2. 652 07
256.61365|| tt||31. 238 48
15.740 21
11.163 62
7. 847 26
7. 066 74
6. 518 94
6, 112 08
5. 797 12
5. 339 17
5. 166 75||tt| |5. 020 21
14.893 90
4. 783 77
4. 686 75
4. 600 56
4. 890 71|| tt||4. 333 19
4. 187 23
4. 145 71
4. 107 10
4. 071 07
4. 005 76
3. 976 04
3. 921 69
3. 896 57
3. 872 86||tt| |3. 850 35
3. 808 56
3. 789 12
3. 770 56
3. 752 81
3. 735 81
3. 719 53
3. 674 47
3. 660 58
3. 446 84
3. 257 84
-2.747 79
264. 250 25
32.187 61
16.224 97
11.510 95
8. 095 09|| tt||6. 727 06
5. 334 70
4840 57
4. 600 79
4. 475 65
4-422 42
4. 243 97
4. 109 11
4. 080 30
4. 053 09
4. 002 95
397979
3. 936 80
3. 916 80
3. 879 44
3. 845 20
3-813 69
3. 798 85
3.784 56
3. 646 94
3. 564 72
3-500 67
3. 449 06
3- 339 43||tt ||GE/T 14438—93
2. 878 17
274.65308
33. 481 06
16.885 75
11. 984 47|| tt||8. 433 01
7. 597 31
6. 575 35
6. 238 25
5. 968 88
5. 748 21
5. 271 86
5. 154 07
5. 050 31
4. 958 14||tt ||4. 875 60
4. 801 22
4. 733 76
4. 672 27
4. 615 94
4. 516 25
4. 471 88
4. 430 61
4. 392 11
4. 290 56
4. 260 64
4. 232 38
4. 180 33
-1.133 42
4- 111 64
4. 052 09
4. 033 94
3. 968 42
3. 953 60
3. 939 32
3. 725 41
3. 658 95| |tt||3. 605 39
3. 491 64
0. 001 00
291.57267
35.685 88
17.961 36
10-354 72
8. 983 29
8. 095 78
7:473 04
6 . 652 73
6. 132 54
5. 936 74
5. 770 36
5. 391 90
5. 294 11|| tt||5. 056 07
4. 990 85
4. 931 10
4. 778 31
4. 734 54
4. 693 71
4. 619 70
4. 586 03
4. 524 35
-4. 469 16||tt ||4. 443 67
4. 333 21
4. 295 54
4. 077 43
3. 916 61
3. 812 97
3. 773 38
307.55345
37. 574 99
18. 978 17
13.484 33
10,9589
8. 567 22
7. 122 31
7. 044 76
6. 496 05
6. 289 54
6. 114 07
5. 962 87
5. 714 98
5. 519 54
5. 136 35| |tt||5. 171 22
5. 117 71
4. 978 94
4. 900 94
1-865 45
4. 832 02
4. 800 45
4. 715 43
4. 689 89
4. 665 56||tt| |4. 620 22
4. 599 05
4. 559 35
4. 505 62
4. 489 06
4. 473 12
4. 457 75
4. 234 35
4. 009 38
3. 973 61
3. 719 02
341.741 12
41. 833 11
21.155 69
15.045 71
12.228 09
10.618 67
9. 577 33
7. 8B4 80
7. 274 99
6. 682 61
6- 536 19
6- 292 73| |tt||6. 190 21
6. 097 83
6. 014 06
5. 937 72
5. 867 79
5. 744 06
5. 590 04
5. 503 48
5. 426 99||tt| |5. 358 8a
5. 327 44
5. 146 04
5. 124 49
5. 083 97
4. 764 10
4. 681 91
4. 615 70
4. 514 76
4. 475.13
385.294 48
47. 261 93
23. 933 11
17.037 77
10. 042 23
9. 430 38
8 . 578 84
7. 601 22
7. 161 71
6. 942 03
6. 847 63
6. 761 60|| tt||6. 682 81
6. 543 39
6. 423 67
6. 319 55
6. 272 36
6. 228 00
6. 146 76
6. 109 44
6. 040 51
6. 008 60||tt| |5. 978 21
5. 895 12
5. 869 80
5. 778 44
5. 757 76
5. 114 73
25-521 64
6. 765 15
4. 340 49
2. 977 54
2. 687 46
2. 488 20
2. 341 84
2. 065 58
2. 003 93
1. 951 43||tt| |1. 966 07
1. 746 82
1. 665 51
1. 648 98
1. 619 30
1. 581 64
1. 570 42
1. 559 92
1. 540 57
1. 51§ 02
1. 507 29
1. 499 91
1-467 40
1-456 11
1- 445 63
1- 440 67||tt| |1- 435 87
1.395 48
1. 464 99
1. 340 96
1. 921 41
1. 305 11
1-291 25||tt ||1. 279 30
1-66265
3-205 96
2, 684 11
2. 408 33
2. 113 32
2. 023 16
1-92332
1. 896 51
1. 849 85
1. 829 39
1- 761 70
1. 747 55
1. 734 30
1. 721 84
1. 699 02||tt| |1. 688 54
1. 678 61
1. 669 18
1. 635 75
1. 621 19
1. 614 36
1. 607 81
1. 589 63
1. 578 60
1- 568 32Www.bzxZ.net
1. 468 57
1. 448 04
1. 416 42
1. 403 88
.10000
29-43115
5. 035 35
3-47058
2. 911 17
2. 744 33
2. 513 89
2. 430 30||tt| |2. 300 97
2. 249 67
2. [30 10
2. 09R 51
2. 069 97
2. 020 33
1. 996 58
1. 959 96
1. 926 65
1. 911 63
1. 897 55||tt ||1. 884 33
1. 871 87
1. 849 00
1. 838 47
1. 809 90
3. 777 59
1. 763 42
1. 756 75
1- 732 48
1- 726 95
1- 721 61
1- 676 ​​67
1. 616 14
1. 594 47
1- 561 10
1. 547 88||tt| |GB/T14438—93
8. 083 57
5. 204 01
4. 143 13
3. 590 43
2. 333 25
2. 287 18
2. 246 53
2. 210 34
2. 177 88
2. 148 55
2. 121 91
2. 097 56
2. 075 22
2. 054 62
2. 001 36||tt| |1. 985 94
1. 971 49
1. 945 14
1. 900 59
1. 890 84
1. 864 23
1. 833 86
1. 827 03
1. 814 12
1. 808 03
1. 796 48
1. 791 00
1. 744 93
1- 660 72
1. 642 24
1. 626 55||tt| |-1. 405 07
3. 720 91
3. 367 90
2. 701 29
2. 615 64
2. 511 57
2. 424 26
2. 264 29
2. 137 47
2. 000 76
1. 989 65
1. 979 10
1. 969 08
1. 877 96
1. 872 14
1. 866 51||tt| |1-71383
1. 697 74
32.529 07
8. 671 04
5. 589 66
4+455 22||tt ||3. 499 55
3. 249 50
2. 521 55
2. 475 60
2:432 42
2. 359 52
2. 328 40
2. 300 12
2. 274 30
2. 250 61||tt| |2. 189 79
2. 126 29
2. 099 98
2. 065 60
2. 045 45
2. 018 57
2. 010 38
2. 002 54
1. 995 01
1. 974 13
1-955 48
1+949 69
1. 864 38
1. 812 15
1. 761 86
1. 554 77||tt| |5. 815 75
4. 638 28
2. 936 11
2. 762 14
2- 691 85
2. 586 17
2. 501 75
2. 166 11
2-353 51
2-330 94
2. 290 67
2-272 60
2. 255 73
2- 239 92
2. 225 06
2. 211 08||tt| |2. 197 89
2. 173 60
2162 38
2. 141 58
2. 131 90
2. 097 28|| tt||2. 089 51
2. 082 05
2. 067 97
2. 061 32
2. 054 91
2. 048 72
1. 054 76
1. 925 04
1. 849 09
-1.644:85||tt| |4. 209 48
2. 825 41
2. 554 55
2-323 45
2. 251 43
2. 205 54
2. 197 49
2. 161 66
2. 155 25
2. 057 99
2. 027 25
1. 981 51
1. 963 89
1. 948 70
-1.750 69
6. 377 95
3. 366 83
2. 861 39
2.813 01
2. 769 98
2. 664 95
3. 636 09
2. 609 60
2.-541 68|| tt||2. 503 94
2. 486 86
2. 470 82
2. 455 73
2. 441 43
2. 428 02
2. 415 27
2. 403 17
2. 351 68
2. 380 73
2. 350 81
2. 341 70
2. 332 96
2. 324 59
2. 316 54
2. 308 81||tt| |2. 301 87
2. 294 20
2. 220 13
2. 179 47
2. 147 50
2. 099 97
2. 081 66
-1.880 79
38.968 27
10. 438 89
6 752 21
5. 396 97
4. 692 71
4. 258 01
3. 576 59
3- 245 39||tt| |3. 044 79
2. 993 94
2. 948 70
2. 90R 16
2. 780 22
2. 754 60
2. 708 90
2. 588 12
2- 669 28
2. 651 36
2. 644 53
2. 618 69
'2. 603 75
2. 589 62
2. 576 24
2. 540 01||tt ||2. 518 61
2. 508 63
2. 499 07
2. 489 91
2. 481 13
2-47270
2- 464 59
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11. 195 80||tt ||7. 250 63
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GB/T14438—93
46.094 115
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4-36184
1- 201 44
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4-43218
4-27255
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52.815 J0
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14-81318
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5-49678
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GB/T14438—93
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1827 89
1-81609
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282855
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GB/T14438—93
8-637 33
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0. 008 00
6. 412 65
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3- 741 72
3-66316
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319953
3. 186 92
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2-25017
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GB/T14438—93
8-637 33
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24.040 48
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3. 809 00
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319953
3. 186 92||tt ||3. 174 91
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2-25017
2-242 38
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2. 334 08||tt| |2-32850
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GB/T14438—93
8-637 33
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2-278 56
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3. 186 92||tt ||3. 174 91
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