semi合集-English.pdf - 第474页
SEMI E67-0304 © SEMI 1997, 2004 9 # of cycles to 50% failure = 3000 from grap h µ * = LOG (# of cycles to 50% failure) µ * = LOG (30000) µ * = 4.477 # of cycles to 16% failure = 11000 from graph σ *= µ * − LOG (# of cycl…
SEMI E67-0304 © SEMI 1997, 2004 8
APPENDIX 1
RELIABILITY ANALYSIS
NOTICE: This appendix was approved as an official part of SEMI E67 by full letter ballot procedure.
NOTE 1: The method for reliability analysis provided herein is one of many possible methods which may be used. It is up to the
user to determine if this method or another (e.g., Weibull) is to be used for determination of MFC reliability.
A1-1 Reliability Analysis
A1-1.1 Almost all reliability studies of entities whose failure is unplanned, focus on the time until a small
percentage has failed (time until 10% of the population has failed, for example). Focus is on the left tail of the time-
to-failure probability distribution. Nelson’s book, Applied Life Data Analysis, (Wiley, 1982) gives a simple method
for estimating the time to 10% failure for a lognormal distribution (n = 2 to 10) from units put on test. Table A1
(from page 272 of Nelson’s book) can be used as follows:
A1-1.1.1 Calculate the % failed from the following equation:
Plot % failed vs. # cycles to failure for each MFC that failed on lognormal probability paper (see Figure 4).
A1-1.1.2 Estimate the mean, µ*, and the standard deviation, σ*, from the plot with the following equations:
A1-1.1.3 Calculate a 90% lower confidence limit for the (log of) 10% failure percentile (y
10
,
lcl
) from the following
equations:
y* = LOG (y
10, lcl
) =
µ
*+ t* [
δ
= 0.10, P = 0.10, n =# tested,
r
=# failed]×
σ
*
where t * is found from Applied Life Data Analysis, Table A1
y
10, lcl
= 10
y*
A1-1.1.4 Here is a sample set of data to illustrate the procedure.
i Cycles to Failure % Failed
1 6.3 K 8.3
2 15.8 K 25.0
3 25.1 K 41.7
4 40 K 58.3
5 63 K 75.0
6 did not fail did not fail
The % failed column was calculated from the equation in Section A1-1.1.1.
A1-1.1.5 See Figure 4 for a plot of this data.
A1-1.1.6 Use Figure 4 to calculate µ* and σ*.
SEMI E67-0304 © SEMI 1997, 2004 9
# of cycles to 50% failure = 3000 from grap
h
µ
* = LOG (# of cycles to 50% failure)
µ
* = LOG (30000)
µ
* = 4.477
# of cycles to 16% failure = 11000 from graph
σ
*=
µ
* − LOG (# of cycles to 16% failure)
σ
* = 4.477 − LOG (11000)
σ
* = 4.477 − 4.041
σ
* = 0.436
A1-1.1.7 From Table A1 (from page 272 of Nelson’s book), look up t*:
This data indicates, with a 90% confidence limit, that 10% of the devices will fail by 2443 cycles.
A1-1.1.8 Table A1 percentiles t* (d: 10, n, r) for limits for y
.10
.
n
φ
r
φ
pÆ 0.005 0.01 0.025 0.05 0.1 0.5 0.9 0.95 0.975 0.99 0.995
2 2 -183.9 -88.09 -36.3 -16.4 -7.869 -1.405 -0.327 -0.118 0.083 0.444 0.888
3 2 -117.6 -59.41 -26.14 -13.45 -6.786 -1.38 -0.495 -0.256 -0.0715 0.898 2.072
3 2 -17.6 -12.28 -7.761 -5.497 -3.691 -1.326 -0.473 -0.305 -0.154 0.047` 0.172
4 2 -113.5 -56.59 -21.5 -11.55 -5.934 -1.348 -0.537 -0.28 0.236 1.864 4.305
4 3 -15.58 -11.52 -7.112 -5.071 -3.503 -1.313 -0.558 -0.399 -0.252 -0.0573 0.107
4 4 -9.617 -7.008 -4.985 -3.792 -2.921 -1.29 -0.559 -0.409 -0.265 -0.124 -0.0141
5 2 -112.9 -48.61 -18.13 -9.49 -4.988 -1.322 -0.567 -0.182 0.519 2.436 5.585
5 3 -13.33 -9.911 -6.294 -4.598 -3.208 -1.306 -0.622 -0.463 -0.285 -0.00405 0.271
5 4 -7.956 -6.415 -4.652 -3.636 -2.778 -1.292 -0.624 -0.475 0.335 -0.173 -0.0587
5 5 -5.565 -4.871 -3.892 -3.184 -2.585 -1.287 -0.622 -0.472 -0.344 -0.202 -0.109
6 2 -76.15 -37.64 -17.14 -8.573 -4.669 -1.313 -0.57 -0.0928 0.779 3.427 6.336
6 3 -14.2 -10.33 -6.289 -4.393 -3.107 -1.303 -0667 -0.503 -0.323 -0.0332 0.375
6 4 -7.414 -5.87 -4.386 -3.487 -2.721 -1.302 -0.673 -0.546 -0.427 -0.286 -0.197
6 5 -5.45 -4.681 -3.746 -3.083 -2.498 -1.297 -0.673 -0.547 -0.44 -0.309 -0.219
6 6 -4.663 -4.012 -3.336 -2.826 -2.371 -1.3 -0.678 -0.546 -0.438 -0.322 -0.246
7 2 -68.12 -32.41 -15.19 -8.208 -4.34 -1.303 -0.561 -0.016 0.989 4.067 9.64
7 3 -12.82 -9.162 -5.602 -4.099 -3.005 -1.301 -0.71 -0.529 0.33 -0.0654 0.292
7 4 -7.571 -5.812 -4.171 -3.346 -2.622 -1.298 -0.722 -0.587 -0.464 -0.289 -0.12
7 5 -5.523 -4.604 -3.705 -3.034 -2.417 -1.295 -0.723 -0.595 -0.495 -0.361 -0.243
7 6 -4.636 -4.112 -3.351 -2.791 -2.32 -1.288 -0.722 -0.597 -0.501 -0.381 -0.294
7 7 -4.282 -3.693 -3.041 -2.641 -2.228 -1.285 -0.725 -0.595 -0.501 -0.376 -0.287
8 2 -63.58 -29.95 -13.34 -6.948 -3.728 -1.293 -0.472 0.226 1.645 6.157 14.5
8 3 -10.54 -7.628 -4.967 -3.637 -2.756 -1.297 -0.732 -0.549 -0.309 0.13 0.54
8 4 -6.59 -5.172 -3.937 -3.119 -2.484 -1.286 -0.752 -0.609 -0.468 -0.266 -0.11
8 5 -5.363 -4.296 -3.443 -2.885 -2.361 -1.287 -0.757 -0.629 -0.507 -0.358 -0.242
8 6 -4.515 -3.855 -3.22 -2.756 -2.282 -1.287 -0.758 -0.633 -0.514 -0.386 -0.306
8 7 -4.086 -3.583 -3.019 -2.602 -2.205 -1.284 -0.755 -0.632 -0.514 -0.399 -0.336
8 8 -3.781 -3.414 -2.851 -2.485 -2.162 -1.29 -0.757 -0.63 -0.514 -0.404 -0.338
9 2 -56.28 -30.29 -11.44 -6.353 -3.55 -1.314 -0.465 0.353 2.089 6.581 11.57
SEMI E67-0304 © SEMI 1997, 2004 10
n
φ
r
φ
pÆ 0.005 0.01 0.025 0.05 0.1 0.5 0.9 0.95 0.975 0.99 0.995
9 3 -11.84 -8.048 -5.062 -3.693 -2.704 -1.312 -0.739 -0.551 -0.304 0.209 0.744
9 4 -6.562 -5.165 -3.775 -3.043 -2.457 -1.31 -0.772 -0.64 -0.505 -0.3 -0.167
9 5 -5.034 -4.316 -3.446 -2.851 -2.318 -1.307 -0.777 -0.66 -0.548 -0.427 -0.326
9 6 -4.437 -3.901 -3.21 -2.714 -2.232 -1.305 -0.779 -0.663 -0.566 -0.444 -0.365
9 7 -4.103 -3.651 -3.08 -2.605 -2.177 -1.303 -0.78 -0.665 -0.57 -0.457 -0.373
9 8 -3.813 -3.408 -2.878 -2.49 -2.135 -1.3 -0.776 -0.665 -0.572 -0.459 -0.381
9 9 -3.624 -3.228 -2.752 -2.413 -2.067 -1.298 -0.78 -0.666 -0.571 -0.458 -0.396
10 2 -60.81 -27.39 -10.07 -5.683 -3.326 -1.299 -0.34 0.77 2.744 7.973 15.67
10 3 -9.675 -6.99 -4.618 -3.42 -2.572 -1.301 -0.758 -0.532 -0.255 0.306 1.018
10 4 -6.389 -5.028 -3.792 -2.993 -2.353 -1.297 -0.798 -0.657 -0.528 -0.332 -0.134
10 5 -5.258 -4.324 -3.357 -2.749 -2.257 -1.297 -0.801 -0.684 -0.581 -0.426 -0.315
10 6 -4.559 -3.701 -3.029 -2.569 -2.182 -1.294 -0.802 -0.689 -0.59 -0.488 -0.405
10 7 -3.838 -3.43 -2.853 -2.497 -2.121 -1.293 -0.803 -0.689 -0.593 -0.497 -0.428
10 8 -3.706 -3.173 -2.752 -2.401 -2.091 -1.292 -0.803 -0.688 -0.598 -0.502 -0.431
10 9 -3.458 -3.118 -2.636 -2.353 -2.046 -1.288 -0.804 -0.689 -0.598 -0.502 -0.438
10 10 -3.297 -2.996 -2.561 -2.284 -2.02 -1.29 -0.804 -0.693 -0.598 -0.501 -0.437
NOTE: Reprinted with permission from The American Statistician © 1979 by the American Statistical Association. All rights reserved.
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