Downloaded from https://www.everyspec.com AMCP 706-196 with C' - C, or ignore X1L and use Eq. 2.30b Table 2-8 can be used in reverse to find with C' - C, Table 2-8 can also be used to how many failures must be observed for a find XL and XU. Example No. 6 illustrates given "accuracy" in estimation. For example, the procedure, if a 90% symmetrical s-confidence level is reasonable (95%-5%), then to get a ratio of Tho use of other tables is shown in Ar )u/• L of about 2 will require about 25-30 Six, Mathematical Appendix and Glossary. failures. Several of the tables are more convenient to use.
The ratio of ,/э depends only on Reliability estimates, One of the desirable ko, the failure at which the test is stopped. properties of maximum likelihood estimates It is very difficult to estimate X closely when is that they can be used in any function to there are few failures; see Table 2-8 for give a maximum likelihood estimate of the spec•tc infonation. function. The same is true for s-confidence limits when there is only one parameter In life tests, the total operating time of being estimated from the sample. Example all units (regardless of how obtained) is used No, 8 illustrates the procedure. in Eq. 2-29.
It makes no difference what kind of censoriug is used (if any) or whether failed items are replaced, or whether failed 2-3A4 a-NORMAL units are repaired. The only requirements are that X be a constant, iLe., the process is The continuous random variable x is the Poisson, and that the number of fUl',res is measure of failure resistance, e.g., time-to- not a random variable, This situation is failure or stress-to-failure. Occasionally, the related to par. 2-3.2 on the Poisson process; physical situation prohibits negative values that paragraph is used when the time is fixed of the random variable.
If the probability of and the number of failures is the random their occurrence is very small, the anomaly Is variabie. Example No. 7 illustratcs the pro- usually ignored; if It can't be ignored, consult cedure. a statistician, TABLE 24 s.CONFIDINCE LIMITS POR POIISON RATE PARAMETER IFAILURE RATE) For the stated #.confldence, and given that the test was stopped at failure ko, the body of the table Vives the fbotorm for 5% & 95% and for 2,5% 1h 97.5% ContI X > factor X X Iand the ratio of the upper to the symmetricallower limit. ko 1 a 3 4 a 6 a 10 15 20 WU 5% 8-onf. 3.0 2A 2.1 1,94 1,83 1.75 1.64 1,57 1,46 1.39 1,24 96% i.ionf.
0.062 0.18 0.27 0.34 0.39 0,44 0.50 0.54 0.62 0.66 0.78 56L 58 13 7.7 5.7 416 4.0 3.3 2.9 2.4 2.1 1.60 2.5% conf. 3.7 2.0 2.4 2.2 2.0 1.94 1.80 1.71 1.57 1.48 1.30 97.5% sconf. 0.025 0.12 0.21 0.27 0.32 0.37 0.43 0.48 0.56 0,61 0.74 NU/N. 146 23 12 8.0 163 5.4 4.2 3.6 2.8 2.4 1.7B Ewxanple. If the test Is run until the second failure, ) > 2.4 in 5% of the experiments and X >. 0.14A in 96% of the experiments; the ratio of the upper to the lower limit Is 13. I.e., the true ? is uncertain to within a factor ot 13, at th3 net s-confldence level of 90%. ......... ... ..