Downloaded from https://www.everyspec.com AMCP 706.498 TABLE 2.11 plicated to find the fraction of occasions the correct decision will be made. CALCULATIONS FOR RELAY FAILURE PROBLEM In many cases, the parameters of the hypo- Cmli BsundatIU Numbr In Cell thetical Cdf will be estimated from the sample Ino- n,) (test) data. Under these circumstances the Obsered Expected n critical d-values in Table 2-1 2 are too large and St C ( s) n o f will lead to higher s-confidence levels than anticipated (higher than specified in the table). 0,9 1,46 3 ,26Results of Monte Carlo investigations have 0.9 1.46 3 5 1180 ! 0.8 3.09 7 5 0.80 shown that the following rule-of-thumb adjust.
0.7 4.93 7 5 0.80 ments to Table 2-12 can be made to yield good 0.6 7.07 7 5 0180 critical values for the s-normal and exponential 0.6 9.59 3 5 ,so distributions (Ref. 3). 0.4 12.68 7 5 0,80 0.3 16.65 4 5 0.20 5. In step 4 when estimating mean and 0.2 22.26 4 5 0,20 standard deviation of a s-normal distribution 0.1 31,85 7 o 0.80 from the test data, multiply the value of d 0- from Table 2-12 by 0.67, When estimating 50 50 9.20 the mean life for an exponential distribution, multiply the value of d from Table 2-12 by 0.80. a. Compute the hypothetical Cdf as Fhyp (xr).
Another way of using the Kolmogorov- b, Compute the sample Cdf as FH * PIN and as F, a (r -- I)/N, where N is TABLE 2-12 the sample size, and r is the order number of the sample point. CRITICAL VALUES d OF THE MAXIMUM ABSOLUTE DIFFERENCE BETWEEN SAMPLE c, Calculate d,, the absolute vAlue of AND POPULATION FUNCTIONS FOR THE the maximum difference between the 2-IDED K-S TEST sample and hypothetical Cdf'q. Do this by (ADAPTED FROM RIF. 3) finding IFhyP (x,) - F",,Il and IFhyp, (x,) - FL, I; the larger one is d. Semle &Canficam Level 3. Find d,,.,, the largest d, (over all )N 0% abV. 9% 91% 99% in step 2c. 4 0.49 0.52 0.56 052 0.73 5 0.45 0.47 0(51 0.58 0.67 4.
Find the critical value d from Table 10 0.32 0.34 0.37 0C41 0.49 2-12 for the sample size and the selected 15 0.27 0,28 0630 0.34 0.40 s-confidence level. If d,,,mx 4 d, accept the 20 0.23 0.25 0626 0.29 0635 hypothesis that the observed sample could 25 0.21 0.22 0.24 0.27 0.32 have come from the hypothetical distribution 30 0.19 0,20 0.22 0.24 0.29 Fh, (x); otherwise, reject the hypothesis. If 35 0M1 0.19 0.20 0.23 0.27 the s-confidence level Is C, the correct decision 40 0617 0618 0.19 021 0.26 will have been made ort the fraction C of the 50 0.15 0M1b 0.17 0.19 0.23 occasions the test is used when the hypothesis N > 10 1.07 1., 1.22 1.36 1.63 Is true.
If the hypothesis is not true, It is corn- '. V+- . V'+