Downloaded from https://www.everyspec.com AMCP 706-190 S" (Z~xoj)/(Ljx() 2-61) [Ex? 1 2- ((2-66b) a j= , yj - (AI+ &)12)/N - 2)' = •lYl- )2 A•lx]/ny _ 2)•z= Zf•lY# - 5)(N -1 12) 6o (2.-62) The sampling distribution oL p is given in The uncertainties in b, k, and j" are Refs, 18 and 30 and elsewhere. For small measured by sample sizes, the uncertainty in p, given p, is distressingly large. For example, if p - 0 Var {b}) - 3/N and N - 10, then 5% of the time wil be greater than 0,57; or if э - 0.5 and Vari{m}. o 2 /({fxl) N - 10, 95% s-confldence limits on э are - 0.18 and + 0.84, Example No.
14 illustrates the procedure, Vae(Y*W)}- Var{g) + xVari{,} (2-64) 2-9 ACCEPT/REJECT TESTS-t TEST FOR where ;4* is a value of ; to be predicted MEAN OF A s-NORMAL DISTRIBU. from x. TION Tests can verify that an equipment meets Those uncertainties are usually estimated a minimum level or they can be used to by substituting s3 for a2. Eq. 2.64 Is most compare and select the more reliable unit important because it shows the "lever-arm" or approach from several alternatives. These effect.
For x large enough, the standard tests can be used during system design and deviation of 5* is directly proportional to development to provide guidance to the x; this means that the uncertainty in extra- engineers who must select among alternate polation can be tremendous, Eq. 2-63 can designs (Ref. 18). A typical statement of be used to put s-confidence limits on b and alternatives is (Ref. 18): m. Eq. 2-64 gives prediction limits for j7 (x). Student t-distributlon is usually used. I. There is a difference between the re- liability of the units. One ought never to calculate a T* (x) without %lso estimating its standard devia- 2. No difference has been demonstrated. tion by means of Eq.
2.64; it is very often an unpleasant surprise. If, in addition to Another statement of alternatives is: W' (x), one wishes the uncertality in y*, then ol must be added to Var 1. I The reliability of equipment A Is greater than that of equipment B. The linear correlation coefficient p be- tween y and x is 2. There is no reason to believe that the reliability of equipment A Is greater than , Cov (xY (2-66) that of equipment B. Px V y •Statistical tests are applied to the data and a decision is made between the two alterna- It is estimated by tives. The hypotheses are selected prior to the test. Ј•5ayg (2-66a) {!Z " ]['i(y, - Because test information usually is ob- ' *. . . . . . . ... i . .
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