Downloaded from https://www.everyspec.com AMCP 706-1N consulted. Many statistical packages for kind of cenuolng, and provide a measure of computers have prepared programs for mak- the uncertainties and correlations in the ing, this calculation. estimates of a and P. 24A.3 #.Confldenos Llmitt for aRellabillty 2.3.6 LOGNORMAL Because two parameterm (instead of one) The continuous random variable I is the have been esdmated irom the data, s-con- measure of failure resistance, e.g., time to fidence limits are virtually imposuible to failure or stress-to-fallure, "calculate for the s-realability. A statistician ought to be consulted in this case. Perhaps Use the following notation:
Prediction Intervals or Tolerance Intervals can be used, t a random variable (e~g, time to failure) 2.3.5 WEIBULL a N scale parameter (median) The continuous random variable I is the w * shape parameter measure of failure resistance, emg,, time-to. failure or stre.sto-fnllure. IA w mean of in t Use the following notation:
a w standard deviation of hI t t n random variable (e,g., time to failure) 1 * exp 111(21A)1 a a scale parameter (characteristic value) 'The CJf is 1 shape parameter Cdff{t;(V,Рэ lrauf(in If,"N)1 (2-40) Thn Sf is The mean and variance are WCOfc UIX P) 5f 0; a, H l (2-41a)j GXq e - (t/0)01 (2-38) Var 0, a2BI(Bi - 1) (2-41b) The mean and varian('e are The usual statistical problem is to estimate a and 0 from a sample, Probably the sim- E o ro. + ip) (2-.39g) plest procedure is to take natural ltog of all the data and to proceed as if the distribution Var (4 a{'(1 + 2/11) were ,.normal. The unbiased property of the estimators will disappear, but the maxi.
- [L(i + i/o)wl• (2-39b) mum likolihoud property and .- confldence limit transferance remailn, The usual statistical problem is to estimate a and 0 from a sample. Unfortunately, there OAp (A) (2-42a) :4 tre no good, simple estimators for a, 13, See IQ Ref, 15 or Part Six or a statistiHan/pro- ( 1/0 (2-42b) graminer. Maximum likelihood methodti of'ten are used bcaCOuse they allow most any Se por. 2-3.4 for the s-normal distrib-ition, ,'It