Downloaded from https://www.everyspec.com AMCP 706-196 horizontal and vertical lines; they will be arm well known (see Part Six, Mathematk'al parallel to, and KS, from, the sample Cdf, Appendix and Glossary), The mean, mode, Then "I ... s-confidence" is the fraction of and median of Pk,N are times you-do-this-procedure that the true (d4 will partly lie outside the 2-aided scon- E {p O} = k/(N + 1) (2-4a) fidence bounds. In general, you will be dis- heartened at how little you know about the e mode{PSN} ' (k - 1)1(N - 1) (2..4b) true CO.
median{paNI ( - W.3)/(N + 0.4) Drawing the data-lines; draw the two par- (2-40 allel lines, farthest apart, that lit reasonably well wilhin the s-conf~donce bounds; use The mean value, Eq. 2.4a, is used often and both to estimate boui-ds on the "intercept" reasonably as the plotting position-simply parameter of the straight line (eW.&,,the mean because It is .o easy to calculate; but it, for the s-normal distribution), Draw the two alone ives no idea of the uncertainty In- Intersecting lines, with steepest and smallest vaolved due to the random nature of the data. slopes, that fit reasonably well within the s-conlidence bounds; use both to estimate The median, Eq.
2- 4 c is also reasonable to bounds on the "slope" parameter of the use, but Is less popular because of Its gteater straight line (e,.g,, the standard deviation for complexity. The expression (k .-, 0,5)N is a linor e(gl ( ,ist ribu tion) d fairly popular as a plotting position, and is as reasonable as any single one, but it has way: If a true Cdf is drawn, then all %ample Table 2-1(B) lists 3 plotting positions for points will lie within ±KS,, from it, with the each point; so the uncertainty is plainly stated s-confldence. Sveral examples are shown on the graph. These are the points given it the paragraphs that follow for using for which the Cdf in Eq.
2-3a Is 5%, 50%, this method of K-S Bounds, The K.S stands 95%; i&e,, only I point in 10 would be out- for Kolmogorov-Smirsiov (two Russians who side that range, Later paragraphs in this developed much of the theory) chapter Illustrate the use of' these plotting Table 2-1(A) also can be used the other no simple prorty to give it a name. positions. 2-2.1.2 Plotting (Bsts Bounds) This method of plotting Is called "Bets If a sample of N is drawn from the uni- Bounds", Just to have a short name for it. form distribution (representing a Cd/).
and then the resuilts are put in order from lowest 2-2.2 PLOTTING POSITION3 (CUMULA- to highest, the pdJ and Cdf of the k-th TIVE HAZARD) order-statistic are When iiome of' tho; items are removed from .NIN\ test before they fail, and the test is continued Cdf {Pa,N} = \plH(1 - ph,,)N) for other I'ailureo, the plotting positions for (2-3a) the (df' are very difficult to calculate. Ref. 23 shows how data can be simply plotted in Pdf {P•.N}"( - N this situation, The errors Incurred in using f - 1.P• -pt,)' this method are probably small compared to (2-3b) the uncertainties involved.
Unfortunately, it is not feasible to provide a rigorous measure This is a beta distribution and its properties of' that uncertainty.