Downloaded from https://www.everyspec.com AMCP 709106 TABLE 24 The samee data set is plotted by the Beta Bounds method for comparison with the DATA SET 6 K-S Bounds method; see Example No, I(E). Ordired failure time (simulated) of bell bearinp, 2.2.4 WEIBULL DISTRIBUTION Test stpped at the 5th failure, 6 unfalled. N - 10. cc'p' Plot. The form of the Weibull distribution being Sused is Failurtlen Ra tirn,_hr i%. (Tdle2-1) a Sf i{t;oa,P}1 - exp [- (t/a)O] (2-10) 1 407 10 0.51/6.7/26 Eq. 2-Sb shows that the cumulative hazard 2 64 20 U.41/2 for the Weibull is 3 567 30 6.7/16S1, 4 673 40 WW/II 1() - (t/40)? (2-l1) 6 710 50 22/45/70 .- The Weibull papet is derived by taking log On) of Eq. 2-10.
TABLE 454 DATA SIT C Ordered feilure times (simulated) of bell bearings, log ('- In R) - P log t. -- P lOg (-12b) Entire bat of 10 was failed. (This Is the same mia B, sexcpt the tent wee continued until all bed filld) So log t plottod against log (-In A) is a No 10. straight line. Most Weibull papen use In 1-In(R)] for Eq. 2-12b and so have to COY Plot- use awkward methods to find P. Failure ties, % The procedure for trying the Weibull Rank tile, hr r/N. % 2l - 2.1) distribution is quite similar to that for the s-normal, exctpt that Weibull probability 2 407 20 0.61/17/26 paper is used. This is shown in detail for 3 557 30 0.7/26/31 Data Set D later in this parafWaph.
4 673 40 15/36/61 5 790 50 22/45/70 Data Set A from Table 2-3 is plotted in 6 we so 3015/17 Fig. 2-4; the K-S Bounds method is used, 7 1150 70 301/4/85 with 95% s-confidence bounds (N w 20, a 1450 s0 40/74/11.3 KS, n 0.29). Following the insttuctions on 0 1690 g0 61/164/5.3 the reverse side of Fig. 2-4, one obtains 10 300D 100 74/03.3/19.49 1- 1/N 0-0%; uLe 90% conkld•nce. KS, - 0.37 U 1700 hr. a - 2200 hr, ""u - 2900 hr the utility of the graph paper. Data Set B is censored as shown in Table 24; the 4 col- Q09, ,z 2.1, ('4 - 6 umns have been prepared as for Data Set A, and the points plotted; see Example No%, I(C) This sample could easily have come from a and I(D). Weibull distribution.
If the true distribution I text continues on tvse 2.27] ,. .. .. . .. .