Downloaded from https://www.everyspec.com AMCP 70W196 increment is the reciprocal of the reverse 2. For i&eta Bounds plotting rank for the failed units; the hazard does not increment for nonfalled units. The 3. To show the Hazard plotting technique. times-to-failure are plotted on the time scale of the appropriate paper, and the cumulative Since the data are not censored (they are hazard is plotted on the cumulative-hazard complete), the Hazard plotting is not nec- or on the Cdf scale. This procedure is Mius- eary. But the comparison of plotting posi- trated in some of the examples. tions is useful. Col. 8 (plotting position for Hazard plotting) Is very close to col.
3 2-2.3 s-NORMAL DISTRIBUTION (plotting position for K-S Bounds method). Cols. 5-8 merely ilhdstrate the calculations The basis for the aplih paper is that the for the Hazard plotting and are not used equation elsewhere. (}-•. ) (-) First the K-S Boutids Method is shown. S- s-Normal Practical Probability Paper is used. Cola. 2-3 from Table 2-3 (Data Set A) are can be transformed to used; see Example No. I(A), It is not feasible to put quantitative s-con- gauf(F) M (2-8a) fidence levels on the Interval estimates for p 0' and a; analytic methods are necessary for or that.
Nevertheless, these intervals are a good engineering measure of the uncertainties in- volved, Some of the important conclusions a. pauf "(F) + ' . (2-8b) from this graphical exercise are: The Cdf scale is actually the gauf ' scale. 1. Not very much is known about the dis- The heavy dashed line on s-Normal Practical tribution of failure times of these fuel pumps. Probability Paper is drawn as For example, If one were interested in the J time at which 2% 6of the fuel pumps will F - 50%, x - i. (2-9a) have failed, it is tempting to use line #5, and guess about 240 hr. But that point really is The S-scale is linear in gauf -1.
For exam-A., only known to within the range 0 to 1200 the S - *I points are at hr. F -84.13%, x - p + a, for S -+ 1 2. Whether the data can reasonably be represented (summarized) by an s-Normal (2-9b) distribution is almost irrelevant. F- 15.87%, x - a, fr$ -1. 3. 5% of the time we go through thit (2-90) procedure (the s-confidence was 95%), the true Cdf will not lie wholly within that very Several examples illustrating methods of wide envelope. plotting the dnta are presented-..Example Nos. I(A) through I(F), The data are pre- 4. The fuel pump may have roughly 10% pared 3 ways: defectives (line #4), i.e., lives so short as to be of critical concern. Perhaps this is reason 1.
For K-S Bounds plotting eniough to ground the aircraft until further