Downloaded from https://www.everyspec.com AtWP 70-.19W ExamDle No. 4 In a 1000 hr test, no failures were observed. Assume that the process is Poisson. Estimate the true mean and investigate some a-confidence statements for the mean. Prooedure D .m 1. State the test result. 1. k 0 Find a point estimate of P. p = k 0, 2. Investigate the s-confidence statements; 2. Choose C a 95%. Since h - 0, use Eq. 2-25. the intervals will be 1-sided. 3. Pitk appropriate values of )A and #A*. 3. IA 0.1026/2 - 0.0513 Use •qs. 2-251 and 2-25J. Table 2-7 = 5991/2 =3.00. will suffice. 4. Make the two 8-confidence statements 4. Conf ({ S 3.00) '- 95% (from Eqs. 2-25g and 2-25h). Conf (0, 0513 } 95%.
These s-confidence statements it step 4 and the point estimate in step 1 are of little help. Much has been written for this case (no failures) about estimating IA, but much of it is fruitless because it tries to give the illusion of more certainty when there is nothing but vast uncertainty. Randomized a-confidence limits can often con- siderably narrow the region o: uncertainty (see Part Six Mathematical Appendix and Glossary). The two statements in step 4 cannot be oombinued into one statement with an upper and lower limit; the first one Is the one usually given. Fxamplel No. 5 Use data in Example No. 4; estimate the failure rate. P.rocedure Exa•mle 1. Calculate the point estimate. 1.
X - )/1000-hr - 0. 2. Calculate the interval estimates 2. э = 4,/1.000,.hr = 3.0/1000 hr u L/1000-hr = 0. 051/1000 hr. 3, Make the complete s-coitidence 3. Gont {A : 3.0/1000 hr} - 95% statements. Conf {0. 051/1000 hr : X} :5 95%.