Downloaded from https://www.everyspec.com AMCP 706-198 TABLE 2-7 Pdf t Al ;k} ex h( THE 50h AND Ofth PERCENTILES -(1/e) exp (- t10) (2-27-a) OF THE CH14OUARE DISTRIBUTION 00 f(X 2 ;a' - Cdf IX%')F SfItj.t} -Oxp (- ht) - Oxp ( t18) X2Psuch that ctqf (X2P";&') w P, The Poa an 5%inc and 96%. The table has been abbreviatedThmenadvrncPe The body of the table gives the value$ of (from more extensive tables) for any use inE{t / 9(28) the exarnpies. t /-0(28a 065 9% Var {t} -- 1/X2 - 0 (2-28b) 0.1028 5.991 The usual statistical problem is to estimate 4 0,7107 9.487 X (or 0). Tests are often run until ko. fail- 0 1.835 12.50 ures have been observed.
Theon the maximum 82.733 15.51 likelihood, unbiased ustimate 6 for 9 Is 10 3,940 18.31 12 5.226 21.03 ~(-9 where tk atotal operating time up to fai- firut failure and then discarded, or whether ure ko. units are repaired; the only requirement Is that h. be a constant, i~o., the process is The reciprocal of 6 Is the maximum likell- Poistson, This situation is related to par. hood estimator for W, but It Is no longer 2-3,3 on the exponential distribution since unbiased. both deal with a Poisson process. s-Confidence statements about X aru found 2-3.3 EXPONENTIAL from the fact that 2, ko (X/A) has a chi-square distribution with '2 ko dcprees-c'f-freedom.
The continuous random variable t Is the An equivalent statement Is that A4~ has a time to first failure (tirne of failurc-free chi-square/nu distribution with 2 ko degrees- operation), It is related to the Poisson of-freedom. For a 2-sided symmetrical s- process of' par. 2-3.2, but instead of count- confidence Interval, we have ing events (e.g., defects or failures), the time to the first failure (aren to first defect) is Conf [;AL -- X :5Ad C (2-30a) measured, where C' is defined by the equation Use the following notation:
I *.-- C-(I- Q)/2, and A'L and XU are defined by X-failure rate (Poisson rate parameter) t -time to failure csqf(2koXU1.rj/X 2k 0 ) -u C' (2-30b) csqf(2k 0 XL/A^; 2k 0 ) -1 C' (2-30c) = IA (often used for convenience) I-sided s-confidence intervals are imalogous to Vie pdf and Sfare EAI. 2-30; i.e., ignore Nu and use Eq. 2-30c "I .. .. .. .. .. .. .. .. .. .............. .. .. ..