Downloaded from https://www.everyspec.com AMCP 706-190 T I being considered is rarely rejected, or to S in ~(10-1) take so many data that the model is virtually always rejected. Usually, the uncertainty in (10-2) the projected value of Wh) will be dishearten- ing enough. X(t) = (T)(t/T)b' (10-3a) Example No. 37 illustrates the procedure. W,(T% .nT (10-3b) 10-2.2 DUANE MODEL NO. 2 u(t) = u(T)[ + ] + lin (t/T)12}/21 1 2 The following assumptions apply: -4(T)1[1 + {1 I In (m(t)/nrJ11I/2 1 t/2 I. There are 2 kinds of time: (10-4a) a. The cumulative test-time of all units on test, up to the time of the last fix. U(T) a (2/n1-)1/1 (10-4b) b.
The test time of a unit, as measured 1U(t) =t exp [- 2;(t)] (10-5a) from the time of its most recent fix. j(t) ;•(t) Pxp [+ 2A(t)} (10-5b) 2. The failure rate of a unit is constant between fixes. The uncertainty limits on X, (,L and XU) are approximate and are chosen at twice the 3. The log failure-rate of a unit when it estimated asymptotic standard deviation of is fixed is a linear function of log cumulative- Rn э. They have no exact probabilistic inter- test-time ;ee Assumption la). pretation, but serve adequately for engineers and managers who want to know whether Notation follows: the estimate is within 10% or a factor of 10.
Indeed, the factor of 2 on & could as easily t, - test time of unit I (see Assumption have been 3. 1 b) For W(T) smrnll, i.e., W(T) 1, the relative T1 = cumulative test-time of all units on uncertainty in X is, from Eqs. 10-4 and 10-5; test up to the time of the last fix 1 T 2 &7 -8 thus to know эТ within for unit I (see Assumption Ia). t, and ± 10% requires about 800 failures; (n 7 = 800). T, are independent. "For most situations this is an outlandish num- ber, which shows that rarely will we know ni number of failures during tj Sto within ± 10%. Xj failure inte of unit I Statisticians are divided on the worth of running goodnwss-of-fit tests.
The reasons From Assumption 3, it follows that for not paying much attention to them are that their interpretation is narrowly statis- In = h 0 + (8 - 1) In Tj (10-6) ticai, iathir than engineering, and that the result teimds to be very sensitive to the size Eq. 6 has the formalism of Ref. 4, where the .- )f the sample (number of faiiure-occjrrenct: .. I- and Qi'T,. of Eq. 10-6 correspond to For any physical situation, it is usually pos- the E ard xi of Eq. 12 in Ref. 4, respective- sib'e to take so few data that the mode! ly. The solution for Wj and the uncertainties