Downloaded from https://www.everyspec.com AMCP 706-1N number r, The region between lines, U and 2.6.1 MOMENTS L is the s-confidence envelope; iLe., the true Cdf lies entirely within the U, L-envelopc he Imean and standard deviation of a with the s-confidence level chosen in step 1, population can be estimated by equating "The larger the s-confidence level, the wider them to the sample mean and standard de- the envelope and the less informative is the viation, respectively, This can be done conclusion to be drawn, without regard to the actual distribution, This is the way the parameters of the s- It the plot is made on special graph paper normal and exponential distributions are such that the desired distribution Is a estimated.
Weighted sample moments can straight line, then a distribution of' that form he used If desired. For example, the is completely acceptable (with s-confidence logarithm of the moan can be estimated as C) if a straight line f1t4 within the envelope. the Itmean of the logarithms of the data. Each weighting will give u different answer, Of course, as usual, no guarantees are but the scatter is probably less than the un- made for extrapolations outside the range certainly anyway, of the data, If extrapolations are made, be sure to show the uncertainty range (this pro.
Since moments of a population can de- sunies that the form of the distribution Is pend very heavily on the tail regions of the correct).
The actual uncertainty, which in- distribution, and since very few (if any) cludes doubt about the form of the distri, data are collected there, it is usually best to bution, is usually much greater, But oven use quantile estimators, Quantile estimators the cahlulated range of statistical uncertainty are remarkably insensitive to the actual be- is usually discouraging enough, havior In tail regions, 2.6 NONPARAMETRIC ESTIMATION If there are contractual obligations con- cerning nonparainctric estimation of Nonparametric methods can le used to moments, a competent statistician ought to estimate reliability and mean lifo; ie., It be consulted.
is not necessary to make any assumptions concerning the time-to-failure distribution 2.6.2 QUANTILES (Retf. 3 and 10). Nonparumetric reliability applies to the test time interval only and Sample quantiles often are used as esti- cannot be extrapolated in the time domain. imattes of population quantiles. Population This is the saine as estimating a binomial quantiles (and combinations thereof) often parameter, Seac par, 2-3,1 for more details. are used to indicate population character. if the failure times are known, a nonpara- Istics.
For example, the median is a good metric .- confidence limit for the Cdf can be nmeasure or the "central tendency", and the calculated as shown in par, 2-5, See par, distance between the 75% and 25% points 2-2,2 when censoring occurs, For cases Is a good measure of the dispersion, which do not fit the techniques in this hand- book, a statistician ought to be consulted; Point estimates and s-confidence limits it is very easy to go astray, can be obtained using the method in par, 2-5. Par. 2-2,1 also contains material on 'lie simplest way to estimate the unrell- point estimates and s-confidence limits, ability for a time interval, is to calculate the proportion of items that fail over that in.
If the sample has been severely censored, teryad, it may not be feasible to use these methodi. 07 r, w, Ai'