Uncertainties

Uncertainties exist in the estimation of reliability data. In case of technical components these may be due to differences in the performance of components of the same class and grouping of similar but not identical components working under similar but not identical operating conditions. If data from the literature is used this leads to the necessity to select values from different sources without knowing whether component designs and operating conditions are comparable and it is very probable that they are not. For this reason use of a statistical distribution for unavailabilities and failure rates is indicated instead of a single point value. A lognormal distribution is usually chosen for this purpose because it fits observed data reasonable well [86]. The corresponding probability density function (pdf) for failure rate (l) (and analogous for unavailability, u) is given by [86]:

-Jlnls exp

The mean value, m, and, variance, s , of the natural logarithms are calculated as follow:

and,

Where N is the total number of measured values or data taken from the literature and 150 is corresponding to median. The mean value of the distribution is given by l = 150 exp f s2 ^

And the dispersion of the data is characterized by K-95 factor:

Where 1.6449 is a constant value of the exponential function made the probability of encountering value of l in the interval 105 = 150/K < l < 150.K = 195 equal to 90%, with the probability of l lying below of above these limits being 5% each 86]. Therefore, they represent the 5% and 95% centiles of the distribution, respectively. If insufficient data are available for calculating the dispersion factor K, an estimate is frequently made which reflect the analyst's subjective judgement as to the uncertainties. Uncertainties of human error probabilities and other basic event are treated in the same way in the context of the analysis.

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