Minimising the Influence of the Distribution Law on the Reliability of Accuracy Estimation

The problem of minimising the influence of distribution laws of input values on the reliability of results in evaluation models in the field of metrology is considered. Aim of this work was to substantiate rational approaches and methods of correct solution of the problem in the case when the distribution law of input values differs from normal. Classification of variants of solutions to the problem of normality of input values in models of estimation of uncertainty of measurement method, metrological reliability of measuring instrument, etc. is presented. The complex problem of estimating the law of input quantity distribution and bringing it to normal by correcting its probabilistic characteristics is formulated. It is substantiated that such a solution of the problem will provide ‘frequency equivalence’ of empirical and normal distribution laws. Methods of solving the problem for two possible cases are considered: the input values of the model are estimated a priori and empirically. The variants of the rational solution of the problem for the case of a priori estimation of the input value of the model (type B), generally accepted in metrological practice, are considered. The main attention is paid to the case of estimating the input value of the model empirically (by type A). Chebyshev's and Vysochansky-Petunin's inequalities are taken as theoretical prerequisites for solving the problem which determine the estimates from above of the probability of deviation of a random variable from the mean without taking into account the exact form of its distribution law. A graphical method of estimating the ‘degree of normality’ of the empirical law of distribution of an input quantity and bringing it to normal by correcting its statistics is proposed. Implementation of the method assumes use of statistical packages of applied programs, for example, Statistica package, and visual comparison of the histogram of empirical distribution with the theoretical curve of normal distribution. For all possible situations an algorithm of actions is defined including analyses of the degree of mismatch between distributions and decisive rules for correcting the initial statistics of the input quantity.