Influence of Stochastic Characteristics of Properties for Materials, Products and Processes on Evaluation of Regulatory Parameters
For the last one hundred years development of mathematical statistics has reached rather high level. A universal relative and non-dimensional factor which is known as a coefficient of variation is widely used for practical calculations, analysis and comparison of various stochastic processes. A variety of methodologies for evaluation of possible variations in definienda is used in case when a small amount of measurements (less that 30) is made in order to study the required parameter. While doing that a number of measurements executed with the help of these regularities can be significantly increased that permits reliably (correctly) to assess numerical characterristics of the investigated parameters. However according to GOST (All Union State Standard) 21153.2-84 some corrections in methodology for determination of minimum required number of measurements (less 30) have appeared to be insignificant for obtaining a reliable safety, for example, in the field of civil construction (catastrophic accidents: in Moscow - Transvaal Park and Basmanny Market; assembly and other constructions: in Poland, France and others). In 2007 it has been proposed to use chisquare criterion for determination of the required number of measurements when their number is less than 30 and appropriate patents of Eurasian Patent Organization and the Republic of Belarus have been obtained for the proposal. For this purpose Brownlie's proposal has been used to assess confidence limits of dispersion values with the help of the chi-square criterion and the proposal has been supported by N. Kolmogorov who is an originator of exact mathematical probability calculus. The paper presents results of calculations for the required number of measurements in accordance with four methodologies and comparative analysis of the obtained results. It has appeared that in case when we are using chi-square criterion for the reliability level of 0.9 or even more it is necessary to make the largest number of measurements (determinations). While increasing variation coefficient and predicted reliability level the number of the required measurements is also increased. An effort has been made to apply a robust methodology, which does not depend on the form of a distribution law, for determination of minimum number of the required measurements. Having multi-year experience on practical usage of stochastic characteristics for various parameters classification of non-stability has been proposed on the basis of variation coefficient values.