Method for constructing estimates of accuracy of measuring equipment based on Bayesian scientific approach

Abstract

Before putting new unique samples of technical systems into commercial operation, as well as before introducing new technologies into production, as a rule, all kinds of tests are carried out. Small and very small volume of statistical data during testing is a characteristic feature of unique and small-scale products and technical systems. Therefore, the problem of constructing effective statistical estimates with a limited amount of statistical information is an important practical problem. The article proposes the development of the Bayesian approach to the construction of point and interval estimates of the parameters of the known distribution laws. The joint use of a priori and posterior information in the processing of statistical data of a limited volume can significantly increase the reliability of the result. As an example, we consider two most typical distribution laws that arise when testing new unique samples of measuring devices and equipment: normal distribution with an unknown average value and a known dispersion, as well as with an unknown average value and an unknown dispersion. It is shown that for these cases, the parameters of the distribution laws themselves are random variables and obey the normal law and gamma normal law. Recalculation formulas are obtained to refine the parameters of these laws, taking into account a posteriori information. If these formulas are applied several times successively, the process of self-learning of the system or self-tuning of the system occurs. Thus, the proposed scientific approach can find application in the development of intelligent self-learning and self-turning systems.

Application of bayesian scientific approach to constructing the statistical estimations for solving metrological and measurement problems

“…Algorithm for correcting these parameters is described with joint consideration of a priori and posterior information was created. Examples of constructing of point estimates and of interval estimates are presented : Volchkov et al, 2019: Khayrullin, 2019.…”