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.
Highlights
The Bayesian scientific approach is widely used to create effective statistical estimates in various fields of activity [1,2,3,4,5,6,7,8,9,10,11,12]
Classification theory, machine learning, the creation of self-learning and self-tuning systems are just some of the areas where the Bayesian approach is effectively used
This paper describes the application of the Bayesian approach to the problems of constructing effective statistical estimates of accuracy of new and innovation measurement devises and instruments [13,14,15]
Summary
The Bayesian scientific approach is widely used to create effective statistical estimates in various fields of activity [1,2,3,4,5,6,7,8,9,10,11,12]. This paper describes the application of the Bayesian approach to the problems of constructing effective statistical estimates of accuracy of new and innovation measurement devises and instruments [13,14,15]. The algorithms for constructing the distribution density function of the average value and the distribution function of the mean square deviation are described. The results of the paper are used in determining the accuracy class of measuring instruments according to the results of acceptance tests, of state tests or tests directed to confirm the type of measuring device and instrument [13,14,15]
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