Bayesian models for testing large groups of service device

A. A. Kudryavtsev^a, O. V. Shestakov<sup>ab

a</sup> Department of Mathematical Statistics, Faculty of Computational Mathematics and Cybernetics, M. V. Lomonosov Moscow State University, 1-52 Leninskiye Gory, GSP-1, Moscow 119991, Russian Federation
^b Institute of Informatics Problems, Federal Research Center “Computer Science and Control” of the Russian Academy of Sciences, 44-2 Vavilov Str., Moscow 119333, Russian Federation

Abstract: The paper considers a new approach to the verification tasks for the declared performance indicators of large groups of complex servicing devices when the total verification is impossible or expensive. The method used is based on the study of the asymptotics of statistics in the framework of the Bayesian approach to the problems of the queuing theory. By the example of the readiness coefficient in the $M|M|1$ model, the authors prove the proposition relating to the class of transfer theorems which makes it possible to compare real data in bench tests of complex aggregates with theoretical predictions. The specifics of the application of the method from the point of view of a device manufacturer and a customer of a large batch of similar devices are considered. The described method and results can find application not only in the field of Bayesian queuing problems but also in other areas that use randomization of the basic parameters of the model.

Keywords: Bayesian approach; mass service systems; mixed distributions; transfer theorem; statistical methods.

Received: 12.06.2017

DOI: 10.14357/19922264180113

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