Bayesian models of factors balance with a priori Weibull and Nakagami distributions

Bayesian balance models are considered. Within this approach, it is assumed that the parameters affecting a system can be divided into positive, which support system functioning, and negative, which interfere with the functioning. Thus, the ratio of negative to positive factors — balance index — is considered as an indication of system's functioning effectiveness. The study is carried out assuming that the factors depend on the environment state and their exact value cannot be obtained due to external reasons, e. g., equipment faults, lack of resources, etc. It is also assumed that the principles of factors' changes are known a priori and remain invariable. Considering these assumptions, it is natural to use the Bayesian method, which implies randomization of the initial parameters supposing that their a priori distributions are known. As a result, the balance index becomes a random variable as well. This paper continues a series of studies by the authors devoted to the application of Bayesian methods in the problems of queuing and reliability. In this work, the obtained probability characteristics of the factor balance index in the case of a priori Weibull and Nakagami distributions are presented. The results are formulated using gamma-exponential function.