A priori Weibull distribution in Bayesian balance models

This paper is devoted to Bayesian balance models, which imply separation of factors affecting the system under study, into positive, i. e., contributing to functioning, and negative, i. e., impeding functioning. To study the effectiveness of the system, the balance index, equal to the ratio of negative and positive factors, is concerned. It is assumed that the factors depend on environment, and it is not possible to determine their exact values due to lack of time and material resources, imperfect measuring equipment, etc.; however, the laws governing factors' alterations remain unchanged and are known a priori to the researcher. Under these conditions, it is reasonable to use the Bayesian method, which implies randomization of the initial parameters and, hence, the balance index, under the assumption that a priori distributions of the factors are known. In this paper, the probabilistic characteristics of the balance index in the case when both factors have a priori Weibull distribution are concerned. This work continues a series of studies on the application of Bayesian methods in problems of mass service and reliability.