Advantage index in Bayesian reliability and balance models with beta-polynomial a priori densities

This work is devoted to the research of the probabilistic characteristics of the advantage index in Bayesian balance models, when negative and positive factors affecting the functioning of the system have an a priori beta-distribution and distribution with polynomial density, for example, uniform or parabolic distribution. The results of the work can be used to research marginal reliability of complex modifiable information-communication systems and other advantage indexes, for example, availability ratio and probability of staying in working condition in reliability theory, probability that the call will not be lost, in the theory of mass service, etc. The given method can be used for similar formulations of the problems in the research of distributions with piecewise polynomial a priori densities, for example, Simpson distribution, Irwin–Hall distribution, Bates distribution, etc.