Bayesian recurrent model of reliability growth: beta-distribution of parameters

One of the topical problems of modern applied mathematics is the task of forecasting reliability of modifiable complex information systems. Any first established complex system designed for processing or transmission information flows, as a rule, does not possess the required reliability. Such systems are subject to modifications during development, testing, and regular functioning. The purpose of such modifications is to increase reliability of information systems. In this connection, it is necessary to formalize the concept of reliability of modifiable information systems and to develop methods and algorithms of estimating and forecasting various reliability characteristics. One approach to determine system reliability is to compute the probability that a signal fed to the input of a system at a given point of time will be processed correctly by the system. The article considers the exponential recurrent growth model of reliability, in which the probability of system reliability is represented as a linear combination of the “defectiveness” and “efficiency” parameters of tools correcting deficiencies in a system. It is assumed that the researcher does not have exact information about the system under study and is only familiar with the characteristics of the class from which this system is taken. In the framework of the Bayesian approach, it is assumed that the indicators of “defectiveness” and “efficiency” have beta-distribution. Average marginal system reliability is calculated. Numerical results for model examples are obtained.