A comparison of the expected and statistical probability distribution of system failures

Abstract

The possibility of applying the information theory in the problem of comparing the expected and statistical probability distribution of failures of a technical system are considered. The paper presents a brief analysis of the processes of additive and multiplicative growth of the system indicators, among which the probability of failure-free operation and failure rate were considered. These indicators were considered in order to analyze the reliability of the system. The increase in reliability of the indicators is associated with the fixing of the failure rate of the system elements and the construction of probability distributions. In order to compare the two distributions, a method for measuring uncertainty is proposed, which includes Shannon’s measure of uncertainty, cross-entropy and Kullback-Leibler divergence. Together, they make it possible to determine the connection between the two different probability distributions of failures, to calculate the distance between the distributions, to identify the degree of difference between the real and desired state of the system during operation. An example of calculation confirming the importance of the participation of the offered method for measuring uncertainty in the problem of comparison of the expected and statistical probability distribution of system failures is given.