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.
Highlights
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
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
When considering compliance with the high level of reliability of complex technical systems, the analysis of indicators and statistics obtained during testing or operation is not excluded from consideration
Summary
When considering compliance with the high level of reliability of complex technical systems, the analysis of indicators and statistics obtained during testing or operation is not excluded from consideration. It is possible to use the information theory because of a probabilistic measure рi [5, 6] In all cases, рi – the relative number of discrete states of the system, that is, failures related to each of the i-th elements. According to information theory [5, 7], signals ( are failures) can be considered as discrete states.
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