Determination of the amount of entropy of non-recoverable elements of the technical system

Abstract

A mathematical model for determining the amount of information applied to non-recoverable elements of the technical system is proposed. The quantitative indicators of the model are the probability of failure-free operation; frequency of failure; failure rate and mean time to the first failure. One of the criteria for assessing the reliability of the system adopted information entropy, which is considered as a measure of uncertainty of the outcome of a random event. The model allows to express the reliability indicators through information entropy for the analysis of the state of elements and the system. Multiplicative and additive properties of entropy growth in the case of aging and testing of system elements for resistance to failures are considered. An integral part of the model is a method for calculating the information entropy of systems consisting of non-recoverable elements. The method is based on the Shannon’s model to determine the amount of information and allows to calculate the entropy for both operable and non-operable states of the system. The peculiarity of the method is as follows: 1) the probabilities of the operable state and the probability of failure in the case of considering the flow process of system states without taking into account the individual properties of the element are used to determine the information entropy. In this case, the result of the calculation allows to monitor the manifestation of randomness in the opposite states of the system; 2) it uses the individual properties of the element characterized by private (or own) entropy. With this approach to the calculations, the obtained quantitative values of entropy allow to monitor the growth rate of the states of each element and system as a whole. The method is tested on the presented example.