System Analysis of Reliability Theory Foundations

The relevance of the problem under study is attributed to the need to enhance reliability of the complex engineering systems used in forestry, agriculture, transport, machine engineering, etc. The purpose of the article is to build a mathematical model that would generalize reliability theory fundamentals from a perspective of the theory of dynamic systems based on the symmetry group concept determined by the probability function – dependence of no-failure (failure) probability on external time for system elements. The new approach to study this problem implies building of a multiplicative group under multiplication between no-failure (failure) probability rates as a number of units of the probability measure per unit of external (physical) time and the rate of functional (internal) time as the amount of external (physical) time per unit of the probability measure. The range of probability measures is [0, 1]; it is counted by the unit of measure defined by a set of elementary events. Based on the combination of functional times determined for each element of the system, the system becomes a single deeply integrated structure bound with external and internal time. Traditional reliability criteria of dynamic systems in the “space – time” functional space are dually related to their analogues in “functional time – probability”. Information credibility of the system dynamic state is enhanced by introducing additional confidence intervals of no-failure (failure) probability in conjugated times and their analysis. This study is intended for engineers, graduates, and students of technical universities.