Practical application of continuous distribution laws in the theory of reliability of technical systems

Aim. One of the stages of dependability analysis of technical systems is the a priori analysis that is usually performed at early design stages. This analysis a priori has known quantitative dependability characteristics of all used system elements. As unique, non-mass produced or new elements usually lack reliable a priori information on quantitative dependability characteristics, those are specified based on the characteristics of technical elements already in use. A priori information means information retrieved as the result of dependability calculation and simulation, various dependability tests, operation of facilities similar in design to the tested ones (prototypes). From system perspective, any research of technical object dependability must be planned and performed subject to the results of previous research, i.e. the a priori information. Thus, the a priori analysis is based on a priori (probabilistic) dependability characteristics that only approximately reflect the actual processes occurring in the technical system. Nevertheless, at the design stage, this analysis allows identifying system element connections that are poor from dependability point of view, taking appropriate measures to eliminate them, as well as rejecting unsatisfactory structural patterns of technical systems. That is why a priori dependability analysis (or calculation) is of significant importance in the practice of technical system design and is an integral part of engineering projects. This paper looks into primary [1] continuous distributions of random values (exponential, Weibull-Gnedenko, gamma, log normal and normal) used as theoretical distributions of dependability indicators. In order to obtain a priori information on the dependability of technical systems and elements under development, the authors present dependences that allow evaluating primary dependability indicators, as well as show approaches to their application in various conditions. Methods. Currently, in Russia there is no single system for collection and processing of information on the dependability of diverse technical systems [3] which is one of the reasons of low dependability. In the absence of such information, designing new systems with specified dependability indicators is associated with significant challenges. That is why the information presented in this article is based upon the collection and systematization of information published in Russian sources, analysis of the results of simulation and experimental studies of dependability of various technical systems and elements, as well as statistical materials collected in operation.

Results. The article presents an analysis of practical application of principal continuous laws of random distribution in the theory of technical systems dependability that allows hypothesizing the possible shape of system elements failure models at early design stages for subsequent evaluation of their dependability indicators.

Conclusions. The article may be useful to researchers at early stages of design of various technical systems as a priori information for construction of models and criteria used for dependability assurance and monitoring, as well as improvement of accuracy and reliability of derived estimates in the process of highly reliable equipment (systems) development.

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