Quality Assessment of "Stress-Strength" Models in the Conditions of Big Data

Abstract

The conceptual approach to assessing the quality of complex structural systems based on the large data generated during the monitoring of structures of controlled objects is justified. The methodological basis of the proposed study is the big data analytics, the methods of processing unstructured information, the technology of representing the process of changing structures of complex objects in the form of a Markov's type sequence, as well as methods of statistical analysis. It is proposed: to structure monitoring data by time slices (in the form of subsets of "stress" level measurements of controlled parameters) corresponding to a certain stage of the object's life cycle; to simulate a change in the structure of an object in the form of a dichotomous Markov chain; on the basis of the "stress-strength" model, to evaluate probabilistic quality indicators of the structural state of the controlled object, while the indicator of the transition from state to state is the fact that the level of "stress" exceeds the value of "strength". The study of the "stress-strength" model is reduced to the problem of finding the extremum of a definite integral with equality constraints, which is one of the isoperimetric problems. The results can be used in decision support systems during the structural analysis of complex systems. The effectiveness of the investigation is confirmed by a numerical example.