A Probabilistic Physico-Chemical Diffusion Model of the Key Drifting Parameter of Measuring Equipment

Abstract

(1) Background: A new probabilistic physico-chemical model of the drifting key parameter of measuring equipment is proposed. The model allows for the integrated consideration of degradation processes (electrolytic corrosion, oxidation, plastic accumulation of dislocations, etc.) in nodes and elements of measuring equipment. The novelty of this article lies in the analytical solutions that are a combination of the Fokker–Planck–Kolmogorov equation and the equation of chemical kinetics. The novelty also consists of the simultaneous simulation and analysis of probabilistic, physical and chemical processes in one model. (2) Research literature review: Research works related to the topic of the study were analyzed. The need for a probabilistic formulation of the problem is argued, since classical statistical methods are not applicable due to the lack of statistical data. (3) Statement of the research problem: A probabilistic formulation of the problem is given taking into account the physical and chemical laws of aging and degradation. (4) Methods: The author uses methods of probability theory and mathematical statistics, methods for solving the stochastic differential equations, the methods of mathematical modeling, the methods of chemical kinetics and the methods for solving a partial differential equations. (5) Results: A mathematical model of a drifting key parameter of measuring equipment is developed. The conditional transition density of the probability distribution of the key parameter of measuring equipment is constructed using a solution to the Fokker–Planck–Kolmogorov equation. The results of the study on the developed model and the results of solving the applied problem of constructing the function of the failure rate of measuring equipment are presented. (6) Discussion: The results of comparison between the model developed in this paper and the known two-parameter models of diffusion monotonic distribution and diffusion non-monotonic distribution are discussed. The results of comparison between the model and the three-parameter diffusion probabilistic physical model developed by the author earlier are also discussed. (7) Conclusions: The developed model facilitates the construction and analysis of a wide range of metrological characteristics such as measurement errors and measurement ranges and acquisition of their statistical estimates. The developed model is used to forecast and simulate the reliability of measuring equipment in general, as well as soldered joints of integrated circuits in special equipment and machinery, which is also operated in harsh conditions and corrosive environments.