Comparison of fuzzy semi-Markov models for one unit with mixed standby units with and without preventive maintenance using regenerative point method

Temraz, Neama Salah Youssef

doi:10.1016/j.heliyon.2021.e07717

Cited by 6 publications

(4 citation statements)

References 18 publications

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“…If initial and boundary conditions are set in the general form for Equation (9), the problem will be formulated in the same way as the classical problem of heat propagation in an infinite rod, whose lateral surface is thermally insulated [14]:…”

Section: Methods Of Solving Equation (9) If Initial and Boundary Cond...mentioning

confidence: 99%

“…We show that the problems ( 9) and ( 10) can be obtained as a special case using problems ( 14)-( 16). If we make a substitution in ( 14), (x = y, t = τ − τ 0 , a T = 1/ √ 2, u(x, t) = ω 1 (x, t)), we obtain Equation (9).…”

Section: Methods Of Solving Equation (9) If Initial and Boundary Cond...mentioning

confidence: 99%

“…Many branches of mathematics, including the theory of continuous Markovian diffusion processes [8][9][10][11][12][13], the theory of differential equations [14], probabilistic physical diffusion and physico-statistical models [15][16][17][18][19], are used to develop methods for calculating reliability, serviceability and failure-free operation. In [15], the technology of development of diffusion models is described, including monotonic diffusion (MD) and non-monotonic diffusion (ND) distributions, which belong to the class of probabilistic physical models.…”

Section: Introductionmentioning

confidence: 99%

“…The correct selection of a theoretical model of the failure distribution for high-reliability specimens of measuring equipment (ME) [8][9][10][11], which include electronic components (integrated circuits, semiconductors, chips, soldered joints, etc. ), as well as components of mechatronic systems, turns out to be a difficult task.…”

Section: Introductionmentioning

confidence: 99%

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

Khayrullin

2024

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(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.

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Section: Methods Of Solving Equation (9) If Initial and Boundary Cond...mentioning

confidence: 99%

Section: Methods Of Solving Equation (9) If Initial and Boundary Cond...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

Khayrullin

2024

Axioms

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To the Design of Medium- and Long-Term Programs of Innovative Development of Some Areas of Mechanical Engineering

Ershov

Levina²,

Malahov

et al. 2023

Lecture Notes in Mechanical Engineering

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Sensitivity and performance analysis of a three-unit soft biscuit manufacturing system with two types of repairers

Monika,

Chopra,

Sheetal

2024

Int J Syst Assur Eng Manag

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Comparison of fuzzy semi-Markov models for one unit with mixed standby units with and without preventive maintenance using regenerative point method

Cited by 6 publications

References 18 publications

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

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

To the Design of Medium- and Long-Term Programs of Innovative Development of Some Areas of Mechanical Engineering

Sensitivity and performance analysis of a three-unit soft biscuit manufacturing system with two types of repairers

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