Partial differential analytical expression for the failure rate change of electrical components under multi-fault coupling

Tiejun Cui; Pengpeng  Wei; Shasha  Li

doi:10.59400/adecp3444

Partial differential analytical expression for the failure rate change of electrical components under multi-fault coupling

Tiejun Cui School of Environmental and Chemical Engineering, Shenyang Ligong University, Shenyang 110159, China
Pengpeng Wei School of Environmental and Chemical Engineering, Shenyang Ligong University, Shenyang 110159, China
Shasha Li School of Environmental and Chemical Engineering, Shenyang Ligong University, Shenyang 110159, China

Article ID: 3444

(This article belongs to the Special Issue Mathematical Analysis Advances in System Fault Analysis, Prediction and Control (Close))

Keywords: safety system engineering; electrical components; multi-fault coupling; factor influence; failure rate; partial differential

Abstract

With the trend of high integration and complex working conditions of electronic equipment, multi-fault coupling failures have become a key threat to operational reliability. To study the influence mechanism of multi-factor-induced multi-fault modes on the failure of electrical components and consider the time-dependent effect of component operation, an analytical expression in the form of a partial differential equation for the component failure rate is established. The time-dependent of failure rate, multi-fault coupling terms, and coupling coefficients in the expression are further determined. The research shows that constructing the partial differential expression for failure rate should consider electromigration, corrosion, hot carrier, and dielectric breakdown faults and their influencing factors. By introducing multi-fault coupling terms, the impacts of parameters such as temperature, current density, etc. on various fault modes and component failure rates are reflected. Electromigration-corrosion, heat-carrier-dielectric breakdown accelerate the occurrence of faults, and the analytical and approximate formulas for coupling coefficients are provided. Case analysis obtains the failure rates of each fault, the component failure rate, and two coupling coefficients; and it is found that the failure rate changes significantly at 100s, serving as a critical life point. This study provides a method for analyzing the failure rate of electrical components under multi-factor influences over time.

Published

2025-09-30

How to Cite

Cui, T., Wei, P., & Li, S. (2025). Partial differential analytical expression for the failure rate change of electrical components under multi-fault coupling. Advances in Differential Equations and Control Processes, 32(3). https://doi.org/10.59400/adecp3444

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Issue

Vol. 32 No. 3 (2025)

Section

Article

This work is licensed under a Creative Commons Attribution 4.0 International License.

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