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Discontinuity, Nonlinearity, and Complexity 13(1) (2024) 1--15 | DOI:10.5890/DNC.2024.03.001

Elsayed E. Elshoubary$^{1}$, Mohammed Alqawba$^{2}$, Taha Radwan$^{2,3}$

$^{1}$ Department of Basic Science, El-Ahram Institute for Engineering and Technology, Cairo, Egypt

$^{2}$ Department of Mathematics, College of Science and Arts, Qassim University, Ar Rass, Saudi Arabia

$^{3}$ Department of Mathematics and Statistics, Faculty of Management Technology and Information Systems, Port Said University, Port Said, Egypt

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Abstract

This paper applies reliability analysis to the fuel control system of an airplane. The rates of transition to fail states follow exponential distributions. Two types of repair are compared, with the Gumbel-Hougaard copula yielding higher profits under our model. General repair is sufficient while a system is working in a degraded state. However, if the system is fully failing, copula distribution should be used for quick system maintenance. Reliability indicators are computed over time, including availability, mean time to failure, and sensitivity. To develop explicit formulations for profit, mean time to failure, and steady-state availability, differential difference equations are constructed and resolved. The system is solved using a supplementary variable technique. Numerical results were generated using the Mathematica software.

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