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Reliability Analysis of a System Designed to Withstand a Specified Shock Magnitude Range |
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PP: 1215-1232 |
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doi:10.18576/jsap/130407
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Author(s) |
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S. M. Bakry,
N. A. Mokhlis,
A. E. B. Abd Elghany,
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Abstract |
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| The system under consideration has 𝑛 independent components, and its operation relies on the functioning of at least 𝑘 components, 1 ≤ 𝑘 ≤ 𝑛. The system experiences (𝑛 + 1) distinct shocks. Shock 𝑗 impacts the 𝑗!" component, 𝑗 = 1, 2, . . . , 𝑛, while shock (𝑛 + 1) simultaneously impacts all components. Any shock is lethal if its magnitude is below or above the component-designed thresholds 𝑑# or 𝑑$, respectively. A shock is characterized by its magnitude and arrival time, forming a bivariate random vector. The bivariate random vectors specifying the magnitudes and the arrival times of the shocks are assumed to be independent and follow non-identical bivariate distributions. The reliability of a 𝑘-out-of-𝑛: 𝐺 system under the influence of this type of shocks is derived. The reliability of parallel and series systems is obtained as special situations. The bivariate Pareto type I distribution is applied as an example of the bivariate distribution of the magnitude and arrival time of the shocks. Furthermore, numerical illustrations are conducted to highlight the theoretical results obtained.
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