NEW APPROACH TO EVALUATE THE FAILURE PROBABILITY OF A $K-OUT-OF-N$ SYSTEM UNDER HARMFUL SHOCKS

Moujib Jarray; Nizar Mannai; Soufiane Gasmi

NEW APPROACH TO EVALUATE THE FAILURE PROBABILITY OF A $K-OUT-OF-N$ SYSTEM UNDER HARMFUL SHOCKS

Abstract

This paper introduces a novel approach to calculating the failure probability of $k-out-of-n$ systems under harmful shocks, which occur randomly and affect at least one component. Traditional methods for this calculation face challenges such as high computational costs and complexity, especially for large systems. The new approach simplifies the computation by developing an easily executable algorithm, saving time and resources. The proposed formula has been shown to be equivalent to existing ones. Additionally, it has been demonstrated that the failure probability under certain conditions follows a binomial distribution, with system design influencing the failure probability for each shock.

Keywords

Thanks

The authors would like to extend their gratitude for the reviewers for the valuable feedback and insightful comments, which have greatly contributed to improving the clarity and quality of this work. Thank you for the time and effort you dedicated to guiding this work in the right direction.

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Details

Primary Language

English

Subjects

Applied Statistics, Operations Research İn Mathematics

Journal Section

Research Article

Authors

Moujib Jarray
0000-0001-7920-7183
Tunisia

Nizar Mannai ^* This is me
0000-0003-4454-4926
Tunisia

Soufiane Gasmi
0000-0002-7583-5286
Tunisia

Publication Date

November 3, 2025

Submission Date

September 4, 2024

Acceptance Date

December 19, 2024

Published in Issue

Year 2025 Volume: 15 Number: 11

IZ

https://izlik.org/JA27HP75NW

Cite

RIS / Bibtex

APA

Jarray, M., Mannai, N., & Gasmi, S. (2025). NEW APPROACH TO EVALUATE THE FAILURE PROBABILITY OF A $K-OUT-OF-N$ SYSTEM UNDER HARMFUL SHOCKS. TWMS Journal of Applied and Engineering Mathematics, 15(11), 2624-2637. https://izlik.org/JA27HP75NW

AMA

1.Jarray M, Mannai N, Gasmi S. NEW APPROACH TO EVALUATE THE FAILURE PROBABILITY OF A $K-OUT-OF-N$ SYSTEM UNDER HARMFUL SHOCKS. JAEM. 2025;15(11):2624-2637. https://izlik.org/JA27HP75NW

Chicago

Jarray, Moujib, Nizar Mannai, and Soufiane Gasmi. 2025. “NEW APPROACH TO EVALUATE THE FAILURE PROBABILITY OF A $K-OUT-OF-N$ SYSTEM UNDER HARMFUL SHOCKS”. TWMS Journal of Applied and Engineering Mathematics 15 (11): 2624-37. https://izlik.org/JA27HP75NW.

EndNote

Jarray M, Mannai N, Gasmi S (November 1, 2025) NEW APPROACH TO EVALUATE THE FAILURE PROBABILITY OF A $K-OUT-OF-N$ SYSTEM UNDER HARMFUL SHOCKS. TWMS Journal of Applied and Engineering Mathematics 15 11 2624–2637.

IEEE

[1]M. Jarray, N. Mannai, and S. Gasmi, “NEW APPROACH TO EVALUATE THE FAILURE PROBABILITY OF A $K-OUT-OF-N$ SYSTEM UNDER HARMFUL SHOCKS”, JAEM, vol. 15, no. 11, pp. 2624–2637, Nov. 2025, [Online]. Available: https://izlik.org/JA27HP75NW

ISNAD

Jarray, Moujib - Mannai, Nizar - Gasmi, Soufiane. “NEW APPROACH TO EVALUATE THE FAILURE PROBABILITY OF A $K-OUT-OF-N$ SYSTEM UNDER HARMFUL SHOCKS”. TWMS Journal of Applied and Engineering Mathematics 15/11 (November 1, 2025): 2624-2637. https://izlik.org/JA27HP75NW.

JAMA

1.Jarray M, Mannai N, Gasmi S. NEW APPROACH TO EVALUATE THE FAILURE PROBABILITY OF A $K-OUT-OF-N$ SYSTEM UNDER HARMFUL SHOCKS. JAEM. 2025;15:2624–2637.

MLA

Jarray, Moujib, et al. “NEW APPROACH TO EVALUATE THE FAILURE PROBABILITY OF A $K-OUT-OF-N$ SYSTEM UNDER HARMFUL SHOCKS”. TWMS Journal of Applied and Engineering Mathematics, vol. 15, no. 11, Nov. 2025, pp. 2624-37, https://izlik.org/JA27HP75NW.

Vancouver

1.Moujib Jarray, Nizar Mannai, Soufiane Gasmi. NEW APPROACH TO EVALUATE THE FAILURE PROBABILITY OF A $K-OUT-OF-N$ SYSTEM UNDER HARMFUL SHOCKS. JAEM [Internet]. 2025 Nov. 1;15(11):2624-37. Available from: https://izlik.org/JA27HP75NW