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Interval valued reliability indices assessment of multi-state system using interval $$L_{z}$$ L z -transform

Author

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  • Vaibhav Bisht

    (G.B. Pant University of Agriculture and Technology)

  • S. B. Singh

    (G.B. Pant University of Agriculture and Technology)

Abstract

This research introduces a new method, called Interval $${L}_{z}$$ L z -transform (ILz), designed to estimate the reliability indices of Multi-State systems (MSS) even when data is uncertain or insufficient. Traditionally, precise values of state probabilities and performance metrics for each component were required, which could be challenging when data is lacking. To address this, the Interval $${L}_{z}$$ L z function is proposed, along with corresponding operators, enabling the calculation of interval-valued reliability indices for MSS. To demonstrate the effectiveness of the proposed method, it is applied to a numerical example of a series–parallel system. In this example, we determine interval-valued reliability indices such as reliability, availability, mean expected performance, and expected profit, considering uncertain values for the performance and failure rates of each multi-state component.

Suggested Citation

  • Vaibhav Bisht & S. B. Singh, 2024. "Interval valued reliability indices assessment of multi-state system using interval $$L_{z}$$ L z -transform," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 15(7), pages 3293-3305, July.
    • Handle: RePEc:spr:ijsaem:v:15:y:2024:i:7:d:10.1007_s13198-024-02337-4
    DOI: 10.1007/s13198-024-02337-4
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    References listed on IDEAS

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    1. Richard E. Barlow & Alexander S. Wu, 1978. "Coherent Systems with Multi-State Components," Mathematics of Operations Research, INFORMS, vol. 3(4), pages 275-281, November.
    2. Negi, Seema & Singh, S.B., 2015. "Reliability analysis of non-repairable complex system with weighted subsystems connected in series," Applied Mathematics and Computation, Elsevier, vol. 262(C), pages 79-89.
    3. Lisnianski, Anatoly & Frenkel, Ilia & Khvatskin, Lev, 2017. "On sensitivity analysis of aging multi-state system by using LZ-transform," Reliability Engineering and System Safety, Elsevier, vol. 166(C), pages 99-108.
    4. Anatoly Lisnianski & Ilia Frenkel & Lev Khvatskin, 2021. "Modern Dynamic Reliability Analysis for Multi-state Systems," Springer Series in Reliability Engineering, Springer, number 978-3-030-52488-3, July.
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