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

Vaibhav Bisht () and S. B. Singh ()
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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

International Journal of System Assurance Engineering and Management, 2024, vol. 15, issue 7, No 34, 3293-3305

Abstract: 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.

Keywords: Interval $$L_{z}$$ L z -transform (I $$L_{z}$$ L z ); Universal generating function (UGF); Failure and repair rate; Multi-state system (MSS) (search for similar items in EconPapers)
Date: 2024
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DOI: 10.1007/s13198-024-02337-4

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