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Exact Reliability for a Multi-State Consecutive Linear (Circular) $k$ -out-of- $r$ -from- $n : F$ System

Y. Amirian

Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

E-mail Address: y_amirian@sbu.ac.ir

Corresponding author.

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A. Khodadadi

Department of Statistics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

E-mail Address: a_khodadadi@sbu.ac.ir

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https://doi.org/10.1142/S0218539321500145Cited by:3 (Source: Crossref)

Abstract

The multi-state consecutive linear (circular) $k$ -out-of- $r$ -from- $n : F$ system consists of $n$ linear (circular) ordered multi-state components. Both the system and its components can have $m$ different states: from complete failure (zero state) up to perfect functioning (( $m -$ 1) state). In this paper we suggest, for the first time, exact reliability for these models. The system is at state below $j$ if and only if at least $k_{j}$ components out of any $r$ consecutive are in state below $j$ $(k_{1} \leq k_{2} \leq \dots \leq k_{m - 1})$ . Recent efforts in these branches have focused on simple situations or approximation bands for their reliability in two-state or multi-state models but closed form and exact amount not gained. In the continuation, there are the matlab programs of linear (circular) reliability system and $j$ state probability for $k_{j}$ in system. In the following, we applied comparative and numerical results and calculated the exact reliability of this strategic systems. Finally, we calculated the exact reliability for two real-world practical examples.

Keywords:

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