State distribution and reliability of some multi- state systems with complex congurations

Abstract

In this paper, our goal is to investigate, rst, the multi-state consecutive k_n-out- of-m_n : G series systems and second, the multi-state consecutive k_n-out-of-m_n : G parallel systems (see denitions 1 and 2).We begin by giving a non recursive formula which calculates the state distribution and the reliability of multi-state consecutive k-out-of-n : G system in the case where the number k of functioning components depends on the system state level (see agreement 1), then we extend the used method to the multi-state consecutive k_n-out- of-m_n : G series and multi-state consecutive k_n-out-of-m_n : G parallel systems. In the end, we illustrate the obtained theoretical results by a numerical application.

Keywords: Reliability; Multi-state system; Consecutive k-out-of-n : G system; Consecutive