Reliability of three-state k-out-of-n:G system with non-homogeneous Markov dependent components

TL;DR

This paper derives a closed-form reliability formula for a three-state k-out-of-n:G system with non-homogeneous Markov dependent components, using probability generating functions, and demonstrates it with numerical examples.

Contribution

It introduces a novel closed-form reliability formula for complex three-state systems with Markov dependencies, expanding reliability analysis methods.

Findings

Closed-form reliability formula derived

Applicable to increasing and decreasing three-state systems

Numerical examples validate the formula

Abstract

In this paper, we study the reliability of a three-state k-out-of-n:G system. We consider the situation where the system components are non-homogeneous Markov dependent, and we derive a closed-form formula for the system reliability, including increasing three-state k-out-of-n:G system and decreasing three-state k-out-of-n:G system. Our study is based on the probability generating function method. Two numerical examples are presented to demonstrate the use of the formula.