Bounds for increasing multi-state linear k -within-(r ,s )-of-(m ,n ):F lattice system
International Journal of Quality & Reliability Management
ISSN: 0265-671X
Article publication date: 8 May 2018
Abstract
Purpose
A multi-state linear k-within-(r, s)-of-(m, n): F lattice system consists of m×n components arranged in m rows and n columns. The possible states of the system and its components are: 0, 1, 2, …, H. According to k values, the system can be categorized into three special cases: decreasing, increasing and constant. The system reliability of decreasing and constant cases exists. The purpose of this paper is to evaluate the system reliability in increasing case with i.i.d components, where there is no any algorithm for evaluating the system reliability in this case.
Design/methodology/approach
The Boole-Bonferroni bounds were applied for evaluating the reliability of many systems. In this paper, the author reformulated the second-order Boole-Bonferroni bounds to be suitable for the evaluation of the multi-state system reliability. And the author applied these bounds for deriving the lower bound and upper bound of increasing multi-state linear k-within-(r, s)-of-(m, n): F lattice system.
Findings
An illustrated example of the proposed bounds and many numerical examples are given. The author tested these examples and concluded the cases that make the new bounds are sharper.
Practical implications
In this paper, the author considered an important and complex system, the multi-state linear k-within-(r, s)-of-(m, n): F lattice system; it is a model for many applications, for example, telecommunication, radar detection, oil pipeline, mobile communications, inspection procedures and series of microwave towers systems.
Originality/value
This paper suggests a method for the computation of the bounds of increasing multi-state linear k-within-(r,s)-of-(m,n): F lattice system. Furthermore, the author concluded that the cases that make these bounds are sharper.
Keywords
Citation
Radwan, T. (2018), "Bounds for increasing multi-state linear
Publisher
:Emerald Publishing Limited
Copyright © 2018, Emerald Publishing Limited