Comparison of two lower bounds for availabilities in multistate monotone systems -an established one and a new one

Abstract

The lower bounds are used to determine availabilities of a system, and are used in many different companies. Such is for example a company that supplies water to a city. The company would most likely want to know how reliable the water system is. Does the water system deliver minimum 40% or more of its water capacity to the city? It is important to have a lower bound that is close to the real value. I will therefore in this paper show, and explain, what a Multistate Monotone System (MMS) is, and compare two lower bounds. The bounds are a new lower bound and an established lower bound. I will also present the theorems linked to the bounds, and establish some points to make computer implementation easier. I am also going to show something that I have figured out, a new theorem, and an algorithm which makes it easier to identify minimal cut vectors. Part of the computer code will be discussed and explained, where some of the algorithms will be shown as Pseudocode. The computer simulation gives data that will be shown in plots and used to compare the two bounds. The comparison of the two bounds shows that the new bound is better than the established bound.