Erlang Strength Model for Exponential Effects

Abstract

All technical systems have been designed to perform their intended tasks in a specific ambient. Some systems can perform their tasks in a variety of distinctive levels. A system that can have a finite number of performance rates is called a multi-state system. Generally multi-state system is consisted of components that they also can be multi-state. The performance rates of components constituting a system can also vary as a result of their deterioration or in consequence of variable environmental conditions. Components failures can lead to the degradation of the entire multi-state system performance. The performance rates of the components can range from perfect functioning up to complete failure. The quality of the system is completely determined by components. In this article, a possible state for the single component system, where component is subject to two stresses, is considered under stress-strength model which makes the component multi-state. The probabilities of component are studied when strength of the component is Erlang random variables and the stresses are independent exponential random variables. Also, the probabilities of component are considered when the stresses are dependent exponential random variables.