| Summary: | 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.
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