Reliability analysis of multi-state system with three-state components and its application to wind energy

In most real life situations, the system's components contribute differently in different performance levels. Such a situation can be modeled by systems with multi-state components having more than one working status, e.g. perfect functioning, and partial working. In this paper, a multi-state system that consists of two types of three-state components is defined and studied. An explicit formula for the probability that the performance of the system is at least a given level is obtained for the most general case when the components are statistically dependent. The model is applied to evaluate the wind power system that consists of two wind plants in different regions. An optimization problem is formulated to find the optimal number of wind turbines that must be installed in the wind plants by minimizing the total cost under specific power production.