This paper defines a new utility importance of a state of a component in multi-state systems. This utility importance overcomes some drawbacks of a well-known importance measure suggested by William S. Griffith (J. Applied Probability, 1980). The relationship between this new utility importance and the Griffith importance is studied and their difference is illustrated with examples. The contribution of an individual component to the performance utility of a multi-state system is discussed. Examples show that a meaningful index for measuring the performance of individual components in a multi-state system can hardly be defined in general, without considering the actual values of the utility levels and the distributions of the component-states in the system. An example illustrates how genetic algorithm, simulated annealing, and tabu search can be used in selecting components and defining the position order of components so that the performance utility of a multi-state system is optimized.