Risk reduction in service contract fullfilment

In the service industry, performance-based contracts are a growing trend. Companies provide a service, and their yearly revenues depend on the quality or performance of that service during this year. This means that long-term averages are no longer sufficient for predicting cost-flow, the system also has to be analyzed during specific time intervals. This is usually done by considering an appropriate Markov chain, however closed form expressions for higher moments of the interval availability are only known for 2-state Markov chains. We have extended this model to a 3-state Markov chain, for which we have derived a closed form expression for the second moment of the interval availability under a few general constraints. We consider possible expansions of our model by examining specific cases, and for these cases we give results on the second moment and the constraints under which these results hold. We also provide a general framework for analyzing larger systems by considering their components individually. Using a few numerical examples, we outline the possible uses of our results.