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Web services providers often commit service-level agreements (SLAs) with their customers for guaranteeing the quality of the services. These SLAs are related not just to functional attributes of the services but to performance and reliability attributes as well. When combining several services into a composite service, it is non-trivial to determine, prior to service deployment, performance and reliability values of the composite service appropriately. Moreover, once the service is deployed, it is often the case that during operation it fails to meet its SLA and needs to detect what has gone wrong (i.e., performance/reliabilty bottlenecks).To resolve these, we develop a continuous-time Markov chain (CTMC) formulation of composite services with failures. By explicitly including failure states into the CTMC representation of a service, we can compute accurately both its performance and reliability using the single CTMC. We can also detect its performance and reliability bottlenecks by applying the formal sensitivity analysis technique. We demonstrate our approach by choosing a representative example of composite Web services and providing a set of closed-form formulas for its bottleneck detection.