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Specification mutation involves mutating a specification, and for each mutation a test is derived that distinguishes the behaviours of the mutated and original specifications. This approach has been applied with finite state machine based models. This paper extends mutation testing to finite state machine models that contain non-functional properties. The paper describes several ways of mutating a finite state machine with probabilities (PFSM) or stochastic time (PSFSM) attached to its transitions and shows how we can generate test sequences that distinguish between such a model and its mutants. Testing then involves applying each test sequence multiple times, observing the resultant behaviours and using results from statistical sampling theory in order to compare the observed frequency and execution time of each output sequence with that expected.