The adoption of the object-oriented (OO) technology for the development of critical software raises important testing issues. This paper addresses one of these issues: how to create effective tests from OO specification documents? More precisely, the paper describes a technique that adapts a probabilistic method, called statistical functional testing, to the generation of test cases from UML state diagrams, using transition coverage as the testing criterion. Emphasis is put on defining an automatic way to produce both the input values and the expected outputs. The technique is automated with the aid of the Rational Software Corporation's Rose RealTime tool. An industrial case study from the avionics domain, formally specified and implemented in Java, is used to illustrate the feasibility of the technique at the subsystem level. Results of first test experiments are presented to exemplify the fault revealing power of the created statistical test cases.