When fracture toughness testing is carried out over the ductile to brittle transition temperature region cleavage instability may be observed at the initiation of cracking or after some prior ductile crack growth. The amount of precleavage ductile crack growth increases with increasing temperature. At the lower test temperatures, it is possible to assume that all tests will result in cleavage instability. However, as the test temperature increases, at some limiting temperature, the failure mode during the final instability changes from cleavage to ductile. These two different types of behaviour can be accommodated in a statistical analysis which is based on the method of competing risks. A statistical approach is presented for the analysis of data by competing risks and a procedure is given for the estimation of the probability of cleavage failure.