ABSTRACT

In industrial reliability testing, it may be fruitful to classify individuals by the physical mode of failure. Alternatively when the failure of a system is involved, the particular component or subsystem failing may define the type of failure. The notion of 'eliminating' a type of 'failure' may have a clearcut meaning, as for example when the types of failure refer to separate subsystems. Product-limit estimates can be formed separately for the different types of failure and their statistical fluctuations treated as asymptotically independent. For a historical review of competing risk theory, see H. L. Seal, and for an account of the extensive actuarial work on multiple types of failure, R. C. Elandt-Johnson and N. L. Johnson. The chapter considers briefly some ideas useful when, associated with each failure, there is a further measurement, additional to the failure time, this additional measurement being in some sense a 'response', to be interpreted in conjunction with the failure time.