Defining mean time-to-failure in a particular failure-state for multi-failure-state systems

In multi-failure-state systems which have both dangerous (critical) and safe (noncritical) failure states, it is both meaningful and important to be able to measure the MTTF in a particular failure state separately from MTTF in general. MTTF_D (fail dangerous) and MTTF_S (fail safe) are defined, emphasizing the engineering context of the problem. Methods are developed for computing these indexes. These methods require only finding the MTTF of a modified Markov model. The model modifications are relatively simple and can account for the effects of various repair and maintenance policies. An example illustrates the methods. These developments are related to the classic theory of Markov models. Several other methods for computing `mean time to critical failure´ are shown to be special cases of the more general method presented here