Conditional MTTF and its computation in Markov reliability models

The authors discuss the notion of conditional MTTF (mean time to failure) and develop an efficient computational method for the absorption probability and conditional MTTF in a finite state-space Markov model. The method requires the solution of two systems of linear equations of size n, where n is the number of transient states in the Markov chain. The concept of cumulative conditional MTTF is introduced and applied to computation of the mean time to critical (unsafe, hazardous) failures.<>