Conditional MTTF and its computation in Markov reliability models

Mean time to failure (MTTF) is one of the most frequently used dependability measures in practice. MTTF is the expected time for a system to reach the predefined failure states due to any of the failure causes. If system failures are classified into different types, conditional MTTF may well be useful. In this paper, we discuss the notion of conditional MTTF and develop an efficient computational method of computing 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. We introduce the concept of cumulative conditional MTTF and apply it for the computation of the mean time to critical (unsafe, hazardous) failures.