A simple Markovian method for MTTF calculation

The MTTF of a system design with constant failure and repair rates and with some forms of stand-by redundancy and switching is an important characteristic of the system. Commonly, calculation of the MTTF requires knowledge of the reliability function R(t), which is integrated to yield the MTTF. In many cases obtaining the reliability function is a non-trivial task and its analytic integration may be quite tedious. In the following we describe a simple method of obtaining the MTTF of such systems which avoids the need of knowledge of R(t). The method is Markovian in nature and is based on summing the probabilities of all the possible routes (in the space of states) by which the system can get from its initial state at t = 0 to an absorbing state (failed state), where each such probability is multiplied by the average time required for the system to follow that route. This weighted sum yields the MTTF for any given initial conditions. The method is demonstrated on some useful systems and analytical formulas for the MTTF are derived. It is further demonstrated how the results of the method may be used in the calculation of the MTBF of the system in steady-state.