Determinations of MTTF from the Transition Probability Matrix & Diagram

In designing complex repairable systems it is often important to assess system MTTF for a variety of component reliability characteristics and repair capabilities. Two procedures are given for systems for which a state transition diagram is possible. The first allows such calculation to be perforned iteratively without solving each time the system of state equations from the beginning. The approach involves matrix manipulations which split the matrix formulation into two parts; one contains the solution from the previous iteration (at the beginning, the MTTF is calculated in the usual manner) and the other incorporates the changes in the transition probabilities. The second procedure allows the determination of MTTF by decomposing the transition probability diagram into a number of smaller diagrams. For systems with a large number of states and suitably decomposable diagrams the approach reduces considerably the computation time. Simple examples demonstrate the procedures.