Availability of Repairable Units When Failure and Restoration Rates Age in Real Time

In reliability engineering and practice an important role is played by those units whose life characteristics change with time. The case is herewith considered where change underlies a nonhomogeneous Markov model. Simple repair processes then deal with a 2-state alternating policy resulting from the superposition of failure and restoration, both showing a continuous aging with time. Availability can be expressed through linear differential equations or by means of integral equations; the approaches are equivalent. A computer code is then described which calculates (i) availability, and (ii) transition densities for any continuous time dependence of failure and restoration rates. Numerical results are shown for a few examples.