Bivariate optimal repair replacement policy for a deteriorating system

A replacement model using stochastically deceasing and increasing processes for successive survival and repair times is studied. A system is repaired on failure. With probability p it is returned to the ‘good as new’ state (perfect repair) while the repair is imperfect with probability 1 − p. The successive survival and repair times following imperfect repairs are governed by processes which are stochastically non-increasing or non-decreasing respectively. Using a bivariate replacement policy (T, N) explicit expressions for the long-run average cost per unit time are obtained. Optimal policy (T, N)* is shown to be superior to policies T* and N* studied hitherto.