OPTIMAL NUMBER OF MINIMAL REPAIRS BEFORE REPLACEMENT OF A SYSTEM SUBJECT TO SHOCKS

A system is subject to shocks that arrive according to a nonhomogeneou s Poisson process. As shocks occur a system has two types of failures. Type 1 failure (minor failure) is removed by a minimal repair, wherea s type 2 failure (catastrophic failure) is removed by replacement. The probability of a type 2 failure is permitted to depend on the number of shocks since the last replacement. A system is replaced at the time s of type 2 failure or at the nth type 1 failure, whichever comes firs t. The optimal policy is to select n to minimize the expected cost pe r unit time for an infinite time span. A numerical example is given to illustrate the method. (C) 1996 John Wiley & Sons, Inc.