Replacement Policies for an Independent Damage Process.

This paper discusses preventive replacement policies for an independent damage process, in which successive shocks occur at random times, and the independent damages caused by shocks are random variables. It is assumed that a unit fails when the damage has exceeded a prespecified level K. We consider three models: Model 1: the unit is replaced at the M th shock for damage Z , at damage K , or at time T , whichever occurs first. Model 2: the unit is replaced at the M th shock for damage Z , at damage K or at shock N , whichever occurs first. Model 3: the unit is replaced at the M th shock for damage Z , at damage K , at shock N or at time T , whichever occurs first. We obtain the expected cost rates for each model and discuss analytical optimal T ∗ and N ∗ to minimize their expected cost rates. Numerical examples are given when the damage has an exponential distribution and shocks occur at a gamma distribution. [ABSTRACT FROM AUTHOR]