A bivariate mixed policy for a system with multistate failure

The paper studies a geometric process model with multistate failure based on preventive repair. Assume that the system has two types of failures when it fails. One is minor failure that a new system is installed after the Nth failure, the other is catastrophic failure that the system can only be removed by replacement. The preventive repair is adopted when its reliability drops to an undetermined constant R. An optimal replacement policy (R, N)* is determined by minimizing the average cost rate. Finally, a numerical example is studied that the operating time of system is a Weibull distribution.