Bivariate Preventive Repair Policies For A Repairable System Assuming Geometric Process

The preventive repair policies of repairable system are importantly discussed and studied in the mathematical theory of reliability, which are of some practical significane in raising the availability, extending the operating life of the system.Firstly, this paper presents a bivariate preventive repair policy with no failure waiting time (R,N) assuming geometric process.We shall adopt an assumption that the interval of the preventive rapair will depend on the reliability of the system instead of the fixed length of the preventive rapair. When the reliability of the system drops to a constant R which is called a critical reliability of the system,the system is closed and the preventive repair is executed at once, no failure waiting time, the preventive repair is not as good as new. the explicit expression of the average cost rate is derived. By MATLAB, the optimal policy (R*, N") is derived which make the average cost rate minimized.Secondly, a bivariate preventive repair policy with failure waiting time (L,N) assuming geometric process is presented. We assume that when the system fails, it will be replaced in the next preventive rapair time rather than at once, so there will be a failure waiting time between failure time and the replaced time. the explicit expression of the average cost rate of this model is derived. By MATLAB, the optimal policy(L*,N*) is derived which make the average cost rate minimized.Thirdly, this paper combine the above two policies, a bivariate preventive repair policy with failure waiting time (R,N) assuming geometric process is studied. The explicit expression of the average cost rate of this model is derived. By MATLAB, the optimal policy (R**,N**) is derived which make the average cost rate minimized.At last, compare the optimal policies(L**,N**) and(R**,N**) with failure waiting time, the later is better.