The Researches In Renewal-geometric Process And Maintenance Policies Problems

The maintenance problem of repairable system is a hot issue of the reliability theory researches. In the research of mathematical theory about the maintenance strategy problems, it is crucial that the system reliability model is built better subjected to reality. Basing on the actual situation, the maintenance model can help us control the balance between high reliability and limited resources. In this paper, the main work was made as follows:Firstly, on the basis of the existing renewal process and geometric process, basing on the idea that the system is deteriorative stage by stage, the paper first introduces a class of new stochastic process, namely the renewal-geometric process. After giving the related definitions of the renewal-geometric process, the paper studies some distribution functions of the renewal-geometric process and the related properties.Secondly, the paper studies maintenance strategy problems basing on the idea that the system is deteriorative stage by stage. Without considering the effect of external shock and assuming the system occurs in a stable situation, this paper builds two maintenance models. Model Ⅰ considers that the system occurs deterioration at different probability during the different running period and running process of the system is divided two stages. Basing on above assumes, the paper obtains the expression of the average cost rate with the maintenance policy N, and verifies the validity of the model according to the change of the parameter sensitivity analysis. Model Ⅱ also divides the process into two parts, which are forward renewal process and afterward geometric process. Furthermore, we study the relationship of maintenance policies between the geometric process model and the second maintenance model based on the renewal-geometric process. Meanwhile, the optimum values N* and N** for minimizing the average cost rate could be determined respectively numerically.Finally, this paper builds model Ⅲ with considering the system is affected by external shock. In this model, mainly studies binary maintenance policy. Moreover, numerical formulas are given.