Research On Maintenance Policy For Degenerative Repairable Systems Based On Geometric Process

In the research of maintenance policy for the system, the degenerative repairable systems based on geometric process are very common. In a degenerative system based on geometric process, the consecutive repair times after system failure are increasing and the successive survival times of the system are decreasing. Degenerative systems based on geometric process are widely applied in many systems, such as in computer network systems, power systems, aerospace equipments, nuclear power plants, large weapon equipments, and production line systems. These systems could cause a great of loss if they fail in the working stage. So the research on the maintenance policy for degenerative system based on geometric process has very important theoretical and practical significance.In recent years, the research on maintenance policy for the degenerative repairable systems based on geometric process has got some achievenments. However, the modeling and analysis on these systems are difficult due to their complexity. There are still some problems need to be solved. This dissertation considers some complex systems in practical applications and develops some degenerative system models in which the working times and the repair times form geometric process. The main aim is to seek for optimal maintenance policy for such models.Firstly, the inspection policy and replacement policy for degenerative system in finite time is considered. The following three models are considered: the system will not be replaced; the system will be replaced; and the system which will be replaced and has backup copy. In every model, different policies are proposed. Using probability analysis methods and the properties of geometric process, the explicit expression of the average cost before the first failure is derived. Through the numerical examples, we compare every policy to determine the most suitable policy for the system.Secondly,the maintenance policy for the d-shock model with cold standby and two types of failures is analyzed. The two kinds of failures are considered. One is the common failure and the other one is the failure caused by shocks. Using renewal process and geometric process theory, the explicit expression of the long-run average profit per unit time is derived. Then, for the specific distribution functions, the maintenance policy which makes the average profit maximized is studied, and the sensitivity analysis of important parameters are given to reveal the affect of these parameters on optimal policy and average profit.Subsequently, the preventive maintenance and inspection are considered in the series system with two components and the optimal maintenance policy is studied. Through probability analysis methods, the average working time and repair time of the system are derived, and using the renewal process theory and geometric process theory, the explicit expression of the long-run expected average profit per unit time and the average downtime are derived. Then, the maintenance policies which make the average profit maximized and the average downtime minimized are studied. In addition, we compare this policy with that has not inspection or preventive maintenance to emphasize the important of preventive repair and inspection in improving the realiability of the system.Then, the study of maintenance policy for degenerative repairable systems based on geometric process which has lead time is generalized to multiple unit system and multiple failure state system. If the unit needs to be replaced, the new one should be ordered in advance. In this case, the cost of storage and the cost of loss due to the shutdown of the system must be considered. In every model, the explicit expression of the long-run average profit per unit time is derived, and the existence and uniqueness of the optimal policy and the method of searching for the optimal policy are given. Then, the maintenance policies which make the average profit maximized are studied.Finally, the preventive maintenance and ordering policy which make the average downtime minimized or average profit of the production line of ring-pull can maximized are analyzed. These quantitative analyses may have practical value for improving the realiability of the system and the production efficiency.