Maintenance Policy For Two-Unit Series System With A Cold Standby Component Based On Geometric Process

Due to the speedy development of hi-tech industrial science and technology,the structure of mechanical products is becoming more and more complex,the manufacturing cost is high,and the replacement of the product will result in a large amount of abundant resources.Therefore,the research on maintenance policy for complex system gets great attention in reliability engineering applications.Based on the geometric process,two-unit series system with a cold standby is studied.This paper mainly studies three different maintenance policies,and then three policies are compared and analyzed.For the failure maintenance policy of the system,this paper takes the number of failures N as the maintenance policy.Firstly,using the geometric process and renewal compensation theorem,the expected cost per unit time under long-term operation of the system is analyzed.Then,the geometric process is extended to the generalized geometric process to analyse the expected cost of the system.Finally,the numerical analysis is used to find the optimal maintenance strategy N,which makes the expected cost of the system minimized.For the opportunistic maintenance strategy of the system,it assumes that the working parts of component 2 or 3 will be repaired opportunely when component 1fails,when component 2 or3 is being repaired and another component is in the state of waiting for maintenance,component1 will be repaired by chance,taking the number of failures of component 2 as the replacement strategy,the expected cost per unit time under long-time operation of the system is calculated to find the optimal solution by use of geometric process and generalized geometric process.For the system's maintenance policy with limited working and maintenance time,considering that too short working time and too long maintenance time will increase the maintenance cost,a threshold for the working time and maintenance time of component 2 is respectively set up to reduce the influence.Then it takes the numberof failures of component 2 as the update strategy,and uses two models to compare and analyse the expected cost of the system.Finally,the numerical results of three different maintenance strategies under the same model are compared and analyzed by numerical analysis method for a specific system.It is found that with the more restrictive conditions of maintenance strategy,the maintenance cost of the system maintenance strategy with limited working and maintenance time is the highest,followed by the opportunistic maintenance,which is in line with the actual situation under the geometric process model.Under the generalized geometric process model and the bounded number of failures,the expected cost of the maintenance restrictive strategy is the highest,at the same time,the expected cost of the failure maintenance strategy is less than that of the opportunistic maintenance strategy when the number of failures is between 3 and13.the expected cost of the opportunistic maintenance policy will be the least when N is greater than 13,so the opportunistic maintenance policy is better than the other two strategies.