Research On Delayed Failure Model Based On Random Work Time

Preventive maintenance and production planning are two important activities in the actual production of the system.If the arrangement is unreasonable,it will cause adverse effects such as system failure,poor production quality,and order delay.In order to ensure the normal operation of the system and the completion of the production plan,these two activities need to be properly planned.Under the framework of the two-stage delayed failure model,this paper combines periodic inspection and production plan to carry out different types of maintenance modeling for different actual production needs.Considering the frequent occurrence of false detection in the actual inspection process,we propose an inspection-maintenance policy for a two-stage delayed failure model.The system performs periodic inspections at time intervals T,and the probability that the periodic inspection judges the defect state as a normal working state is β.At the same time,the system successively executes missions with random working time,and performs random inspection after the completion of each mission.The system can be replaced in two ways:preventive replacements are carried out when the system is in the defective state and failure replacements are carried out when the system fails.Using the renewal reward theorem,the long-term running cost model of the system is established,aiming to optimize the periodic time interval T and the number of periodic inspections M by minimizing the mean cost rate of a renewal cycle.A numerical example is presented to demonstrate the applicability of the proposed maintenance policy.On the other hand,maintenance activities generate demand for spare parts,and the availability of spare parts also affects the maintenance activities,so we propose an orderinspection-maintenance policy for a two-stage delayed failure model.The system has two inspection methods:random inspection and periodic inspection.Spare parts are ordered when the system fails or is defective at an inspection(whichever comes first),and the spare part takes time Lt to arrive.Based on two replacement policies:replacement after completing the task and immediate replacement,aiming to optimize the periodic time interval T by minimizing the mean cost rate of a renewal cycle.A numerical example is presented to demonstrate the applicability of the proposed maintenance policy.