Optimal maintenance strategy for systems with two failure modes

This paper considers a single-unit system subject to two types of failures: a traditional catastrophic failure and a two-stage delayed failure. Periodic inspections are carried out to identify the defective stage of the two-stage failure process, whereas preventive replacements are implemented to avoid any potential failure due to the catastrophic failure mode. We construct a basic maintenance model and then extend it to the cases of imperfect inspections (i.e., inspections that do not always notice a defective state). We analyze the renewal process of the system and establish the expected long-run cost rate (ELRCR). The optimal inspection period and preventive replacement interval are determined by minimizing the ELRCR. A case study on infusion pumps is presented to illustrate the proposed model

Modified age-based replacement

The maintenance policy of age-based replacement (ABR) is widely specified in OEM instructions. The practical application of ABR raises concerns about ensuring consistent adherence to prescribed replacement schedules for extended periods. ABR lacks periodicity, resulting in scheduling asynchrony with designated time slots, while alternative policies such as block replacement (BR) provide periodicity at the expense of efficiency. Additionally, scepticism about ABR is based on its simplicity and restrictive assumptions, which include ideal replacements and the one-component system assumption. The task of estimating component lifetime distributions and defining critical parameters such as cost of failure, which is an average cost with varying downtime, presents significant challenges. We study “modified age-based replacement” (MABR) in response to the limitation of periodicity, so that preventive replacements exhibit quasi-periodic behaviour. We quantify the cost-inefficiency of MABR compared to ABR, thus informing the practical implications of introducing periodicity into the ABR policy and highlighting the need to incorporate real-world constraints, such as time slots for maintenance actions. The findings indicate that MABR and a special case are reasonably efficient provided the slot-interval is not too large. This is a useful insight for practical application of ABR type policies for scheduling preventive maintenance

Jointly optimizing lot sizing and maintenance policy for a production system with two failure modes

In the reliability literature, there are studies that jointly study maintenance and production and that is typically restricted to one failure mode, and fail to address the case where multiple failure modes exist. This study in-vestigates the problem of joint optimization of lot sizing and maintenance policy for a multi-product produc-tion system subject to two failure modes. The failure of the first mode refers to the soft failure that occurs af-ter defects arrive. The failure of the second mode is a hard failure that occurs without any early warning sig-nals. Products are sequentially produced by the system and a complete run of all products forms a production cycle. The system needs to be re-set up before producing a different product. Both the production cycle and the set-up point depend on the lot sizes of products. Models are proposed for two maintenance policies: 1) arranging the maintenance to be at the end of each production cycle; 2) arranging the maintenance to be at set-up points. The expected profit per unit time is formulated to obtain the optimal lot sizing and maintenance policy. Some properties of proposed models are proved, which show that the optimal lot sizing and mainte-nance policy can be obtained under certain conditions. Case studies and sensitivity analyses are presented to illustrate the proposed models of two maintenance policies. Basically, the results show that the producer will gain the most profit if the optimal lot sizing and maintenance policy are adopted. The results of comparing both maintenance policies reveal that the excessive maintenance is not economic. The sensitivity analyses il-lustrate that reducing the cost caused by failures and improving system reliability are effective ways to in-crease the expected profit per unit time