Spare parts supply with incoming quality control and inspection errors in condition based maintenance
Introduction
Nowadays, sensing and communications technology see a dual improvement in measurement accuracy and cost reduction (Balaji, Nathani, & Santhakumar, 2019). This development motivates companies in different industries to move from traditional time- and age-based preventive maintenance strategies to condition-based (predictive) maintenance. Condition-based maintenance (CBM) is a just-in-time maintenance strategy that intervenes to restore a system whenever it shows signs of deviation from its assumed standard functionality. This operation strategy benefits from the system's whole useful lifetime, which cuts the untimely maintenance activities. Additionally, it is possible to proactively prepare the resources needed to quickly restore the worn out system, reducing costly downtime estimated at $ 260,000 per hour across several businesses (Aberdeen Group, 2020). Maintenance resources include, for example, spare parts, maintenance equipment, and repair tools.
In CBM, remote monitoring of system degradation forms advanced demand information for spare parts requirements. Therefore, it is unnecessary to store an excessive stock of spare parts locally and the maintenance planner can order them in enough time before the system reaches a complete failure state. For many manufacturers, the quality of spare parts is one of the serious issues that affects the availability of their production line (Copperberg, 2021, Deloitte). The reason for this is that the installation of defective spare parts can cause injuries to operators in addition to severe damage to the equipment and, subsequently, costly repairs. In the best case, defective spare parts suffer from an accelerated degradation mode with a much shorter lifespan than a good spare part. Consequently, there is wasted time due to frequent replacements of defective, low quality parts. As a prevention mechanism, the incoming quality control is put in place to systematically inspect the spare parts upon reception before the technicians replace them in the equipment, see, e.g., Chap. 15 in (Montgomery, 2020). As a result, defective spare parts are returned to the vendor and the rest are accepted as good spare parts. It can be difficult and costly to have a perfect inspection process. Therefore, it is reasonable to include inspection errors in the modeling. That is, the Type I error, known as false positive, is defined as the probability that a good item will be found to be defective after inspection. Type II error, known as false negative, is defined as the probability that a defective item is found to be good. In the sequel, we shall use the term ‘defective’ part to mean a part with an inferior quality.
The success of CBM implementation lies in capturing the impact of the quality of the spare parts and the imperfect inspection on the maintenance cost and the system availability. We propose an integrated maintenance model taking into account spare part quality, spare part order lead time, Type I and II inspection errors, and maintenance cost factors, e.g., replacement cost, holding cost, and shortage cost. Our objective is to minimize the monthly maintenance cost subject to a constraint on the system availability by deciding on the proper level of degradation at which a spare part is ordered. As the inspection is subject to errors, we consider that some spare parts installed in the system are defective and have an accelerated degradation mode. The system of interest is a continuously monitored system with a gradual degradation process. This type of degradation is prevalent in modeling, e.g., the crack growth of wind turbine rotor blades, the diminishing capacity of Lithium-Ion batteries used in electric vehicles, and the corrosion spread in oil and gas pipelines. In a case study from wind energy, we show that the optimal monthly maintenance cost increases at the same rate as the mean degradation per time unit. The squared coefficient of variation of the degradation per time unit has a minor impact on cost. The spare part lead-time and the spare part price are the leading parameters influencing the optimal monthly maintenance cost. The value of a proper inspection process pays back up to 22 % cost savings as the reliability of spare parts deteriorates. Finally, costly process of detecting defective parts after their installation in the system has a limited impact on maintenance costs.
The rest of the paper is organized as follows. In Section 2, we give a comprehensive literature review on CBM, spare part quality, and inspection issues. We show a gap in the literature in CBM optimization that considers the quality of spare parts and the inspection errors. Due to the problem of analytical complexity, we propose in Section 3 a new approximate closed-form model for the performance analysis, namely the monthly maintenance cost and the average availability. In Section 4, we analyze our model's accuracy and optimize it for a case study constructed from the literature. Finally, Section 5 gives the main conclusions and defines several promising future research directions.
Section snippets
Literature
This section first surveys the literature on the joint optimization of preventive maintenance planning and spare parts inventory. Second, it focuses on the literature with the integration of spare parts quality and maintenance planning.
One of the seminal papers to integrate the optimization of spare parts planning and age-based maintenance was (Armstrong & Atkins, 1996). They showed empirically that the integrated optimization outperformed the separate optimization of spare parts apart from the
Model
In this section, we first give the model description followed by the notation and the model assumptions. Finally, we derive the key performance measures analytically.
We consider a part that suffers from gradual degradation. The part is continuously monitored. Whenever the part’s degradation reaches a predetermined (ordering) limit, a spare part is ordered. Note, some of the spare parts supplied by the vendor are defective. The spare part needs a lead-time, , to arrive at the site. During the
Model accuracy
In this section, we test the model accuracy by comparing the results with those of discrete-event simulation in Arena software. We consider an item with a degradation modelled as a Gamma process with a shape parameter and a rate parameter . In the simulation, we relaxed the Markovian assumption of the part’s evolution over time and the assumption of at most two rejections in a sequence of reordered items. In total, we consider 1,536 different scenarios as follows.
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Conclusion
In this paper, we considered a part suffering from gradual degradations and monitored it continuously. We proposed an accurate maintenance model integrating the spare part quality issues, inspection errors, and the supply lead-time in addition to the different cost factors, e.g., replacement cost, holding cost, and shortage cost. In a case study of a wind turbine rotor blade, we optimize the monthly maintenance cost subject to a constraint on the part’s availability. Our crucial decision is the
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgment
This work has been supported by the Research Center on Smart Mobility and Logistics, King Fahd University of Petroleum & Minerals under grant INML2103.
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