Joint optimization of multi-window maintenance and spare part provisioning policies for production systems

https://doi.org/10.1016/j.ress.2021.108006Get rights and content

Highlights

  • A state-based maintenance-inventory model is formulated for production systems.

  • Three levels of maintenance windows are set to enhance decision-making robustness.

  • The system net profit is maximized by optimizing the inspection interval and delay time.

Abstract

Advanced asset management emphasizes the collaborative schemes of maintenance and spare part resources driven by asset health status. This paper formulates a joint optimization model of maintenance-spare part provisioning policy for a production system with observable defect information and postponed spare part supplies. Three levels of state-based maintenance windows, (a) regular inspection window (RIW); (b) defect removal window (DRW), and (c) pre-specified overhaul window (POW) are integrated to promote the timeliness and robustness of maintenance decision-makings, and mitigate production downtime due to spare part delays. In particular, a spare part order is induced upon defect identifications at DRW and the system continues production until being replaced as soon as the order arrives at the maintenance base, or being renewed at POW when the system attains a specified age. As such, spare part replacement is delayed, so as to leave enough time for resource preparation, and prolong the remaining useful lifetime. The system net profit is maximized through the interval optimization of RIW and DRW. A numerical experiment on maintenance engineering of a steel convertor plant is used to demonstrate the proposed methodology.

Introduction

Preventive maintenance (PM) is essential to reduce downtime losses and improve the availability of diverse industrial systems, which is broadly reviewed in the literature, see, e.g., Syamsundar et al. [1], Wang et al. [2], Yang et al. [3], Zhao et al. [4], Mizutani et al. [5]. Substantially, PM can be divided into two categories, i.e., (a) age-based maintenance (ABM) that schedules maintenance based on the operational age, and (b) condition-based maintenance (CBM) action, carried out mainly based on deterioration level. Powered by the rapid development of monitoring/inspection technology, inspection-based CBM is drawing increasing attention, particularly for production/manufacturing systems with multiple observable performance indicators [6,7]. Wang [8] pointed out that over 80% of PM activities were driven by inspection outcomes, either periodic or aperiodic. Scott [9] and Sarker et al. [10] studied a periodical inspection-based preventive repair model. Fauriate and Zio [11] optimized an aperiodic inspection-driven CBM policy for a randomly deteriorating system. Peng et al. [12] and Zhang et al. [13] demonstrated that either periodic or aperiodic inspection played an important role in maintenance decision processes.

A representative application of inspection-based maintenance was delay-time-based maintenance (DTM), which was first reported by Christer [14]. As proved by Nicolai and Dekker [15], DTM had a significant advantage in exploring the effect of inspection, which had been widely and successfully applied in industry. Such definition divides the malfunction process into two independent stages, from new to the defect initialization, and then to the ultimate malfunction (also known as delay time). The hidden defective state is a crucial basis for PM decisions, which can only be revealed by inspections. A common assumption shared by DTM model is to replace/repair the system immediately upon the defect identification. In a contrast, the latest advancement implies to postpone such maintenance, as the remaining delay time can be better exploited. Berrade et al. [16] and Zequeira et al. [17] concluded situations that maintenance actions can be postponed. Chen [18] indicated a postponed replacement could avoid an unrecoverable job caused by the replacement. Besides, Van Oosterom et al. [19] proposed that the delay to replace the defective system could provide enough time and resources to prepare for maintenance. Scarf and Cavalante [20] expressed that postponed replacement could avoid the ineffective early replacement as a result of a false inspection whereby the perfect system may be replaced by a weak system. Adkins and Paxson [21] were concerned with the timely replacement action that may reduce the probability of extending the residual life of systems. Zhang and Yang [22] further explored the effects of environmental damage and health state variation on postponed replacement.

Notably, most DTM models e.g., Liu et al. [23], Berrade et al. [16], Zhang and Yang [24], ignored the inventory problem or assumed that spare parts were always available upon maintenance. Nonetheless, actual production/manufacturing processes often suffer from the problem of spare part shortage, due to resource/cost limitations. The ignorance of spare part provisioning problems can mislead maintainers and lead to unnecessary production losses. Although the maintenance and spare part provisioning problems were strongly interconnected, their collaborative optimization approach was rarely addressed, particularly in DTM models. Regarding ABM, Falkner [25], Sarker and Haque [26], and Brezavscek [27] jointly optimized the age-based replacement policy and spare parts inventory policy. Wang et al. [28] further extended the policy to a hybrid CBM-ABM case. Wang [29] was one of the first to employ DTM to integrate maintenance scheduling and spare part allocation, where inventory decision was made according to inspection outcome. However, maintenance actions in practice are not only up to the system state, but also depend on the level of spare parts. Herein, maintenance has to be delayed unless the spare part arrives at the base, whose waiting time is usually non-negligible. It is then of practical interest to explore how PM decision-making is affected by both heath status and limited spare part resources, which, to the best of our knowledge, has never been reported in current literature.

To answer this question, this paper formulates a novel multi-window, state-based maintenance-inventory model for production systems with hidden defective information. The proposed approach is different from current models from three perspectives. Firstly, most DTM models assumed a single maintenance window for inspection, see, e.g., Wang [30], Yang et al. [31]. Our model, as a contrast, sets three levels of maintenance windows (regular, urgent, pre-specified) to enhance decision-making robustness, with full consideration of system state and operational age. Secondly, by ordering spare parts upon defect identification, we actually allow renewals of a defective system to be postponed, until the spare part arrives at the maintenance base, or a pre-specified window, which can sufficiently utilize the remaining useful delay time. Finally, we evaluate the comprehensive impact of both state variation and order arrival time on maintenance and production plans, which improves the responsiveness of the policy. Through joint optimization of multiple window intervals, the net profit of the production system is maximized, whose effectiveness is validated by numerical experiments on a steel convertor plant.

The remainder of this paper is structured as follows. Section 2 introduces the basic system characteristics. The joint maintenance and spare parts provisioning policy is elaborated in Section 3. Section 4 calculates the steady revenue of the system through renewal scenario analysis. An illustrative example is given in Section 5 to illustrate the model. Section 6 concludes this paper and discusses possible directions of future research.

Section snippets

System characteristics

We consider a single-unit production system subject to a two-stage deterioration failure. The first stage is the defect initialization stage, during which the system works normally without incurring any warning signals. The second stage is the defect propagation stage, during which early-warning signals such as cracks, dents, over-vibration, abnormal temperature can be revealed, indicating that the system has entered a high-risk operational status. Without advanced maintenance interventions,

The policy

As aforementioned, three crucial messages affect the decision-making of maintenance and spare-part programming, including (a) real-time state of the production system, (b) spare part arrival time (random), and (c) the operational age of the system. Notably, the identification of the system state and the further spare part replacement are only feasible at discrete time epochs, due to technical and resource limitations. To this end, we design a comprehensive, state-based maintenance and spare

Revenue optimization

To formulate the revenue optimization model, we need to calculate the expected cycle length, expected cycle cost and expected production revenue over a cycle. To this end, the probabilities of system renewal scenarios are evaluated.

Numerical experiment

A numerical experiment on a steel convertor plant in a steel mill is used to illustrate the proposed maintenance-inventory policy. The function of this plant is to convert molten iron into steel by removing impurities through the oxidation process. The condition of the plant can be detected by periodic inspections, and the convertor plant is found defective if signals such as reduced quality of steels, fatigue cracks, pitting corrosion are revealed. All maintenance actions, including manual

Conclusions and future research

Joint maintenance and spare part provisioning policy for a production system with defective information is investigated. A prominent is that it schedules three levels of PM windows: (a) regular inspection window (to reveal defects), (b) defect-removal window, and (c) pre-specified overhaul window, so as to mitigate defect-induced malfunction risks and production losses. The policy allows spare part preparation upon defect identification to be postponed, which can naturally exploit the remaining

Author statement

Article title: Optimal inventory policy for a balanced system subject to hard failure

I have made substantial contributions to the design of the work; AND

I have drafted the work and revised it critical for important contents; AND

I have approved the final version to be published; AND

I agree to be accountable for all aspects of the work in ensuring that questions related to the accuracy or integrity of any part of the work are appropriately resolved.

Persons who have made substantial contributions

Declaration of Competing Interest

None.

Acknowledgment

This work is supported partially by the National Natural Science Foundation of China (Grant No.72101010, Grant No. 52075020 and Grant No. 72071005), and the National Key Laboratory Foundation (Grant No. KZ42004001), the Double-First Class Special Budget (Grant No. ZG216S21C3).

References (35)

Cited by (37)

View all citing articles on Scopus
View full text