Maintenance strategies play a crucial role in the operational efficiency and economic performance of manufacturing enterprises. Traditional maintenance models often focus solely on minimizing costs, neglecting the broader impact of maintenance activities on system reliability and net profit. This paper introduces a novel maintenance/replacement strategy based on the Generalized Renewal Process (GRP), which optimizes net profit over the system’s lifecycle by considering both cost and revenue dynamics.
Introduction
Industrial equipment maintenance is a critical aspect of modern manufacturing, ensuring operational efficiency, reducing downtime, and extending equipment lifespan. As automation and intelligent manufacturing advance, the complexity of industrial systems increases, necessitating more sophisticated maintenance strategies. Traditional approaches, such as “maintenance limit” policies, focus primarily on cost minimization but fail to account for the varying effectiveness of different maintenance actions. These models often assume that maintenance either fully restores a system to a “good-as-new” state (perfect repair) or leaves it in a “bad-as-old” condition (minimal repair). However, real-world maintenance activities typically result in intermediate states, where the system’s condition lies somewhere between these two extremes.
To address this limitation, Kijima et al. introduced the Generalized Renewal Process (GRP), which incorporates the concept of “virtual age” to quantify the effectiveness of maintenance actions. Virtual age represents the system’s perceived condition after maintenance, reflecting how much the system has been rejuvenated. This approach provides a more accurate representation of system reliability and enables better decision-making regarding maintenance and replacement.
System Maintenance Model
The proposed model considers a multi-state production system where components degrade over time according to a GRP. The system’s reliability is characterized by two key factors: the number of failures and the virtual age. Virtual age is updated after each maintenance action, depending on whether the system undergoes repair or replacement.
When a component fails, the decision to repair or replace it depends on the expected net profit over the system’s remaining lifespan. Repairing the component reduces its virtual age by a certain degree, while replacement resets it to zero. The model evaluates the trade-off between repair costs, replacement costs, operational revenue, and operational expenses to determine the optimal maintenance action at each decision point.
The system operates in three possible states: normal operation, post-repair, and post-replacement. Transitions between these states are modeled using a semi-Markov process, which allows for flexible modeling of maintenance durations and effects. The net profit function accounts for revenue generated during operation, costs incurred due to maintenance or replacement, and operational expenses.
Model Solution
Solving the proposed model involves estimating transition probabilities and optimizing maintenance decisions using dynamic programming. The system’s failure behavior is assumed to follow a Weibull distribution, a common model for mechanical systems. The Weibull parameters are estimated using maximum likelihood methods, enabling accurate simulation of failure intervals.
The transition probabilities between system states are computed numerically, considering the virtual age and failure history. Dynamic programming is then applied to determine the optimal sequence of maintenance actions that maximizes net profit over the system’s lifecycle. The algorithm iteratively evaluates potential maintenance decisions, updating the expected net profit at each step until convergence is achieved.
Numerical Example
To validate the model, a case study was conducted using failure data from the A2-5 spindle of a Haas TL-1 CNC machine. The spindle’s failure intervals were analyzed, and the Weibull parameters were estimated. The model was then applied to determine the optimal maintenance strategy over a five-year period.
The results demonstrate that the proposed model outperforms traditional cost-minimization approaches, such as the Rosqvist model, by increasing net profit by an average of 19.96%. The optimal strategy involves a mix of repairs and replacements, depending on the spindle’s virtual age and remaining lifespan. Sensitivity analyses reveal that key parameters, including repair costs, replacement costs, operational revenue, and failure rates, significantly influence maintenance decisions.
Impact of Key Parameters
- Repair and Replacement Costs
The ratio of replacement cost to repair cost plays a critical role in determining the optimal strategy. When replacement costs are high relative to repair costs, repairs are favored unless the system’s condition deteriorates significantly. Conversely, if replacement costs are low, replacements become more frequent, particularly when the system’s virtual age is high. - Operational Revenue and Costs
Systems with rapidly declining revenue or increasing operational costs benefit more from replacements, as restoring the system to a lower virtual age helps sustain profitability. In contrast, systems with stable revenue and costs may prioritize repairs to minimize expenses. - System Lifespan
The remaining lifespan of the system influences the choice between repair and replacement. Near the end of the system’s lifecycle, repairs are preferred since replacements may not provide sufficient time to recoup costs. For longer lifespans, replacements become more viable as they offer sustained reliability and profitability. - Failure Rate Characteristics
Systems with rapidly increasing failure rates benefit more from replacements, as they significantly reduce future failure probabilities. In contrast, systems with stable failure rates may not justify the higher costs of replacements. - Degree of Repair Effectiveness
The effectiveness of repairs, measured by the reduction in virtual age, also impacts maintenance decisions. Highly effective repairs (close to perfect repair) make repairs more attractive, while less effective repairs (close to minimal repair) make replacements more favorable.
Conclusion
This paper presents a comprehensive maintenance optimization model based on the Generalized Renewal Process, incorporating virtual age to better represent system reliability. By considering both cost and revenue dynamics, the model provides a more realistic and economically viable maintenance strategy compared to traditional cost-minimization approaches.
The case study of the Haas TL-1 spindle demonstrates the model’s effectiveness, showing a significant improvement in net profit over existing methods. Sensitivity analyses highlight the importance of key parameters in shaping optimal maintenance decisions, providing valuable insights for industrial applications.
Future research could focus on integrating predictive failure time estimation into the model, further enhancing its practical applicability. Additionally, extending the model to multi-component systems and considering dependencies between components could provide even more robust maintenance strategies.
DOI: 10.19734/j.issn.1001-3695.2024.08.0260
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