Joint optimization of maintenance strategy and buffer capacity for a multi-state buffered serial system considering self-repair actions

This paper investigates a multi-state buffered serial system with machines experiencing multiple states. Unlike previous studies that primarily focus on fixed buffer capacities or ignore the interaction between internal degradation and multi-level external shocks, this work introduces a comprehensive framework that integrates these aspects. The competitive failure process between internal degradation and external shocks is considered. External shocks are classified into degradation, large, and failure shocks based on their attributes, sizes, and specific impact on internal degradation. The multi-layer self-repair mechanism is proposed to quantify the uncertainty of the self-repair actions, and correlated with machine reliability and time required for maintenance, the time required for imperfect maintenance is analyzed. By dividing a given total time period into a series of mutually independent sub time periods based on a unique segmentation algorithm, the Minimum Expected Cost Rate for Multiple Stacked Maintenance (MECRMSM) framework is presented. All possible situations of the two machines and buffer are discussed within each sub-time period, and the expected cost rate of the system within the total time period is calculated. The solution for minimizing system costs while maintaining reliability is provided by jointly optimizing the maintenance threshold and buffer capacity. Finally, the effectiveness of the proposed framework and algorithm is demonstrated through three numerical cases, which highlight its ability to dynamically balance maintenance strategies and buffer capacity under varying operational conditions.