機台維修一直是工業管理中的一大挑戰，尤其是在機台故障和維修成本日益增高的當下，機台的高效運作變得極為重要。在機台維修問題存在著許多不確定因素，例如機台的狀態和可能的狀態轉變。近年來，隨著數據科學和機器學習技術的發展，利用預測模型來建構維修決策已成為一種新的趨勢。透過實時數據分析，可以更準確地預測機台可能的故障點和維修時機，從而有效地降低機台長期維修和運營成本。此外，機台設備的價值高昂，管理者難以承擔由此帶來的損失，因此維修問題一直是工廠管理者必須面對的重大挑戰。
在機台維修中，判斷何時該進行維修是一個至關重要的決策，何時維修關乎機台的耐久度以及維修成本的考量等等。本研究的主要目的是開發一套基於馬可夫決策過程的機台維修優化模型，並引入預測資訊作為決策支持。我們開發了一個離散時間的有限馬可夫決策過程，並引入了預測狀態給予決策者一個重要參考基準。在我們的模型中，我們考慮單一機台，目標是為最小化維修成本，因此決策者希望能找到一個最佳的時間點進行維修將機台維修的成本降至最低。機台狀態在當期是可知的，決策者根據每期所產生的價值函數作為採取何種決策的依據。此外預測資訊主要用於預測機台在下一個時間點的可能狀態，這是通過從歷史數據中學習機台行為模式來實現的。預測的準確性則通過誤分類矩陣來驗證，該矩陣顯示了預測結果與實際狀態之間的對應關係。本研究證明了加入預測資訊對於維修最佳化決策是有幫助的，隨著準確度的提高確實能有效降低維修成本，即便準確度僅達到一定水準。我們的結果表明，透過結合有限馬可夫決策過程與有效的狀態預測，可以顯著優化機台維修管理策略，為工廠管理者提供實際可行的解決方案。

Machine maintenance has always been a major challenge in industrial management, especially as machine breakdowns and maintenance costs continue to rise, making the efficient operation of machines critically important. Machine maintenance issues are fraught with uncertainties, such as the state of the machine and potential state transitions. In recent years, with the development of data science and machine learning technologies, using predictive models to construct maintenance decisions has become a new trend. Through real-time data analysis, it is possible to more accurately predict potential machine failure points and the optimal timing for maintenance, thereby effectively reducing long-term maintenance and operation costs. Additionally, as machine equipment is costly, managers struggle to bear the losses incurred, making maintenance issues a significant challenge that factory managers must face.

We have developed a discrete-time finite Markov decision process and introduced predictive states to provide decision-makers with an important reference point. We consider a single machine with the objective of minimizing maintenance costs, so decision-makers seek to find the optimal time for maintenance to minimize the cost of machine repair. The machine’s state is known in the current period, and decision-makers base their decisions on the value function generated in each period. Additionally, we extend the original model to develop a predictive model, using the added predictive information to forecast the machine’s state in the next period, with the accuracy of the prediction validated through a confusion matrix. We derive the optimal policy and demonstrate that incorporating this predictive information is helpful for optimization,and also prove that accuracy at a certain level can effectively reduce maintenance costs.

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