不完美維護下多狀態系統多重行動最佳維護政策

Abstract

在預防維護的領域中，有關多重非置換性維護行動之研究幾近闕如。本論文將有一個有關聯性的系統視為一個多狀態系統，並假設欲改善之系統狀態所須的非置換行動依此當前之狀態而定，藉以解析這些維護行動的特性。據此，本論文提供了兩種預防維護模式。其一，假設每一維護行動接具有一機率性的風險，促使維護行動無效。此種情況於本論文稱為不完美的維護。此維護問題可利用馬可夫理論進行構建，藉以最小化有限幅度下總期望折現成本。另一預防維護模型則假設預防維護的總數可能對系統的故障率有顯著影響，此種情況於本論文亦稱為不完美的維護。此維護問題則以更新理論為磐石，藉以構建促使特定計畫幅度下總期望壽命週期成本達最低之週期性預防維護模型。此外，此兩種預防維護模型的結構性質亦被探討，藉以分別求得容易計算與實施的控制極限法則，以及最佳預防維護之週期。

Although preventive maintenance (PM) problems have received extensive attention, relatively few studies have addressed multiple nonreplacement maintenance actions for a multistate system subject to action-dependent risk and/or the number of PMs. In this dissertation, we examine such multiple maintenance actions by viewing a coherent multicomponent system and the necessary maintenance action and cost which move the current state to an extremely better state dependsa on the current state. Two preventive maintenance models are then presented in this dissertation. One assumes that each maintenance action regarding state improvement has a probablistic risk which is ineffective. Such a situation is referred to herein as an imperfect maintenance action. The above problem is also modeled as a Markov theory-based maintenance problem, thereby minimizing the total expected discounted cost over a specific planning horizon. Another maintenance model assumes that the number of PMs may significantly affect the failures of a multistate system. Such a situation is also referred to herein as an imperfect maintenance action. The above problem is then modeled as a renewal theory-based maintenance model, thereby minimizing the life cycle cost over a specific planning. In addition, two models' characteristics are elucidated to demonstrate that Markov theory-based and renewal theory-based models have an easily computed and implemented control limit rule and the optimal PM cycle time, respectively.