大部份製造業在生產進行一段期間後, 其機器設備開始會有「製程退化」（deterioration）現象，因而製造出不良產品。為了不讓不良品流入市面，一般廠商都會進行產品檢驗。然檢驗過程中有時會因人為因素或技術限制而造成檢驗上的誤判（inspection errors），因此一個最佳化檢驗策略必須考慮檢驗誤差所可能引起的後果。
除了必須擔心不良品的產生外，製程退化有時甚至嚴重到整個設備故障而無法運轉（breakdown）。在某些行業的設備運作，機器故障會造成相當嚴重後果，如飛航管制、醫院病患維生系統、核能電廠等等。因此設備的預防保養與維修是生產管理上一個重要課題。一個有效率的保養策略可協助發揮產量、品質與成本控制的最佳化效果。
儘管生產、品質與保養三者間有相當密切關係，傳統研究模式常視為分別的課題來處理。本研究試著整合這三項課題來探討其彼此間的關聯效果。我們提出數學模式可「同時」決定最佳產量、檢驗與保養策略，而以這樣的架構進一步探究有關檢驗誤差、重新加工（rework）、預防保養（preventive maintenance）與小型維修（minimal repair）等課題。模型可求解出最佳檢驗週期、檢驗次數、生產批量、預防保養水準等等。
以模擬求解來觀測不同參數值對最佳解的影響。這些模擬結果顯示檢驗誤差、重新加工與預防保養對於最佳化生產均有重要影響。如此可印証，要擬定一個最佳化的生產與檢驗策略，我們必須把生產、品質與保養等不同方面的決策放在一個整合模式來考量，而不能視為分別的決策課題。

In spite of the implementation of modern technology and an efficient control procedure to improve equipment, the deterioration of the production process is unavoidable in most manufacturing industries. Inspections and maintenance activities are performed in virtually every production system. In this study, we construct models that allow us to economically determine the optimal inspection/disposition strategy for a batch of items produced by a machine that is subject to random breakdowns. We use the proposed mathematical framework to explore the issues relating to inspection errors, rework, preventive maintenance level, and minimal repair. The operational implications of the optimal strategy are then analyzed with a selected set of numerical results.
We formulate dynamic programming of optimal strategy for two types of inspection activities: inspection of products and inspection of production systems. For inspection of products, we develop models of off-line inspection for a deterioration process having general shift distribution with an increasing hazard rate. To have an off-line inspection following an unreliable process is an appropriate quality assurance tactic in certain systems. Previous work has dealt exclusively with finding the point where the process shifts away from its in-control state to an out-of-control state. Our models incorporate the economic aspects of the inspection activity and of the two types of product inspection errors. Ignoring the true economics of quality assurance can result in unnecessary costs and time delays. We determine the first unit inspected and the average number to be inspected in a batch. We also study the effect of allowing rework on the optimal inspection strategy.
For inspection of production systems, we generalize the classical economic production quantity model to consider possibilities of preventive maintenance errors and minimal repair. Our model solves simultaneously the optimal number of inspections, the duration of the first inspection interval, the economic production quantity, and the preventive maintenance level.
Despite the strong interdependence between production, quality and maintenance, these three main aspects of any manufacturing system are traditionally modeled as separate problems. Few attempts have been made to integrate them in a single model that captures their underlying relationships. Our study essentially explores models for the joint optimization of production quantity, quality assurance inspections, and maintenance level. Our results demonstrate that these different but interrelated aspects of a manufacturing system can be captured rigorously in a united framework. Numerical simulations also illustrate the importance of viewing all theses decisions concerning core manufacturing processes in an integrated manner, rather than as a set of separate decisions.

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