Gamma衰變模型之最可靠產品挑選

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Title:	Gamma衰變模型之最可靠產品挑選
Other Titles:	Selection of the Most Reliable Product Based on Gamma Degradation Model
Authors:	蔡志群
Contributors:	淡江大學數學學系
Keywords:	gamma過程;衰變資料;最佳試驗配置;挑選法則;Gamma process;degradation data;optimal test plan;selection rule
Date:	2013-08
Issue Date:	2015-04-21 14:08:10 (UTC+8)
Abstract:	針對高可靠度產品，如何在眾多元件供應商中挑選出可靠度較高的供應商，是生產者常常面臨到的重要決策問題。唯高可靠度產品之壽命推論，即使使用加速壽命試驗 (accelerated life test, ALT)的技巧，亦很難在有限的測試時間内獲得產品失效資料。衰變分析（degradation analysis)是工業界最常使用來推估高可靠度產品的可靠度資訊之重要分析工具，亦即量測與產品壽命相關之品質特徵值（quality characteristics, QC)，且此 QC會隨時間逐漸衰變（degrade)，再藉由其衰變路徑來推估產品壽命。對於產品的衰變路徑為單調遞增，如金屬疲勞（metal fatigue)或雷射產品的操作電流衰變，此時採用隨時間遞增之gamma過程來描述產品衰變路徑將更為合理。本計劃針對雷射產品衰變路徑服從一個gamma過程，探討從多家雷射產品供應商中，挑選其中可靠度最高的供應商。本計劃首先會訂定一個決策法則來挑選可靠度最高的產品，接下來設計一個最佳化試驗，以便能以最少成本執行衰變試驗，且可精確地挑選出產品可靠度最高的供應商。換言之，在給定的正確挑選機率下，找出一個最佳試驗配置（最佳樣本數、量測頻率與量測次數），使得執行此衰變試驗的總成本達到最少。最後以雷射產品為例，來舉例說明本文所提出的方法。 During the research and development stage of a product, the manufacture usually faces the problem of selecting the most reliable design among several competing products in order to enhance the quality of the products. It is a great challenge for the manufacturer if these competing products are highly reliable, because few or even no failures can be obtained by using traditional life tests or accelerated life tests. In such situation, if there exists a quality characteristic (QC) whose degradation over time can be related to reliability, then more information about product reliability can be obtained by collecting the degradation data. Recently, optimal selection of the most reliable products has been discussed in the literatures assuming that the underlying degradation paths follow Wiener processes or random-effect degradation models. However, the degradation model of many materials (especially in the case of fatigue data) may be more appropriately modeled by gamma processes that exhibit a monotone-increasing pattern. This research will deal with a systematic approach to the selection problem with degradation data when the products’ degradation paths follow gamma processes. First, a selection rule is expected to be provided, and the probability that the selection rule gives a correct decision (CD) will be derived. Then, with a minimum probability of correct selection, the optimal test plan (sample size, inspection frequency, and number of measurement) can be obtained by using the criterion of minimizing the total experimental cost. Finally, a laser data will be used to illustrate the proposed method.
Appears in Collections:	[Graduate Institute & Department of Mathematics] Research Paper

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