- 學位論文
應用區別分析探討高可靠度產品之最佳分類決策
Optimal Classification Policy for Highly Reliable Products
摘要
隨著產品等級市場區隔化及上市時程縮短的影響, 製造商會應映市場需 求對產品做分類, 並且將不同等級之產品配送至不同市場。因此如何在分類 試驗中快速有效地區分出不同等級之產品, 是生產製造商要面臨的一重要決 策問題。針對高可靠度產品, 若存在一與壽命高度相關之品質特徵值(qual- ity characteristic, QC), 則可藉由品質特徵值之衰變路徑建構出衰變模型, 再結合成本來進行篩選分類之程序。本論文首先提出以高斯(Gaussian) 過 程, 來描述包含隨機效應、Wiener 過程以及量測誤差等三種變異來源之混合 衰變模型。接著引進線性區別分析的概念, 提出三階段之分類策略, 包含如 何決定觀測值間之最佳係數、產品分類之最佳區分點以及最佳試驗時間。此 外, 本研究將與Tseng & Tang (2001) 以及Tseng & Peng (2004) 之方法 做理論上的比較分析, 詳細說明不同分類方法在各種使用範圍限制之下, 錯 誤分類損失機率及成本之差異。最後, 以實際LED 產品之衰變資料為例, 說 明分類決策之執行過程。 關鍵字: 分類程序、混合Gaussian 過程、隨機效應、Wiener 過程、量測 誤差、線性區別分析。
並列摘要
Abstract Nowadays in the competitive marketplace, manufacturers need to classify products in a short time according to market demand. Hence, it is a challenge for a manufacturer to implement a classification test that can distinguish the different levels of products quickly and efficiently. For highly reliable products, if quality characteristics do exist whose degradation over time can be related with the lifetime of the product, the degradation model can then be constructed based on the degradation data. In this study, we propose a non-linear degradation model that simultaneously considers unit-to-unit variation with time-dependent error structure and measurement error. Then, by adopting the concept of linear discriminant analysis, we also propose a three-step classification policy to determine optimal vector of coefficients, optimal cut-off point and optimal testing time subject to cost. In addition, we also use an analytic approach to compare the efficiency of our proposed procedure with two methods that is previously reported by Tseng & Tang (2001) and Tseng & Peng (2004). Finally, we use LED data to illustrate the proposed classification procedure. Key words: classification procedure, mixture Gaussian process, random effect, Wiener process, measurement error, linear discriminant analysis.