以無母數管制圖監控兩階段製程品質變數之探討

Abstract

在產品製造過程中，針對產品品質的特性來畫管制圖可增進最終產品的品質。而由於現 今產品的複雜性，產品大部分都是經過多階段的製程才能完成。若製程階段之間互相獨 立，則只要針對各個階段的品質特性去畫舒華特管制圖即可。但一般而言，每一製程階 段的品質特性通常皆會影響到接下來階段的品質特性，在這樣的情形下，便不再適合只 針對每個階段去畫各自的管制圖。Zhang 在1984 年提出了用選控圖來處理這種各階段 品質特性間有相關性的製程。考慮最簡單的二階段製程，選控圖是針對移除掉第一階段 品質特性影響的第二階段品質特性畫一般的舒華特管制圖。而一般皆會假設第一階段的 品質特性和第二階段的品質特性之間的關係為參數線性模型加上常態分配的誤差項，然 而實際上，我們有可能並不瞭解此兩者品質特性變數之間的關係，因此並不適宜假設第 二階段的品質特性是第一階段品質特性的特定參數函數加上一個特定分配的誤差項。這 個計畫希望能研究用核迴歸及小波分析此兩種無母數方法來估計二階段製程的品質特 性之間的關係再進而以無母數選控圖來監控製程平均數的可能性，並以平均串連長度來 和原來的參數選控圖作比較。

To improve the quality of a product, control charts are used to monitor some quality characteristics during the production process. Nowadays, most of the products are produced from several process stages. If the process stages are independent, it may be appropriate to plot Schewart charts in each stage respectively. However, the quality characteristic at a current stage usually affects the quality characteristics at the one or some subsequent stages. To deal with this situation, a different approach called cause-selecting control chart is proposed by Zhang (1984). Consider the simplest case of a two-stage process. The causing-selecting chart is based on the outgoing quality in the second stage that has been adjusted for the in-coming quality in the first stage. A linear or generalized linear model with normally distributed error terms is always assumed to relate the two quality characteristics. In practice, however, it is sometimes difficult to obtain substantial knowledge about the relationship function or the error terms. In this project, we will try to instead use non-parameter methods including (1) kernel method and (2) wavelet method to relate the in-coming and outgoing quality characteristics in a two-dependent-stage process. The non-parametric cause-selecting control charts may thus derived to monitor the means in the dependent process stages. To study the performance of the constructed cause-selecting control charts, a simulation study comparing the average run lengths of the proposed cause-selecting charts for kernel and wavelet approaches will be included as well.