二元反應變數的第I階段輪廓監控

Phase I Analysis of Profile Monitoring for a Binary Response

10.6220/joq.2015.22(2).04

陳明輝(Ming-Huei Chen)

輪廓監控 ； 二元反應變數 ； 型I階段分析 ； 邏輯斯迴歸 ； 虛擬變數 ； profile monitoring ； binary response ； phase I analysis ； logistic regression ； dummy variables

品質學報

22卷2期（2015 / 04 / 30）

121 - 135

繁體中文

輪廓監控（profile monitoring）是近年來統計製程管制（statistical process control）研究中非常重要的一支。在這研究中，管制圖（control charts）的監控目標已由傳統的品質特徵值（quality characteristic）轉為品質特徵值與解釋變數之間的關係（relationship, profile）。一般文獻較常研究的是連續反應變數與解釋變數間線性關係（linear profile）的監控；本文則主要研究當品質特徵值為二元反應變數（binary response）時，如何在第I階段監控二元反應變數與解釋變數之間的關係。本文利用複迴歸（multiple regression）中虛擬變數（dummy variables）的觀念，提出適當的管制統計量以監控二元反應變數與解釋變數之間的關係。研究發現，我們所提出的方法，在很多方面均較現階段的其他方法優異。文中將以一實例與許多的模擬研究呈現此一現象。

Profile monitoring is an important issue in the research of statistical process control. In this category, the control charts are not designed to monitor the quality characteristic of a process or product. They are designed to monitor the relationship between the response variable and the explanatory variables. Most of the research considers the monitoring scheme of the relationship between the continuous response variable and the explanatory variables. In this paper, we consider the phase I analysis of profile monitoring for a binary response variable. We propose a method based on dummy variables in a multiple regression model to compare two or more regression lines. We find that our method has competitive performance relative to other methods in terms of the probability of a signal for out-of-control scenarios. We will use a real example and numbers of simulation studies to show the benefits of our method.

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