監控多變量製程變異性增加之管制圖

Abstract

本文主要利用多變量單邊檢定發展偵測多變量製程變異增加的方法，也就是檢定H0:Σ=Σ0 versus H1:Σ≧Σ0 且 Σ≠Σ0，其中Σ為所監控品質特性的共變異數矩陣及Σ0為在控制狀態下的製程變異，並且分成為Σ0已知或未知兩種情形來討論製程如何監控變異增加的問題。我們導出概似比檢定統計量，並用靴環法得出管制限界。針對此控制圖之績效問題，我們經統計模擬對幾種Σ的變化比較平均連串長度，並以一個實例和模擬例子，證實所提出的單邊檢定方法對多變量製程變異增加的問題在偵測能力上有相當不錯的效率，且與對允許多變量製程變異性可增加或減少之雙邊檢定方法作比較，也有較佳的偵測效率。

In this paper, a method for detecting increases in multivariate process variability has been proposed. It is based on the one-sided likelihood ratio test of H0:Σ=Σ0 versus H1:Σ≧Σ0 and Σ≠Σ0, where Σ is the covariance matrix associated with the monitored quality characteristic and Σ0 is the in-control process variability. We derive the likelihood ratio test statistic for the cases that Σ0 is known and not known, respectively. We further obtain the control limit of the control chart by the bootstrap method. The applicability of the proposed Control chart in detecting increases in multivariate process variability is demonstrated through a real example. The simulation studies further show that the proposed method outperforms the method based on the two-sided likelihood ratio test in most cases.