包含區間, 多變量管制圖 及構面性資料統計品質管制

Abstract

包含區間一般以經驗分位數來估計，本論文提出以對稱型分位數來估計，並且在 論文中可看出對稱型分位數包含區間在非對稱分佈及離群值資料上有比經驗分位數包含區間有較短的長度及較好的穩健度。在對稱分佈尤其是厚尾型對稱分佈, 對稱型分位數包含區間有較小的變異。本論文亦提出以對稱型分位數建構多分位點管制圖，並且探討其大樣本理論。 本論文亦探討非線性混合性構面型資料統計品質管制。我们以主成份分析來建構統計品質管制Phase-I 及Phase-II 的監控統計量。在Phase-I，我們採用主成份計分建構的T2監控統計量。在Phase-II，各別主成份計分圖、主成份計分建構的T2 管制圖及聯合型主成份計分管制圖被提出及比較，在應用面亦有所建議。

Classically the non-parametric coverage interval is estimated by empirical quantiles. We introduce an alternative way for estimating the coverage interval by symmetric quantiles of Chen and Chiang (1996). We further show that this alternative estimator has a better precision in the sense that its asymptotic variances are smaller than the classical one.

In an attempt to develop a scheme for monitoring a vector of distributional quantiles, we propose a symmetric-quantiles-based control chart. Comparative studies in terms of the asymptotic covariance matrix and the average run length show that the proposed control chart is more efficient than the classical empirical-quantiles-based control chart.

The monitoring of process/product profiles is presently a growing and promising area of research in statistical process control. We focus on developing monitoring schemes for nonlinear profiles with random effects in this study. We utilize the technique of principal components analysis to analyze the covariance structure of the profiles and propose monitoring schemes based on principal component (PC) scores. In the Phase I analysis of historical data, due to the dependency of the PC-scores, we adopt the usual Hotelling T2 chart to check the stability. For Phase II monitoring, we study individual PC-score control charts, a combined chart scheme that combines all the PC-score charts, and a T2 chart. Although an individual PC-score chart may be perfect for monitoring a particular mode of variation, a chart that can detect general shifts, such as the T2 chart and the combined chart scheme, is more feasible in practice. The performances of the schemes under study are evaluated in terms of the average run length.