現今製造業的產品或製程的品質特性大多可用一個反應變數對多個解釋變數的函數關係式來表達，這種函數關係式所產生的資料類型稱為輪廓資料 (profile data)。而輪廓資料的函數關係式大致上可分為線性與非線性關係，輪廓(profile)為將產品的品質特性定義為反應變數與解釋變數的一個函數關係。本研究係探討單一個解釋變數的非線性輪廓監控。我們首先使用逆高斯過程模型來配適非線性且具單調遞增特性的輪廓資料。接著，利用所建構的多變量指數加權移動平均（Multivariate Exponentially Weighted Moving Average）管制圖以監控階段II輪廓資料中的主要參數。
在利用逆高斯過程模型配適非線性輪廓資料的模擬分析中，我們考慮四種不同平均函數在不同參數及樣本數組合的情況下，比較MEWMA管制圖在各種製程參數偏離穩定狀態( out-of-control)下的表現。模擬結果顯示，當樣本數較大時逆高斯過程模型可用於分析非線性輪廓資料。此外，本研究所提出MEWMA管制圖的方法在監控線性輪廓資料上的表現較T^2 、MMR管制圖為優。最後，我們以一組藥劑劑量之反應曲線為例，針對MEWMA管制圖在監控非線性輪廓資料上的適用性進行驗證與說明。

In today’s manufacturing industries, if the quality characteristic of a product or a process is assumed to be represented by a functional relationship between the response variable and one or more explanatory variables, then the data generated from such a relationship is called profile data. Generally speaking, profiles are represented as linear profiles or nonlinear profiles, In this research, we will focus on single-variate nonlinear profile monitoring and first use the Inverse Gaussian process model to fit nonlinear and monotonic profile data. Secondly, a Multivariate Exponentially Weighted Moving Average (MEWMA) control chart is constructed to monitor profile data in the Phase II study.
In the simulation studies, four different mean functions under different combinations of parameters and number of samples are considered in the Inverse Gaussian process model. Then, both in-control and out-of-control average run lengths (ARLs) are used as a criteria to evaluate the performance of our proposed MEWMA control chart. The simulation results show that the Inverse Gaussian process model is suitable to fit nonlinear profile data when the sample size is large. Moreover, our proposed MEWMA chart method outperforms T^2, MMR control charts especially in monitoring the linear profile data. Finally, the usefulness of our proposed monitoring method is demonstrated through a dose response curve example.

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