管制圖已經廣汎應用于製造業中的質量監控, 在過程質量發生改變時及時發出報警方面,它扮演著重要的角色. 現有管制圖主要側重單變量或多變量連續型過程分配.爲了處理離散型分配,特別是多項分配過程, 借助皮爾遜卡方統計量來構建管制圖可能是一個共同的選擇. 然而, 這種管制圖嚴重依賴大樣本, 當樣本容量較小或者中等時產生不可靠結果. 本論文中, 我們主要探索多項分配過程管制圖. 我們首先重新審視了皮爾森卡方統計量,并推導出了其任意樣本下的均值和方差. 然後, 建立精確的EWMA比例管制圖. 與現有基於符號的EWMA管制圖和多項CUSUM圖相比, 模擬結果證明了我們方法的檢測性能. 另外, 測量誤差對精確管制圖的影響也得到研究, 一些模擬表明測量誤差延緩失控信號的發出.

Control charts have been widely used for monitoring output quality in manufacturing. It plays an important role in triggering a signal in time when detecting a change in process quality. Most existing control charts focus on the univariate or multivariate process data with continuous distribution. To deal with discrete distributions, in particular, the multinomial distribution processes, Pearson’s Chi-square statistic might be a common approach to construct control charts. However, it depends heavily on large sample sizes, which can yield unreliable result when sample size is small or moderate. In this thesis, we primarily explore the process control chart for multinomial distribution data. We first review Pearson’s Chi-square statistic, and derive the exact mean and variance regardless of sample sizes. After that, the exact exponentially weighted moving average (EWMA) proportions chart is derived under small or large sample sizes. Compared with existing sign-based EWMA chart and multinomial CUSUM chart for monitoring the multinomial distribution processes, simulation study is conducted to assess the performance of our proposed chart. Moreover, affection of measurement error on the exact control chart is also investigated, some simulation results suggest that measurement error delay detecting in out-of -control processes.

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