本研究探討時空資料的監控問題，發展時空統計量技術以偵測時空上的資料是否有平均值偏移現象，在過去的時空偵測程序主要以概似比檢定為基礎，使用累和管制圖作為概念，累積資料在時間及空間上的變異。然而概似比檢定需要偏移相關參數為已知或可良好估計，但在實際問題中，偏移的區域範圍、幅度、時間點等，往往為未知參數。因此本論文發展以指數加權移動平均值管制圖為基礎的時空統計方法，透過整合空間資料及對時間軸加權，有效偵測異常時空型態資料。離偵測時間點越近的資料，將賦予較高之權重；而對時空型態資料作空間軸加權時，距離監控中心越近的資料，將賦予較高之權重。在此概念下發展出六種不同的加權手法，檢測手法無需預知偏移相關參數，僅需對觀察值進行不同方式的加權，便達到有效偵測異常時空資料的目標。本研究並模擬分析六種加權模型對不同異常模式的偵測效果，以輔助決策者制定改善政策或探究發生異常之原因。文末以新墨西哥(New Mexico)州男性罹患甲狀腺癌之發病情形為例，說明本論文兩種模型於實際案例上之運用。

This research investigates the problem of spatiotemporal surveillance and develops statistical techniques to detect the existence of mean shifts in spatiotemporal data. Previous spatiotemporal test procedures focus on likelihood-ratio based methods. The concept of Cumulative Sum (CUSUM) control chart is also applied to cumulate data variation over time and space. However, likelihood-ratio based tests require known or well estimated parameters including shift coverage, magnitude, and change time which are often unavailable in practice. Therefore, this research develops the spatiotemporal analysis methods based on Exponentially Weighted Moving Average (EWMA) control chart. By integrating spatial data and weighting temporal data over time, the proposed methods can effectively detect mean shifts. The data closer to the current time point and to the investigated shift center receives a higher weight. Six models are constructed under such weighting rules. The proposed methods do not require the information about mean shifts but can effectively detect abnormal spatiotemporal data by directly weighting observations. This research simulates different shift patterns and compares the sensitivity of the six models. The results may help decision makers with setting up policies for improvement or exploring contributing factors. Last, an implementation of male thyroid cancer in New Mexico is carried out to demonstrate the practicability of the proposed methods.

摘 要 i
Abstract ii
誌謝 iii
目錄 iv
圖目錄 vi
表目錄 viii
第一章 緒論 1
1.1 研究背景與動機 1
1.2 研究目的 2
1.3 研究架構 2
第二章 文獻探討 5
2.1 統計製程管制 5
2.1.1 Hotelling’s T2 6
2.1.2 累和管制圖 7
2.1.3 指數加權移動平均管制圖 8
2.2 概似比檢定 10
2.3 時空掃描統計量 11
第三章 偵測異常時空資料之加權方法 14
3.1 異常時空群聚問題 14
3.2 時間軸加權 16
3.2.1 模型一：平均加權法 18
3.2.2 模型二：多變量加權法 22
3.3 空間軸加權 25
3.3.1 模型三：距離層級加權法 25
3.3.2 模型四：距離層級多變量加權法 29
3.4 時空雙軸加權法 32
3.4.1 模型五：雙軸加權法(時間空間加權法) 32
3.4.2 模型六：雙軸加權法(空間時間加權法) 36
第四章 時空統計實驗分析 40
4.1 實驗設計 40
4.2 平均加權法偵測成效 41
4.3 多變量加權法偵測成效 47
4.4 距離層級加權法偵測成效 50
4.5 距離層級多變量加權法偵測成效 53
4.6 雙軸加權法偵測成效 56
4.7 模擬成效比較 60
第五章 案例分析 73
5.1 平均加權法偵測成果 74
5.2 多變量加權法偵測成果 76
5.3 層級加權法偵測成果 79
5.4 多變量層級加權法偵測成果 81
5.5 雙軸加權法偵測成果 82
5.6 綜合比較 84
第六章 結論與未來研究方向 85
參考文獻 87

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