當資料序列的生成參數發生結構性異常時，我們稱之為改變點。改變點偵測的核心目的即是精準捕捉這些參數的不規則變化。改變點偵測可分為即時（Online）與線下（Offline）偵測，本篇論文主要聚焦於線下多重改變點偵測。實務上，由於序列型資料往往不滿足獨立性假設，我們採用一階馬可夫鏈模型來捕捉資料間的序列相關性。在聯合分配的建構上，本研究結合二項邊際分配，並探討三種具備不同尾部相依特性的 copula 函數：具左尾相關的 Clayton copula、具右尾相關的 Gumbel copula，以及同時具備雙尾相依特性的 BB1 copula。為了高效且準確地估計多個變動點的位置，我們將 Copula 模型推導出的概似函數，結合訊息準則與懲罰框架（如赤池訊息準則 AIC、貝氏訊息準則 BIC，以及最小描述長度 MDL 原則）來作為演算法的懲罰項，導入精確剪枝線性時間（Pruned Exact Linear Time， PELT）演算法中，藉此大幅降低多變點搜尋的計算複雜度，並探討不同懲罰準則對變點偵測敏感度與模型選擇的影響。 在實證分析中，本研究將此演算法應用於珠寶製造數據，旨在回溯並精確標定製造過程中不良率發生結構性改變的歷史節點，藉此協助檢視製程瑕疵，最終達到降低珠寶不良率之目的。;Structural shifts in the generative parameters of a data sequence are referred to as changepoints. The primary objective of changepoint detection is to accurately capture these irregular parametric variations. This thesis primarily focuses on offline multiple changepoint detection. In practice， since sequential data frequently violates the assumption of independence， the Markov chain model is employed to capture the serial dependence within the data. To construct the joint distribution， this study incorporates binomial marginal distributions and investigates three copula functions characterized by distinct tail dependence structures: the Clayton copula (lower tail dependence)， the Gumbel copula (upper tail dependence)， and the BB1 copula (which accommodates both upper and lower tail dependencies). To efficiently and accurately estimate the locations of multiple changepoints， the likelihood functions derived from the copula models are integrated with information criteria and penalty frameworks—specifically the Akaike Information Criterion (AIC)， the Bayesian Information Criterion (BIC)， and the Minimum Description Length (MDL) principle. These are subsequently implemented within the Pruned Exact Linear Time (PELT) algorithm， which significantly reduces the computational complexity of the multiple changepoint search. Furthermore， this study examines the impact of different penalty criteria on detection sensitivity and model selection. In the empirical analysis， the proposed algorithm is applied to jewelry manufacturing data to retrospectively and precisely pinpoint historical nodes where structural shifts in the defect rate occurred. This assists in diagnosing manufacturing flaws， ultimately aiming to reduce the defect rate in jewelry production.
