在本研究中我們使用消費間隔模式分析顧客間的異質性，並使用混合模型將顧客分成理想狀態、合理狀態和危險狀態。這兩種模式都是使用層級貝式的觀念，並透過馬可夫蒙地卡羅法的方法來估計所需的參數。最後，我們選擇以合理狀態的機率密度函數，運用管制圖的方式來監控顧客消費行為。管制圖通常是被企業用在產品品質的管制上，它提供一個合理的時間點去修正產品品質的偏差。本研究的管制圖包含一個顧客的消費問隔時間和最近消費時間。

　　In this paper, we follow the model of interpurchase to get the heterogeneity across customers. Then we use mixture model to segment customers into three groups as super-active, active and inactive states. Both models are solved by hierarchical Bayes via Markov Chain Monte Carlo method. At last, we employ X chart based on the density of active component to monitor consumer behavior. Control charts have been widely used in industry to control the quality of products. They provide an economical timing to launch corrective actions. The information on X chart includes interpurchase times and recency for an individual customer.