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題名：適應性X-bar管制圖之探討
作者：林裕章
作者(外文)：Yu-Chang Lin
校院名稱：國立雲林科技大學
系所名稱：管理研究所博士班
指導教授：周昭宇
學位類別：博士
出版日期：2005
主題關鍵詞：非常態；適應性管制圖；管制圖；non-normality；adaptive control chart；Control chart
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傳統的Shewhart管制圖是屬於靜態管制圖，即其中三個管制參數(抽樣間隔、樣本大小和管制界限係數)在監視製程的過程中是固定的。而近期發展的適應性管制圖是屬於動態管制圖，其中管制參數是按照目前的製程狀態來調整。這些適應性管制圖包括：變動抽樣間隔(VSI)管制圖、變動樣本數(VSS)管制圖、變動抽樣比率(VSR)管制圖、變動樣本數和管制界限(VSSCL)管制圖和變動參數(VP)管制圖。本研究發現，當製程為常態時，VSSCL和VP管制圖對於偵測製程較小幅度的平均值偏移量效果為佳，SS和VSI管制圖較適用於偵測製程較大幅度的平均值偏移量。而在變動管制參數的效果方面，變動樣本數可以增加管制圖在偵測小幅度偏移量的偵測能力，變動抽樣間隔可以提升管制圖在偵測大幅度偏移量的績效，而管制界限係數與樣本數同時變動時，其偵測效果將會有顯著地改善。另外，從行政實務上的考量，固定時間點的適應性管制圖(只在固定時間點抽樣)則相對容易於實務界來實施。另一方面，非常態製程也常出現在工業界，當製程為常態性的假設被違反時，對於管制圖的錯誤警告率和偵測能力將會造成很大的影響。研究顯示VSI，VSS和VSR管制圖對於常態的假設非常敏感，而採取較大的寬管制界限之VSSCL和VP管制圖不僅可以提升偵測小變動的能力，同時其錯誤警告的情況也會降低。因此，VSSCL和VP管制圖都較其它適應性管制圖更加的合適。
Traditional standard Shewhart (SS) chart is static in the sense that all control parameters (sampling intervals h, sample size n and action limit coefficient k) are fixed for the duration of operation that is monitored. Recently developed adaptive chart is dynamic, which at least one of the parameters is allowed to change in real time based on the actual sample point. These adaptive charts include the variable sampling intervals (VSI), the variable sample size (VSS), the variable sampling rate (VSR), variable sample size and control limit (VSSCL) and the variable parameters (VP) charts. Base on the study, when the process data are normally distributed, the VP and VSSCL charts are more sensitive than other charts in detecting small process shifts. The major advantages of VSI and SS charts are their simplicity and their speed in detecting large shifts. The influence of three parameters is concluded: varying n can increase the sensitiveness of detect small shifts in the process. Varying h can increase the effectiveness of detect large shifts in the process. The improved effect is significantly that combine k with n varies simultaneously. In addition, from the practical viewpoint of administration, the adaptive charts with fixed time, which always sample at the fixed times, are relatively easy to set up and implement. On the other hand, non-normal data commonly exist in industrial processes. As the assumption of normality is violated, the false alarm rate and detect ability for the control chart are adversely affected. This study is show that the VSI, VSS and VSR charts are very sensitive to the normality assumption, and the VSSCL and VP charts with larger wide action limit coefficient not only increase the ability to detect the small shifts, but also decrease the risk of false alarms. Thus, the VSSCL and VP charts are better alternatives than the other adaptive charts for both normality and non-normality.
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