具自我相關之線性輪廓資料的製程能力指標

Process Capability Indices for Simple Linear Profile Data in the Presence of Within Profile Autocorrelation

張傳潔(Chuan-Chieh Chang)

指導教授 ： 蔡宗儒

淡江大學/商管學院/統計學系碩士班/碩士(2015年)

https://doi.org/10.6846/TKU.2015.00230

摘要

本文除針對小樣本且殘差項具自我相關的線性輪廓資料提出一個新的T_new^2管制圖，增加對製程偏移的偵測能力外，也考量當前文獻對輪廓資料的製程能力尚缺乏完整討論，實務上若忽略反應變數與解釋變數之間的函數關係，直接使用多變量的製程能力指標衡量輪廓資料的製程能力，可能導致不適當的估計結果。因此本論文針對殘差項間存在ㄧ階自我相關的線性輪廓資料提出兩個新的製程能力指標。模擬研究結果發現，當輪廓內截距項與斜率項發生變動時，在小樣本及殘差項的相關係數越高時，T_new^2 管制圖對製程的偏移有較好的偵測能力。我們也發現製程能力會受模型殘差項自我相關係數影響，進而影響到輪廓資料的製程能力。

關鍵字

線性輪廓資料 ； 管制圖 ； 製程能力指標

並列摘要

In this thesis, we introduce a new T_new^2 control chart for auto-correlated linear profile data. The T_new^2 control chart is sensitive to detect the process shift. Moreover, we provide two new process capability indices to evaluate the process capability of auto-correlated linear profile data. In practice, we may obtain incorrect process capability information if the linear function relationship between the dependent and explanation variables is ignored, and the process capability is evaluated by using existing multivariate process capability index methods. To the simulation results, the T_new^2 control chart performs well especially for higher auto-correlated linear profile data and small sample size. We also found that the process capability of auto-correlated linear profile data is affected by the autocorrelation coefficient.

並列關鍵字

Linear profile data ； Control chart ； Process capability index

參考文獻

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