第二階段自我相關線性輪廓的監控方法

Phase II monitoring schemes for autocorrelated linear profiles

黃婉瑄(Wan-Hsuan Huang)

指導教授 ： 王藝華

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.2015.00480

摘要

當產品或製程的品質好壞是由資料是否滿足某個函數關係來判斷，這樣的資料被稱為輪廓資料，而監控此種資料的方法被稱為輪廓監控。在大部分的情況，簡單線性輪廓模型的隨機誤差項間都是假設為獨立，然而在某些情況下輪廓資料間可能存在自我相關。因此，在本文中，我們考慮第二階段下，簡單線性輪廓資料間存在一階自我相關時，提出四個監控方法，並與 Noorossana et al. (2008) 所提出的監控方法做比較。由模擬結果得知，本文所提出的管制方法皆比 Noorossana et al. (2008)所使用的方法有更好的監控效果。此外，我們也針對此種輪廓模型，提出一個改變點的估計方法，從模擬結果得知，本文所提出的改變點的估計方法，具有不錯的診斷能力。最後會透過一個例子來說明實際上如何應用本文所提出的監控與診斷方法。

關鍵字

EWMA管制圖 ； 輪廓監控 ； 一階自我相關 ； 改變點

並列摘要

When the quality of a process or product can be characterized and represented by a functional relationship, a collection of this kind of data is called a profile. Profile monitoring is to monitor the stability of this relationship. The error term of simple linear profile is often assumed to be independent. However, in some applications, there is autocorrelation between profiles. Therefore, in this article, we consider the simple linear profiles with a first order autocorrelation relationship over time in Phase II. We propose four monitor schemes and compare these schemes with the shemes proposed by Noorossana et al. (2008). From the simulation results, our schemes have better performance than Noorossana et al. (2008)'s. Moreover, we propose a change point estimation method for this profile model. From the simulation results, the proposed change point estimation method has satisfactory performance. Finally, a practical example is used to illustrate how to apply our monitoring and diagnostic method.

並列關鍵字

EWMA control chart ； Profile monitoring ； First order autucorrelation ； Change point

參考文獻

Chuang, S. C., Hung, Y. C., Tsai, W. C., and Yang, S. F. (2013). “A framework for nonparametric profile monitoring”. Computers and Industrial Engineering, 64, pp. 482-491.

Ghahyazi, M. E., Niaki, S. T. A., and Soleimani, P. (2014). “On the monitoring of linear profiles in multistage processes”. Quality and Reliability Engineering International, 30, pp. 1035-1047.

Kang, L., and Albin, S. L. (2000). “On-Line Monitoring When the Process Yields a Linear Profile”. Journal of Quality Technology, 32, pp. 418-426.

Kim, K., Mahmoud, M. A., and Woodall, W. H. (2003). “On the monitoring of linear profiles”. Journal of Quality Technology, 35, pp. 317-328.

Li, Z. and Wang, Z. (2010). “An exponentially weighted moving average scheme with variable sampling intervals for monitoring linear profiles”. Computers and Industrial