以主成分分析方法建立多元製程位置管制圖之研究

Design of Multivariate Location Control Chart Using Principal Component Analysis Method

林健宏(Lin Chian-Hung)

指導教授 ： 楊素芬

國立政治大學/商學院/統計學系/碩士(2019年)

https://doi.org/10.6814/NCCU201900411

摘要

在監測產品或服務品質的方法中，管制圖是常使用的方法。傳統管制圖受限於常態分佈假設，因此許多學者投入研究非常態或是無母數管制圖的研究。另外，為了改善多變量製程之產品或服務品質，許多學者投入研究多變量管制圖。本文提出一個監控製程的管制圖。在母體分佈未知或非常態情況下，使用主成分分析方法結合符號平均值管制圖方法建立多元製程位置管制圖，EWMA-PM 管制圖，以監測未知多維度母體變數平均值向量。本文以平均連串長度 (ARL) 為指標評估此管制圖的偵測能力。
本文以數值分析方法比較EWMA-PM 管制圖與其它文獻管制圖的偵測能力，結果顯示EWMA-PM 管制圖在樣本數大於5時、製程平均發生小幅度偏移時有較好的偵測效果。接著以半導體製程資料演示EWMA-PM管制圖的建立流程。
此外，本文進一步建立變動樣本的標準多元製程位置管制圖，VSS EWMA-SM 管制圖，藉此提升偵測能力及降低抽樣成本。本文以抽樣的樣本期望值 (EN)、平均連串長度 (ARL) 和管制圖偵測出異常訊息所需平均抽樣的觀測值總數 (ANOS) 評估VSS EWMA-SM管制圖的偵測能力。

關鍵字

多維度管制圖 ； 主成分分析 ； 變動樣本 ； 平均連串長度

並列摘要

The control chart is a common tool to monitor industrial product process. Traditional Shewhart control charts are limited by the assumption of normal distribution. Furthermore, multivariate data are more common. For monitoring non-parametric multivariate quality variables, we propose a new phase II control chart. We propose multivariate exponentially weighted moving average (EWMA) location control chart, EWMA-PM control chart, that combines the methods of the principal component analysis method and sign control chart to efficiently detect an out-of-control process mean vector.
We use the average run length (ARL) to measure the detection performance of the EWMA-PM chart. Comparing the EWMA-PM chart with other existing control charts, the EWMA-PM chart shows the superior detection performance for mean vectors in a small shift when sample size is larger than 5. Then, we use semiconductor process data to illustrate the application of the EWMA-PM chart.
We also propose the EWMA-PM control chart with variables sample size (VSS) scheme, VSS EWMA-SM control chart, to monitor process mean vector, for enhancing the process detection ability and reduce the sampling cost. We use average expected number of samples (EN), ARL and average number of observations till the first signal (ANOS) to measure the detection performance of the VSS EWMA-SM chart.

並列關鍵字

multivariate control chart ； principal component analysis ； variable sample size ； average run length

參考文獻

[1] Abid, M., Nazir, H. Z., Riaz, M., & Lin, Z. (2017). An Efficient Nonparametric EWMA Wilcoxon Signed‐Rank Chart for Monitoring Location. Quality and Reliability Engineering International, 33(3), 669-685.

[2] Amin, R. W., Reynolds Jr, M. R., & Saad, B. (1995). Nonparametric quality control charts based on the sign statistic. Communications in Statistics-Theory and Methods, 24(6), 1597-1623.

[3] Amiri, A., Nedaie, A., & Alikhani, M. (2014). A new adaptive variable sample size approach in EWMA control chart. Communications in Statistics-Simulation and Computation, 43(4), 804-812.

[4] Bakir, S. T. (2004). A distribution-free Shewhart quality control chart based on signed-ranks. Quality Engineering, 16(4), 613-623.

[5] Bakir, S. T. (2006). Distribution-free quality control charts based on signed-rank-like statistics. Communications in Statistics-Theory and Methods, 35(4), 743-757.