一階自我相關多變量多重線性輪廓的監控

On the Monitoring of First-Order Autocorrelated Multivariate Multiple

詹舒涵(Shu-Han Chan)

指導教授 ： 王藝華

淡江大學/商管學院/統計學系應用統計學碩士班/碩士(2021年)

https://doi.org/10.6846/TKU.2021.00224

摘要

當品質的好壞可由函數關係來表示時，我們可以藉由監控此函數關係達到監控品質的目地，我們稱此函數關係為輪廓。監控產品品質的輪廓資料可分為線性輪廓與非線性輪廓，過去的研究，多將資料視為獨立狀態，然而製程資料大多與時間相關，可分為輪廓間相關與輪廓內相關，因此，本研究提出新的管制方法V-MEWMA於多變量多重線性輪廓模型，且輪廓間具有一階自我相關的監控上。並將Soleimani和Noorossana（2014）所提之MEWMA/$chi^2$的監控方法，推廣成可監控多變量多重線性輪廓，且輪廓間具有一階自我相關的資料。最後藉由蒙地卡羅模擬MEWMA/$chi^2$與本研究所提之V-MEWMA監控方法進行比較。

關鍵字

輪廓監控 ； 多變量多重線性模型 ； 一階自我相關

並列摘要

When the quality can be represented by a function relationship, we can monitor the quality by monitoring this function relationship. We call this relationship a profile. The profile data for monitoring product quality could be classified into linear and nonlinear profiles. In the past studies, the data were often assumed to be independent time. However, data collected from the process are often time-dependent. Time dependent data could be classified into inter-profile and within-profile correlations. Therefore, we propose a new control method V-MEWMA to a multivariate multi-linear profile model with first-order between-profile autocorrelation. We extended MEWMA/$chi^2 $scheme proposed by Soleimani and Noorossana (2014) such that monitor multivariate multiple linear profiles with first-order autocorrelation data. Finally, we using the Monte Carlo simulation compared with V-MEWMA our proposed scheme in this study.

並列關鍵字

profile monitoring ； multivariate multiple linearity model ； first-order autocorrelation

參考文獻

勞動部（2020）。印刷電路板製造工。取自

https://www.mol.gov.tw/media/1380813/bg27.pdf

Ahmad,A. Y., Ali,Z. H. and Amirhossein,A.(2020). Multivariate Analysis of Variance (MANOVA). Communications in Statistics - Theory and Methods, 49 ,4117-4132.

Eyvazian,M., Noorossana,R., Abbas,S. and Amirhossein,A. (2011). Phase II Monitoring of Multivariate Multiple Linear Regression Profiles. Quality Reliability Engineering International,27(3),281-296.

Ghashghaei,R., Amiri,A. and Khosravi,P. (2019).New control charts for simultaneous monitoring of the mean vector and covariance matrix of multivariate multiple linear profiles. Communications in Statistics - Simulation and Computation, 48(5), 1382–1405.