在某些工業製程裡，會用一或多個解釋變數及一個反應變數之間的函數關係來描述品質，這種函數關係稱為輪廓。
在過去的文獻中，沒有人對圓柱體產品進行製程的輪廓監控。本文主要是應用Zou, Tsung and Wang (2007)提出的監控一般線性輪廓製程的多變量指數加權移動平均(multivariate exponentially weighted moving average, 簡稱 MEWMA)管制圖在圓柱體製程的監控上。我們會介紹如何利用線性模型來描述圓柱體的資料，並 透過監控圓柱體線性輪廓參數來建立MEWMA管制圖。我們透過統計模擬的方式來比較此MEWMA管制圖和利用監控圓柱度偏差所建立的MEWMA管制圖的監控表現。
同時，我們也在偵測出失控警訊後，提出估計製程改變點和找出導致改變點發生的圓柱體線性輪廓參數的方法。最後，我們用一個例子來說明如何對實際的圓柱體製程進行輪廓監控。

In certain industrial processes, the quality of a product is characterized by the functional relationship
between a response variable and one or more explanatory variables. This functional relationship is called a profile.
In the literature, profile monitoring of cylindrical products has not ever been performed.
In this article, we apply the MEWMA control chart proposed by Zou, Tsung and Wang (2007) to monitor the linear profile process for cylindrical products. We first introduce how to use linear models to describe cylindrical data and how to use the MEWMA control chart to monitor the linear profiles. Then, we compare the simulation performance of this MEWMA control chart with the MEWMA control chart established by using cylindricity deviation.
We also estimate the changepoint in profile monitoring and identify the out-of-control profile parameters when the MEWMA chart signals.
Finally, we use a real example to illustrate how to perform profile monitoring on actual cylindrical data.

目錄第一章緒論........................................1
1.1前言. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1
1.2輪廓製程監控. . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2
1.3研究動機與目的. . . . . . . . . . . . . . . . . . . . . . . . . . . . .3
第二章圓柱體線性輪廓的監控.............................5
2.1圓柱體的線性模型. . . . . . . . . . . . . . . . . . . . . . . . . . . .5
2.2利用MEWMA管制圖監控圓柱體的製程. . . . . . . . . . . . . . . .8
2.3圓柱體製程改變點的估計和異常參數的辨識. . . . . . . . . . . . . . .9
第三章統計模擬......................................11
3.1圓柱體MEWMA管制圖的管制上限. . . . . . . . . . . . . . . . . .11
3.2利用圓柱度偏差的管制圖. . . . . . . . . . . . . . . . . . . . . . . .13
3.3圓柱體參數偏移監控的比較. . . . . . . . . . . . . . . . . . . . . . .14
3.4圓柱體製程改變點的估計和異常參數的辨識. . . . . . . . . . . . . . .17
第四章實例........................................19
第五章結論........................................22
參考文獻............................................23
附表..............................................26
附圖..............................................44

Chen, Q., Tao, X., Lu, J., and Wang, X. (2016). Cylindricity error measuring and evaluating for engine cylinder bore in manufacturing procedure. Advances in Materials Science and Engineering, 2016.

Kakino, Y., and Kitazawa, J. (1978). In situ measurement of cylindricity by the 3-point method. Journal of The Japan Society for Precision Engineering, 44, 1386-1392.

Kang, L., and Albin, S. L. (2000). On-line monitoring when the process yields a linear profile. Journal of quality Technology, 32(4), 418-426.

Keshteli, R. N., Kazemzadeh, R. B., Amiri, A., and Noorossana, R. (2014). Functional process capability indices for circular profile. Quality and Reliability Engineering International, 30(5), 633-644.

Kim, K., Mahmoud, M. A., and Woodall, W. H. (2003). On the monitoring of linear profiles. Journal of Quality Technology, 35(3), 317-328.

Mestek, O., Pavlík, J., and Suchánek, M. (1994). Multivariate control charts: control charts for calibration curves. Fresenius' journal of analytical chemistry, 350(6), 344-351.

Muralikrishnan, B., and Raja, J. (2008). Computational surface and roundness metrology. Springer, Berlin.

Murthy, T. S. R. (1982). A comparison of different algorithms for cylindricity evaluation. International Journal of Machine Tool Design and Research, 22(4), 283-292.

Page, E. S. (1954). Continuous inspection schemes. Biometrika, 41(1/2), 100-115.

Qiu, P., Zou, C., and Wang, Z. (2010). Nonparametric profile monitoring by mixed effects modeling. Technometrics, 52(3), 265-277.

Roberts, S. W. (1959). Control chart tests based on geometric moving averages. Technometrics, 1, 239-250.

Runger, G. C., and Prabhu, S. S. (1996). A Markov chain model for the multivariate exponentially weighted moving averages control chart. Journal of the American Statistical Association, 91(436), 1701-1706.

Shewhart, W. A. (1924). Some applications of statistical methods to the analysis of physical and engineering data. Bell System Technical Journal, 3(1), 43-87.

Tsukada, T., and Kanada, T. (1982). Measurement of cylindrical form errors using a non-contact detector. Precision Engineering, 4(3), 153-158.

Zhang, H., and Albin, S. (2009). Detecting outliers in complex profiles using a X2 control chart method. IIE Transactions, 41(4), 335-345.

Zheng, P., Liu, D., Zhao, F., and Zhang, L. (2019). Statistical evaluation method for cylindricity deviation using local least squares cylinder. International Journal of Precision Engineering and Manufacturing, 20(8), 1347-1360.

Zou, C., and Tsung, F. (2011). A multivariate sign EWMA control chart. Technometrics, 53(1), 84-97.

Zou, C., Tsung, F., and Wang, Z. (2007). Monitoring general linear profiles using multivariate exponentially weighted moving average schemes. Technometrics, 49(4), 395-408.