Monitoring Correlated Proﬁle and Multivariate Quality Characteristics Amirhossein Amiri, a * Changliang Zou b and Mohammad H. Doroudyan a Monitoring multivariate quality characteristics is very common in production and service environment. Therefore, many control charts have been suggested by authors for monitoring multivariate processes. In another side, proﬁle monitoring is a new approach in the area of statistical process control. In this approach, the quality of a product or a process is characterized by a relation between one response variable and one or more independent variables. In practice, sometimes the quality of a product or a process is represented by a correlated proﬁle and multivariate quality characteristics. To the best of our knowledge, there is no method for monitoring this type of quality characteristics. Note that monitoring correlated proﬁle and multivariate quality characteristics separately leads to misleading results. In this article, we speciﬁcally focus on correlated simple linear proﬁle and multivariate normal quality characteristics and propose a method using multivariate exponentially weighted moving average control chart to monitor the correlated proﬁle and multivariate quality characteristics simultaneously. The performance of the proposed control chart is evaluated by simulation studies in terms of average run length criterion. Finally, the proposed method is applied to a real case in the electronics industry. Copyright © 2013 John Wiley & Sons, Ltd. Keywords: statistical process control; simple linear proﬁle; correlated proﬁle and multivariate quality characteristics; MEWMA control chart; phase II 1. Introduction N owadays, the quality of many products or processes is represented by two or more correlated quality characteristics. Hotelling 1 showed that monitoring multivariate quality characteristics separately leads to misleading in results. He proposed T 2 control chart for monitoring multivariate quality characteristics. Multivariate exponentially weighted moving average (MEWMA) 2 and multivariate cumulative sum (MCUSUM) 3 control charts are the other most common multivariate control charts. Reviews of the most usual methods in multivariate process monitoring have been performed by several authors such as Basseville and Nikiforov, 4 Ryan, 5 Frisen, 6 Sonesson and Frisen, 7 Bersimis et al., 8 and Frisen. 9 Recently, a new procedure was proposed by Butte and Tang 10 in some common multivariate control charts to facilitate the identiﬁcation of the source of out-of-control signal. Kim et al. 11 proposed a non- parametric fault isolation approach based on a one-class classiﬁcation algorithm and showed that their proposed method can detect source of variation better than T 2 decomposition in the presence of nonnormal processes. Some kinds of variable sampling rate in multi- variate control charts, which lead to overall better performance rather than standard ﬁxed sampling rate, were proposed by Reynolds and Cho. 12 The applications of multivariate control charts in health care were studied by Waterhouse et al. 13 Sometimes, the quality of a product or a process is characterized by a relation between a response variable and one or more independent variables, which is called proﬁle. The most common type of proﬁle is a simple linear proﬁle in which a response variable has a linear relation with an explanatory variable. Simple linear proﬁle monitoring was ﬁrst investigated by Kang and Albin 14 via proposing two approaches including T 2 and EWMA/R. Then, Kim et al. 15 proposed EWMA-3, Mahmoud and Woodall 16 proposed an F method, Mahmoud et al., 17 Zou et al., 18 and Zhang et al. 19 suggested an LRT-based method, and Saghaie et al. 20 used CUSUM-3 to monitor simple linear proﬁle. Other complicated proﬁles such as multiple linear proﬁle, polynomial proﬁle, nonlinear proﬁle, logistic proﬁle, and multivariate linear proﬁles were also investigated by the authors. For example, multiple linear regression proﬁle was studied by Zou et al. 21 and Amiri et al. 22 . Kazemzadeh et al. 23,24 proposed some methods in phases I and II of monitoring polynomial proﬁles, respectively. Nonlinear proﬁle was monitored by Williams et al. 25 and Vagheﬁ et al. 26 . Logistic proﬁle was monitored by Yeh et al., 27 and multivariate linear proﬁle monitoring was investigated by Noorossana et al. 28,29 , Eyvazian et al., 30 and Zou et al. 31 These are some other issues considered in the literature of proﬁle monitoring. In addition, Woodall et al. 32 and Woodall 33 reviewed common methods in proﬁle monitoring. In addition, Noorossana et al. 34 recently summarized major achievements in the area of proﬁle monitoring. a Industrial Engineering Department, Faculty of Engineering, Shahed University, Tehran, Iran b LPMC and Department of Statistics, School of Mathematical Sciences, Nankai University, Tianjin, China *Correspondence to: Amirhossein Amiri, Industrial Engineering Department, Faculty of Engineering, Shahed University, Tehran, Iran. E-mail: amiri@shahed.ac.ir Copyright © 2013 John Wiley & Sons, Ltd. Qual. Reliab. Engng. Int. 2013 Research Article (wileyonlinelibrary.com) DOI: 10.1002/qre.1483 Published online in Wiley Online Library 1