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Profile monitoring is a technique to test the stability of the relationship between a response variable and explanatory variables over time. The most relevant linear profile monitoring methods have been constructed using the normality assumption. However, the normality assumption could be violated in many quality control applications. In this study, we consider a situation in which the random errors in a linear profile model follow a skew‐normal distribution. The skew‐normal distribution is a generalized version of the normal distribution. A new Shewhart‐type chart and exponentially weighted moving average (EWMA) chart, named the ShewhartR and EWMAR charts, respectively, are constructed based on residuals to monitor the parameters of linear profile model. The simulation results show that the multivariate EWMA chart is sensitive to the normality assumption and that the proposed ShewhartR and EWMAR charts have good ability to detect big and small‐to‐moderate process shifts, respectively. An example using photo mask techniques in semiconductor manufacturing is provided to illustrate the applications of the ShewhartR and EWMAR charts. [ABSTRACT FROM AUTHOR]

In profile monitoring for a multivariate manufacturing process, the functional relationship of the multivariate profiles rarely occurs in linear form, and the real data usually do not follow a multivariate normal distribution. Thus, in this paper, the functional relationship of multivariate nonlinear profile data is described via a nonparametric regression model. We first fit the multivariate nonlinear profile data and obtain the reference profiles through support vector regression (SVR) model. The differences between the observed multivariate nonlinear profiles and the reference profiles are used to calculate the vector of metrics. Then, a nonparametric revised spatial rank exponential weighted moving average (RSREWMA) control chart is proposed in the phase II monitoring. Moreover, a simulation study is conducted to evaluate the detecting performance of our proposed nonparametric RSREWMA control chart under various process shifts using out‐of‐control average run length (ARL1). The simulation results indicate that the SREWMA control chart coupled with the metric of mean absolute deviation (MAD) can be used to monitor the multivariate nonlinear profile data when a common fixed design (CFD) is not applicable in the phase II study. Finally, a realistic multivariate nonlinear profile example is used to demonstrate the usefulness of our proposed RSREWMA control chart and its monitoring schemes. [ABSTRACT FROM AUTHOR]

The Shewhart-type control chart is traditionally developed under the normality assumption. In practice, however, this assumption may not hold. Because the skew normal distribution represents a broad distribution class and is more flexible than is the normal distribution, we propose two new control charts to monitor process mean and spread for skew normal distributed data. Moreover, to facilitate practical implementation, tables of charting constants are provided. We conducted simulation studies to compare the false alarm rates, and the results show that new proposed charts perform better than others as skewness increases. Finally, an illustrative example is provided. [ABSTRACT FROM PUBLISHER]