A Score‐test‐based EWMA Control Chart for Detecting Prespecified Quadratic Changes in Linear Profiles

Abstract

In profile monitoring, some methods have been developed to detect the unspecified changes in the profiles. However, due to the characteristics of a system or process, several prespecified changes may happen in some statistical process control applications, such as the typical form errors in cylindrical surface manufacturing processes. Hence, statistical process control is important and challenging for detecting changes away from the ‘normal’ profile toward one of several prespecified ‘bad’ profiles. A novel score‐test‐based EWMA control chart is proposed to detect the prespecified quadratic changes in linear profiles. Numerical simulation results show that the proposed chart is effective and robust when the vertex varies along one direction, and, in most cases, performs better than alternative methods in detecting small to moderate shifts. Finally, an example is given to illustrate the implementation of the proposed control chart. Copyright © 2015 John Wiley & Sons, Ltd.

CUSUM Schemes for Monitoring Prespecified Changes in Linear Profiles

“…The values of the parameters in the IC model are β 0 = 13, β 1 = 2, and , and the fixed value x i = − 3 + 6( i − 1)/( n − 1) is in the interval [−3, 3], which is the same as that of the IC process model used in Zhang, Zhang et al , and Zhang et al. What is more, we will also investigate the effects of the observation number n in each profile on the performance of the CUSUM schemes, where three different n values with n = 7, 13, and 25 are taken into account.…”

“…In these two typical changes, the specified forms of term f ( x i ) are and sin (2 πx i /6), respectively. The first one represents the quadratic shape changes, which is also considered in Zhang, Zhang et al , and Zhang et al , while the second form describes the sine shape changes. Some profile samples from these two OC process models are shown in Figures and , respectively.…”

“…Based on this basic idea, a second‐order polynomial regression was applied to model the process when any form error, i.e., hourglass, barrel, or banana, appears in the process. In this model, the coefficient of quadratic term could identify the departures toward the bad profiles, and then some monitoring methods were proposed to detect the shape changes from linear profiles to quadratic profiles . To monitor the typical form errors in the manufactured cylindrical surfaces, Colosimo et al developed a control scheme that consists of modeling the manufactured surface via Gaussian processes models and monitoring the deviations of the actual surface from the target pattern estimated in phase I.…”

Domain-Selective Functional Analysis of Variance for Supervised Statistical Profile Monitoring of Signal Data

“…Recently, the studies of Zhang et al . () have extended this concept to profile monitoring applications. Specifically, Zhang et al .…”

“…Specifically, Zhang et al . () studied profile monitoring schemes for linear profiles where the out‐of‐control departure is known in advance and consists of a shape change from a straight line to a second‐order polynomial curve. The underlying idea was to develop control charting schemes based on testing the significance of the quadratic term.…”