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On the Use of the K-Chart for Phase II Monitoring of Simple Linear Profiles

DOI: 10.1155/2013/705450

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Control charts for monitoring linear profiles are used to control quality processes which are characterized by a relationship between a response variable and one or more explanatory variables. In the literature, the majority of control charts deal with phase II analysis of linear profiles, where the objective is to assess the performance of control charts in detecting shifts in the parameters of linear profiles. Recently, the kernel distance-based multivariate control chart, also known as the K-chart, has received much attention as a promising nonparametric control chart with high sensitivity to small shifts in the process. Despite its numerous advantages, no work has proposed the use of the K-chart for monitoring simple linear profiles and that serves the motivation for this paper. This paper proposes the use of the K-chart for monitoring simple linear profiles. A benchmark example is used to show the construction methodology of the K-chart for simultaneously monitoring the slope and intercept of linear profile. In addition, performance of the K-chart in detecting out-of-control profiles is assessed and compared with traditional control charts. Results demonstrate that the K-chart performs better than the control chart, EWMA control chart, and R-chart under small shift in the slope. 1. Introduction In the last decade, control charts for monitoring linear profiles have acquired a prominent role in controlling quality processes characterized by a relationship between a response variable and one or more explanatory variables. A control chart for monitoring linear profiles consists of two phases. In phase I, the parameters of the regression line are estimated to determine the stability of the process. In phase II, the goal is to detect shifts in the process from the baseline estimated in phase I. In the literature, the majority of control charts deal with the phase II analysis of linear profiles. Kang and Albin [1] proposed a multivariate control chart for monitoring both the intercept and the slope, while Kim et al. [2] suggested the use of three univariate exponentially weighted moving average (EWMA3) control charts for simultaneously monitoring the intercept, slope and standard deviation. Zou et al. [3] proposed a multivariate EWMA scheme when the quality process is characterized by a general linear profile. Zhang et al. [4] developed a control chart based on EWMA and Likelihood ratio test. Zou and Qiu [5] developed the LASSO-based EWMA control chart, for monitoring multiple linear profiles. Li and Wang [6] established an EWMA scheme with variable

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