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

Abstract

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 T2 control chart, EWMA control chart, and R-chart under small shift in the slope.