Combination of Sequential Sampling Technique with GLR Control Charts for Monitoring Linear Profiles Based on the Random Explanatory Variables

Abstract

Control charts play a beneficial role in the manufacturing process by reduction of non-compatible products and improving the final quality. In line with these aims, several adaptive methods in which samples can be taken with variable sampling rates and intervals have been proposed in the area of statistical process control (SPC). In some SPC applications, it is important to monitor a relationship between the response and independent variables—this is called profile monitoring. This article proposes adaptive generalized likelihood ratio (GLR) control charts based on variable sampling interval (VSI) and sequential sampling (SS) techniques for monitoring simple linear profiles. Because in some real-life problems, it may be possible that the user cannot control the values of explanatory variables; thus, in this paper, we focus on such a scenario. The performance of the proposed method is compared under three different situations, i.e., the fixed sampling rate (FSR), VSI, and SS, based on average time to signal (ATS) criteria for phase II analysis. Since the SS approach uses a novel sampling procedure based on the statistic magnitude, it has a superior performance over other competing charts. Several simulation studies indicate the superiority as the SS approach yields lower ATS values when there are single-step changes in the intercept, slope, standard deviation of the error term, and explanatory variables. In addition, some other related sensitivity analysis indicates that other aspects of the proposed methods, such as computational time, comparison with other control charts, and consideration of fixed explanatory variables. Furthermore, the results are supported by a real-life illustrative example from the adhesive manufacturing industry.