Monitoring the process mean with a side-sensitive synthetic- X¯ chart

Abstract

Control charts are designed to detect assignable causes that may occur in production processes. They are very simple operationally; however, this operational simplicity, that is, taking samples of fixed size n at regular time intervals and searching for an assignable cause when a point falls outside the control limits, makes the control chart slow in detecting small to moderate shifts in the parameter being controlled. Since this handicap of Shewhart charts was recognized, many innovations have been proposed to improve the charts' performance, such as the synthetic charts. The signaling rule of the synthetic chart requires a second consecutive point beyond the control limit not far from the first one. The number of samples between them cannot exceed L, a pre-specified value. The growing interest in using this rule may be explained by the fact that many practitioners prefer waiting until the occurrence of a second point beyond the control limits before looking for an assignable cause. Recently, a scheme comprising a synthetic chart and an X¯ chart was proposed and it was denoted as the Syn- X¯ chart. This chart signals when a sample point falls beyond the control limits or when a second point, not far from the first one, falls beyond the warning limits, no matter whether one of them falls above the centerline and the other falls below. In this article a side-sensitive version of the Syn- X¯ chart (SS Syn- X¯ chart) is proposed. The SS Syn- X¯ chart does not signal when the points beyond the warning limits are on opposite sides of the centerline. The study performance by simulation show that, in some cases, the proposed chart is more than 30% faster in detecting shifts in the process mean than the Syn- X¯ chart.