Monitoring Series of Dependent Observations Using the sXWAM Control Chart for Residuals

Abstract

Control charts for monitoring residuals are the main tools for statistical process control of autocorrelated streams of data. X chart for residuals calculated from a seties of individual observations is probably the most popular, but its statistical characteristics are not satisfactory, especially for charts designed using limited amount of data. In order to improve these characteristics Hryniewicz and Kaczmarek proposed a new chart for residuals, XWAM chart, using the concept of weighted model averaging. Unfortunately, the design of the XWAM chart is rather complicated, and requires significant computational effort. In this paper we propose its simplification, named sXWAM chart, which is simpler to design, and in some practically important cases has similar statistical properties. 1 Introduction Control charts are nowadays the most frequently used tool of Statistical Quality Control (SQC). They were introduced in the 1920th by Shewhart who at that time worked for an American company Western Electric. Since that time many statistical procedures which have their origins in Shewhart's works have been developed, and their usage in practice is known under a common name of Statistical Process Control (SPC). In the majority of applications control charts are used for monitoring production processes when long series of quality-related measurements are observed. In such a case a well grounded mathematical theory have been established. Later on, control charts have been also applied in cases of short production runs. In