Statistical testing for sufficient control chart performances during monitoring of grouped processes

Abstract

With ISO 7870-8, a standardized application of charting techniques for short runs and small mixed batches was presented in 2017. Similar to various scientific approaches, it requires that sample values from grouped processes follow nearly identical distributions. In practice, however, there tend to be differences between distribution parameters. Moreover, equal parameters do not ensure that distributions are properly aligned to the center line and control limits of the chart. These facts can lead to undesired control chart performances which can be expressed by average run lengths (ARL) during in-control and out-of-control conditions. In this work, a statistical test for sufficient control chart performances during monitoring of grouped processes based on preliminary samples is proposed. Control chart performances are defined as sufficient when they deviate within acceptable ranges from usual performances during single process monitoring in mass production. The ARL resulting from estimated distributions and planned production sequences is used as test statistic and calculated via the Markov chain approach. Exemplary tests are executed for scenarios with individuals and cumulated sum (CUSUM) charts. A simulative determination of error rates resulting from the ARL-based testing demonstrates its effectiveness in testing for sufficient control chart performances compared to an indirect testing with Levene's test and a oneway analysis of variance (ANOVA). K E Y W O R D Saverage run length, control chart performances, grouped processes monitoring, ISO 7870-8, short run SPC This is an open access article under the terms of the Creative Commons Attribution License, which permits use, distribution and reproduction in any medium, provided the original work is properly cited.

Statistical parametric and non-parametric control charts for monitoring residential water consumption

“…The statistical control chart performance can be expressed by the average run length (ARL), which is the average number of samples required to signal that an event is out of statistical control 38 . As stated by Kostyszyn et al 38 , an effective control chart has a large ARL under statistical control conditions and a small ARL when the process is out of control.…”

“…The statistical control chart performance can be expressed by the average run length (ARL), which is the average number of samples required to signal that an event is out of statistical control 38 . As stated by Kostyszyn et al 38 , an effective control chart has a large ARL under statistical control conditions and a small ARL when the process is out of control. According to Sancho et al 39 , this theory is associated to a Type I error (false alarm rate) and a Type II error (false negative) and, when the statistical power of the SCC is increased to signal out-of-control events, so is the false alarm rate.…”