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

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 one-way analysis of variance (ANOVA).