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).

中文翻译：

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在监视分组过程期间对足够的控制图性能进行统计测试

在 ISO 7870-8 中，2017 年提出了针对短期和小批量混合的图表技术的标准化应用。与各种科学方法类似，它要求来自分组过程的样本值遵循几乎相同的分布。然而，在实践中，分布参数之间往往存在差异。此外，相等的参数并不能确保分布与图表的中心线和控制限正确对齐。这些事实可能会导致不希望的控制图性能，这可以通过控制和失控条件下的平均运行长度 (ARL) 来表示。在这项工作中，建议在基于初步样本的分组过程监控期间对足够的控制图性能进行统计测试。当控制图性能在批量生产中的单个过程监控期间偏离通常性能的可接受范围内时，被定义为足够。由估计分布和计划生产序列产生的 ARL 用作测试统计量并通过马尔可夫链方法计算。对具有个体和累积总和 (CUSUM) 图表的场景执行示例性测试。与使用 Levene 检验和单向方差分析 (ANOVA) 进行的间接检验相比，基于 ARL 的检验产生的错误率的模拟确定证明了其在检验足够控制图性能方面的有效性。由估计分布和计划生产序列产生的 ARL 用作测试统计量并通过马尔可夫链方法计算。对具有个体和累积总和 (CUSUM) 图表的场景执行示例性测试。与使用 Levene 检验和单向方差分析 (ANOVA) 进行的间接检验相比，基于 ARL 的检验产生的错误率的模拟确定证明了其在检验足够控制图性能方面的有效性。由估计分布和计划生产序列产生的 ARL 用作测试统计量并通过马尔可夫链方法计算。对具有个体和累积总和 (CUSUM) 图表的场景执行示例性测试。与使用 Levene 检验和单向方差分析 (ANOVA) 进行的间接检验相比，基于 ARL 的检验产生的错误率的模拟确定证明了其在检验足够控制图性能方面的有效性。