Statistical testing for sufficient control chart performances based on short runs and small mixed batches

Kostyszyn, Kevin Nikolai; Schmitt, Robert H. (Thesis advisor); Löwer, Manuel (Thesis advisor)

Aachen / Apprimus Verlag (2021) [Book, Dissertation / PhD Thesis]

Page(s): 1 Online-Ressource (xvii, 145 Seiten) : Illustrationen, Diagramme


With the increasing demand for customized products, small batch production is gaining importance in several industrial branches such as the steel processing industry. For quality control, the application of statistical process control (SPC) is desirable as it has already proved useful in large batch and mass production. However, its effective application requires a sufficient number of measurements which is often not available in a single small batch process. With the standard ISO 7870-8 published in 2017, charting techniques for short runs and small mixed batches were introduced. The standard proposes to group similar processes with similar behavior and to monitor them in joint control charts. Differently distributed measurements can be standardized with appropriate transformation parameters. However, parameters can only be roughly estimated based on preliminary data and thus, identical distributions and precisely constructed control charts cannot be ensured. And this can have a negative influence on control chart performances which can be expressed by the average runlength (ARL). Possible consequences are high false alarm rates and low detection rates during unstable processes. Hence, the target of this thesis was to develop a method which allows to statistically test a given group of processes for sufficient control chart performances based on preliminary individual values. Testing results thus serve as a decision base for or against a monitoring in joint control charts. Corresponding research needs were derived based on a literature review. The method can be integrated as an intermediate step into the procedure proposed by ISO 7870-8. After listing basic assumptions, a Markov-chain-based formula for the calculation of ARLs resulting from non-identically distributed individual values was developed. Exemplary calculation results for different control chart types, process sequences and distribution types were visualized and discussed. All findings were considered in the detailed development of the method. Its core is the application of a new developed statistical hypothesis test. Conditions for sufficient control chart performances are defined as acceptable maximum deviations from ideal ARLs usually assumed during classical SPC for a single process. The fulfillment of these conditions is considered as null hypothesis. The test statistic is the estimated ARL which is derived from estimated distribution parameters. Critical values are derived via Monte Carlo simulation. For the method application, a supporting software demonstrator was developed. In the verification and validation, it was proven that the ARL calculation approach was correctly developed and implemented. Based on a comparison of error rates, it was further shown that the new method performs better in testing for sufficient control chart performances than alternative tests proposed by the scientific literature which only test for equal distribution parameters. The application of the method was demonstrated based on industrial use cases.


  • ISBN: 978-3-86359-944-7
  • REPORT NUMBER: RWTH-2021-01826