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. With the standard ISO 7870-8 published in 2017, charting techniques for short runs and small mixed batches were introduced. However, required parameters for standardization of sample values can only be roughly estimated. And this can have a negative influence on resulting control chart performances which can be expressed by the average run length (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 serve as a decision base for or against a monitoring in joint control charts. 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. The core of the method 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.
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Statistical Testing for Sufficient Control Chart Performances Based on Short Runs and Small Mixed Batches
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KurzbeschreibungWith the standard ISO 7870-8 published in 2017, charting techniques for short runs and small mixed batches were introduced. They all require estimations of standardization parameters which can have a negative influence on control chart performances. In this thesis, a new method allowing to statistically test a given group of processes for sufficient control chart performances is presented. Testing results serve as a decision base for or against a monitoring in joint control charts.