Comparison of grouping algorithms to increase the sample size for statistical process control
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Comparison of grouping algorithms to increase the sample size for statistical process control Jonathan Simon Greipel1,2 · Gina Nottenkämper2 · Robert Heinrich Schmitt2 Received: 9 December 2019 / Accepted: 8 April 2020 / Published online: 20 April 2020 © The Author(s) 2020 OPEN
Abstract In this study, we present and compare four grouping algorithms to combine samples from low volume production processes. This increases their sample sizes and enables the application of Statistical Process Control (SPC) to low volume production processes. To develop the grouping algorithms, we define different grouping criteria and a general grouping process. To identify which algorithm is optimal, we deduct following requirements on the algorithms from real production datasets: their ability to handle different amount of characteristics and sample sizes within each characteristic as well as being able to separate characteristics possessing distributions with different spreads and locations. To check the fulfillment of these requirements, we define two performance indices and conduct a full-factorial Design of Experiments. We achieve the performance indices for each algorithm by using simulations with artificial data incorporating the aforementioned requirements. One index rates the achieved group sizes and the other one the compactness within groups and the separation between groups. To validate the applicability of grouping algorithms within SPC, we apply real production data to the grouping algorithms and control charts. The result of this analysis shows that the grouping algorithm based on cluster analysis and splitting exceeds the other algorithms. In conclusion, the grouping algorithms enable the application of SPC to small sample sizes. This provides companies, which produce in low volumes, with new means of reducing scrap, generating process knowledge and increasing quality. Keywords Grouping algorithm · SPC · Low volume production · Pooling of data · Algorithm performance
1 Introduction Heterogeneous customer requirements and growing competition urge companies to offer more and more product variants [1]. Therefore, they increasingly produce small series, small batches or single pieces [2]. Due to the small quantities, Statistical Process Control (SPC) is no longer applicable as large sample sizes of approximately 125 values are required to achieve reliable estimations and information [3]. Companies can no longer make quality relevant decisions or prove their process capability to their customer. The control limits of control charts
become too large to detect instabilities and are therefore—in practice—no longer useful. Another reason is that the required confidence intervals of the capability indices are dependent on the sample size and become too large to be informative. To overcome the problem of too small sample sizes different approaches exist [4]. Change point models [5], control charts with greater sensitivity [6], self-starting charts [7], pre-control-charts [8], Bayesian approaches [9], control charting proces
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