Comparison of grouping algorithms to increase the sample size for statistical process control

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.