Statistical Certainties of Expert-Supported Quality Forecasts for Groups of Product Characteristics or Process Parameters
In small batch production, statistical methods for derivation of quality forecasts are rarely applied. The reason is that sample data available for statistical analysis is strongly limited. To increase available amounts, several scientific approaches recommend to create and to analyze groups of product characteristics or process parameters. However, those approaches do not quantify statistical certainties of resulting quality forecasts. Also, available expert knowledge and experience regarding process behavior is not applied although experts may regard specific quality forecasts as not realistic. In this case, those forecasts could be excluded from consideration. To overcome all mentioned deficiencies, this work introduces an approach to quantify statistical certainties of quality forecast s for groups of product characteristics or process parameters. Quality forecasts are expected to be based on typical patterns that can be observed in z-charts. Beside empirical distributions of available sample data, possible underlying infinite populations are taken into account. Experts can limit the scopes of considered infinite populations to those ones that are regarded as realistic. This enables a knowledge-based specification of quantified statistical certainties. All considered sample data is assumed to follow normal distributions. In this paper, sample values of an exemplary group are plotted in a chart where a trend pattern is detected. The statistical certainty for this trend will be calculated with the presented approach.