A. SPEERS (1), M. Josey (1);
(1) ICBD- HWU, Edinburgh, U.K.
Technical Session 10 - Fermentation
Wednesday, June 17
1:00–2:15 p.m.
Flores 1–2
The logistic model has been used to fit and predict the decline of wort density in both industrial and laboratory data since 2003. This four-parameter sigmoidal (s-shaped) function fits the decline in apparent extract using a non-linear regression technique and now forms part of ASBC Yeast-14: The Miniature Fermentation Assay. While this logistic model has been shown to fit industrial and laboratory fermentations (MacIntosh, et al. 2012 and 2014, J. ASBC; and Speers et al. 2003 and 2006, J. Inst. Brew.) it would be useful to predict the error of these fits. Prediction intervals (PI) are defined as estimated ranges where future observations will fall above and below the curve. When constructed, these intervals can serve as the equivalent of upper and lower control limits used in univariate control charts. As such, PI values would be a useful addition to the brewing statistical process control (SPC) tool kit. Our objective was to examine data from industrial lager and ale brewing fermentations to see how PIs could be simply constructed. If variance throughout the fermentation is constant (or is homoscedastic) then PIs can be easily calculated via use of Graphpad Prism software. However, if the variance of the data varies with time (or is heteroscedastic) then calculation becomes more difficult. However, PIs can be estimated when repeated fermentation data at fixed fermentation times is available. With fixed fermentation time data, the calculation of sample standard deviations (SD) is possible. Then, one can estimate (at each time), the upper interval (+3SD), the mean, and the lower interval (–3SD). These three curves (i.e., the upper control limit, mean, and lower control limit) can be fit by the logistic model producing an estimate of the change in apparent extract as well as an estimate of the heteroscedastic PI. Examination of the both the lager and ale fermentations revealed that the fermentations were heteroscedastic with a low variation at the beginning and end of the fermentation and a wide variation at the midpoint of the fermentations. However, the data was not measured at fixed interval times precluding the PI estimation technique discussed above. To allow for estimation of apparent extracts at random fermentation times the logistic model was used to fit to individual fermentations thus producing a data set at fixed times. This then allowed estimation of a heteroscedastic PI as discussed above. In examining the ale fermentation, a 99.7% confidence prediction interval made assuming homoscedastic data excluded 4.3% of the data indicating an overly conservative interval. When using the method of 99.7% confidence prediction interval construction assuming hetroscedasticity only 0.33% outliers occurred. With this technique brewers now can produce fermentation prediction intervals which can be used in an analogous method to univariate control charts to help control fermentations.
Alex Speers is a professor and the director of the International Centre of Brewing and Distilling at Heriot Watt. Previously he was a professor in the Food Science program at Dalhousie University. Born in Creston, BC, Canada he gained B.S. (Agr.), M.S., and Ph.D. degrees at UBC in Vancouver, Canada. In the past, Alex has been employed in the Quality Assurance Departments of both Labatt and Molson Breweries. His research interests include various aspects of the brewing and distilling process, including fermentability, yeast flocculation, fermentation modeling, extract calculations, and the properties of (and problems created by) barley malt. He has organized, presented, or judged at brewing events in America, Australia, Canada, China, and Ireland. Alex has spent sabbaticals at CUB/Fosters and the Columbia Brewing Company. He is a past chair of the Editorial Board of the MBAA Technical Quarterly. Alex belongs to several professional societies and is a member of the editorial boards of the JASBC, JIB, and the TQ. He has published or presented more than 200 papers, is a Fellow of the Institute of Brewing and Distilling, and is a Chartered Scientist. In 2011 he received the W.J. Eva Award from the Canadian Institute of Food Science and Technology.
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