Optimal experimental design for estimating the kinetic parameters of processes described by the Weibull probability distribution function

Abstract

The optimum experimental design for determining the kinetic parameters of the model resulting from the Weibull probability density junction was studied, by defining the sampling conditions that lead to a minimum confidence region of the estimates, for a number of observations equal to the number of parameters. It was found that for one single isothermal experiment the optimum sampling times corresponded always to fractional concentrations that are irrational numbers (approximately 0.70 and 0.19) whose product is exactly l/e'. The experimental determination of the equilibtium conversion (for growth kinetics) is vety important, but in some situations this is not possible, e.g. due to product degradation over the length of time required. Sampling times leading to a maximum precision were determined as a function of the maximum conversion (or yield) attainable. For studies of kinetic parameters over a range of temperatures, performed with a minimum of three isothermal experiments, it was proved that the optimum design consists of two experiments at one limit temperature with two sampling times (those corresponding to fractional concentrations of approximate[v 0.70 and 0.19) and another at the other limit temperature for a sampling time such that the fractional concentration is lie. Case studies are included for clarijication of the concepts and procedures.

Survival of Campylobacter jejuni in mineral bottled water according to difference in mineral content: Application of the Weibull model

“…The cumulative form of Weibull frequency distribution model was used to describe Campylobacter survival kinetics in water as it is suitable for quantifying Page 5 / 19 bacterial survival for both log and non-log linear survival curves. The Weibull model has largely been used to describe bacterial inactivation by thermal and nonthermal processes as stress resistance of a microbial population often follows a Weibull distribution (Cunhan et al, 1998;Peleg and Cole, 1998;Fernandez et al, 1999;van Boekel, 2002;Corradini and Peleg, 2003;Virto et al, 2005;Hajmeer et al, 2006). We used a logarithm decimal form of Weibull defined as follows (Mafart et al, 2002;van Boekel, 2002):…”

Contribución al estudio de la aplicación de ultrasonidos de potencia en el secado convectivo de alimentos

“…El modelo empírico de Weibull está basado en una función probabilística usada para describir el comportamiento de sistemas complejos variantes (Cunha et al, 1998). Inicialmente se utilizó para predecir fallos por fatiga de materiales.…”

“…Tanto para las experiencias de secado de zanahoria como de albaricoque, el parámetro β del modelo de Weibull se vio afectado de forma significativa (p<0.05) por la temperatura de secado. A medida que la temperatura de secado aumentó, el valor identificado de este parámetro se redujo, inversamente a la velocidad de secado (Cunha et al, 1998). Este mismo efecto de la temperatura sobre el parámetro β ha sido mostrado anteriormente por otros autores en diversos productos (Cunha et al, 2001;Blasco et al, 2006).…”

Antioxidative Properties of Acyl Ascorbates on Lipid Oxidation in Bulk, Disperse and Microcapsule Systems

“…4.5 µm during the oxidation, indicating that the oxidation processes were appropriate for a stable emulsion. The oxidation kinetics was empirically expressed by the following Weibull equation (Cunha et al, 1998):…”