the handbook of food engineering practice crc press chapter 10 ...

Lund, 1985). The standarized residuals should be randomly distributed around zero and
usually within -2 and +2. Any data that generate standard residuals outside this range are
possible outliers.
An alternative procedure to linear regression for the calculation of k is the point
by point or long interval method (Margerison, 1969; Lund, 1983), in which each data point
is an independent experiment with respect to zero time. The value of k is calculated as the
average of the n individual slopes.
Labuza (1984) showed that one gets similar value
ranges for k from the two methods. A minimum of 8 data points is recommended by
Labuza and Kamman (1983) for reasonably narrow confidence limits in k within the
practical and economic limits of most experimentation.
In some cases higher or fractional order models are clearly indicated by the
experimental data. To determine the apparent order m, two methods can be alternatively
used. As mentioned before, different values for m can be assumed and the fit of the quality
function for m≠1 (Table 1), tested. A second method is to allow m as a parameter and run
a nonlinear least square regression on the equation to determine the order that best
conforms with the experimental data. For example, it was found that second order kinetics
best described the oxidation of extractable color pigments from chili pepper (Chen and
Gutmanis, 1968). Autoxidation of fatty acids in presence of excess oxygen is best
described with a 1/2 order model with respect to the fatty acid concentration (Labuza,
1971), whereas hexanal production from lipid oxidation is shown to theoretically fit a cubic
model (Koelsch and Labuza, 1992).
As has been explained before, the developed food quality loss functions are
based on the stated assumptions and do not necessarly reflect true reaction mechanisms.
In case for which the assumptions are not applicable or the actual mechanism is very
complex due to side reactions or limiting intermediate steps, equations (9) and (10) may
not sufficiently model the measured changes. One approach in this case is to develop a
15