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

esidual plots. Alternatively, instead of the logarithmic equation for the first order reaction
(Table 1) the exponential form can be used, where:
A = A o exp ( - k t ) (15)
and a nonlinear least square fitting computed, for determination of the k parameter. The R 2
for this fit is given by equation (14) and is directly comparable to the R 2 from the linear
regression for the zero-order model.
A final pitfall that should be avoided when determining the apparent order,
concerns reactions that exhibit a lag period. During a typical lag period there is a build-up
of a critical intermediate concentration. The rate of the reaction during the build-up period
is is normally slower. In some cases, the reaction is not detectable due to analytical
limitation as in the case of the formation of brown pigments monitored at 420 nm during a
nonenzumatic Maillard type reaction. The most common approach to deal with a lag
period , is to draw each data point and to look for the time where a distinct change in the
reaction rate occured. Obviously, this approach calls for special attrention as a change in
the reaction mechanism may also take place. Typical reactions where lag period is
observed are nonenzymatic browning (Labuza, 1982; Saguy, et al., 1979) and microbial
growth.
Once the apparent order of the quality deterioration reaction has been decided,
further statistical analysis and statistical evaluation of the parameter k, the rate constant is
required, to get an estimate of the error in the determination of k (Labuza and Kamman,
1983). If a linear regression method is used to estimate the parameters, their 95%
confidence limits can be calculated using the Student t distribution. In addition to the
confidence limits, a list of standarized residuals and a residual plot is a useful statistical tool
that allows evaluation of how well the chosen equation can model the data and also permits
the recognition of extreme or outlier values that may be the result of experimental errors or
other extraneous effects and should be excluded from the calcualtions (Arabshasi and
14