Environmental Engineering Reference
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and 3D graph. Numerical optimization using desirability functions was done to
find the optimum mixture proportions. Statistical analysis for the response
compressive strength, water absorption capacity, shrinkage, density and
leachate characteristics of Cd and Pb content in the jarosite waste bricks were
performed.
In order to verify the obtained responses, the polynomial models described
in classic mixture approach are fit to data using analysis of variance (ANOVA)
and least squares techniques (Box, et al., 1978). Many statistical software
packages have the capability to perform these analyses and data fitting. From
the ANOVA significance of the treatment effect was obtained. There are
several factors/ variables that have an effect on the response variable. For
example, the immobilization of toxic substances in hazardous jarosite waste
may depend on the types of catalyst/ additives used, their quantity,
concentration, process technique, temperature and pressure under which the
reaction is completed. Table 8 summarizes the mixture design parameters with
responses. The run order was randomized to reduce the effects of extraneous
variables not explicitly included in the experiment.
Model Identification and Validation: Measured Responses
In this section, a detailed description of the process of model identification
and validation is provided for the response compressive strength. The models
for other responses were identified and validated in the same way. The first
step in the analysis is to select a plausible model. Even though the experiment
design used permits estimation of a quadratic model, a linear model may
provide a better fit to the data. ANOVA is used to assess the different models.
The average values for compressive strength, water absorption, shrinkage and
density of the jarosite waste composite bricks attained for the designed
experiment, by Response Surface Methodology using mixture design approach
for the 14 design points, are shown in Table 8. A modified-distance method
was chosen to ensure that the design selected could estimate the quadratic
mixture model while spreading points as far away as possible from one
another. For each of the four responses, a model was fit using least-squares
methods, validated (by examining the residuals for trends and outliers), and
interpreted graphically using contour and trace plots. The statistical analysis is
described in detail for brick compressive strength followed by model
identification and validation. The analyses for the other properties such as
water absorption, shrinkage and brick density were performed in a similar
manner. The results of ANOVA for compressive strength are shown in Table
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