**2.3.2 Design of experiments**

The experiments were conducted by standard orthogonal array. The selection of the orthogonal array is based on the condition that the degrees of freedom for the orthogonal array should be greater than or equal to sum of those lightness and reflective percent parameters [2.6-2.9]. In the present investigation, an L16 orthogonal array was chosen, which has 5 rows and 16 columns as shown in Table 2.1. Table 2.2 indicates the factors and their level. The experiment consists of 16 tests (each row in the L16 orthogonal array) and the columns were assigned with parameters. The first row was pH, second row was reaction temperature (T), third row was concentration of SnCl2 solution (C), fourth row was reaction time (t) and fifth row was stirring rate (R). The response to be studied was the lightness and reflective percent with the objective of the bigger the better. The experiments were conducted by orthogonal array with level of parameters given in each array row. The l test results were subject to the analysis of variance.



Table 2.1. Orthogonal array L16(45) of Taguchi [2.4]

Table 2.2. Process parameters with their values at four levels

Ceramic Coatings for Pigments 245

Doing different analyses such as analysis of variance by using Winrobust software, important parameters were identified. This showed that some of these parameters have less effect in synthesis of the pigments than others. The amount of the effects is shown in figure

a b

Since in the Taguchi method it is possible that an optimum does not exist in the performed experiments in the designed array [2.10-2.11], some operations were then done by Winrobust software to determine the optimized point. Optimized levels of identified

pH 3 3

T 2 2

C 3 3

t 2 2

R 2 2

To confirm this statistical method, synthesis is performed at the optimized conditions. If the experimental results equal the results with Winrobust software, it shows that the method is correct. In figure 2.2, normal probability distribution by Winrobust software is shown for the residual amount in which the continuity of the points in this figure is another

Table 2.4. Optimized levels of parameters determined with Winrobust software

confirmation for this method [2.10].

Parameters Optimize level of lightness Optimize level of reflection

Fig. 2.1. Effect of synthesis parameters on the a) lightness and b) reflective percent of

parameters for lightness and reflective percent of pigments is shown in table 2.4.

2.1.

pigments
