Factorial Design with Centre Point Example

2 Factorial Design with Centre Point Example 

Consider a chemical engineer who is studying the yield of a chemical process. There are 2 variables of interest reaction time and reaction temperature. Since there is some uncertainty regarding the appropriateness of a linear model, a single unreplicated 2 -factorial experiment was performed with 5 centre point replicates. The results of the experiment are shown in Table 4.9. Based on the provided results, analyse the model using the methods provided in the above discussion to determine the best model for the process. Be certain to analyse the residuals to determine the adequacy of the model Data taken from Montgomery, Applied Statistics and Probability for Engineers, 4th edn.). 

An Excel -based solution to this problem is presented in Sect. 8.7.3. 

A similar procedure to that used to analyse the results in Sect. 4.7.4.1 will be used in this example. 

Since ric = 5 and k = 2,aa appropriate basis function for the curvature tern can be written as 

---

Figure 8.36 Sect. 4.8.2, Factorial Design with Centre Point Example. 

RSM is quite popular in nanotechnology literature. However, in some cases, the results have been interpreted incorrectly. For example, if a two-level factorial design is used with centre points, it is this design that informs the experimenters as to whether there are second-order effects in the experimental region. It does not suggest which effect is contributing the second-order interaction. We also found that many papers fail to seek a path to reach the optimal experiment condition, which is one of the main reasons for employing RSM. 

We take the example of 3 variables, for a manufacturing or factory scale process whose performance and reproducibility is well known. The factors effects may be investigated by a 2 design (4 experiments) plus centre point. A cycle of the 5 experiments is performed and the effect of each variable determined as described in chapter 2. Since its standard deviation a is already known, each measured effect may be compared with the calculated standard deviation for each effect, c/2. 

---