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Industrial Statistics with Minitab by Xavier Tort-Martorell Llabres, Lluis Marco Almagro, Pere Grima Cintas

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30.5 Microorganisms

In the laboratory of a company of wastewater treatment an experiment is carried out with the aim of detecting how the pH of the water and the temperature affect the microorganisms’ growth rate. In particular, the aim is to find out which pH value and temperature cause the highest growth rate.
The experiments will be performed following the response surface methodology, according to the next steps:
1. A 22 design with centre points is carried out in order to try to fit a linear model. A good model fit would indicate we are far from the maximum.
2. Both factors are moved in the direction of the maximum growth (steepest ascent), to detect where the maximum is.
3. A new 22 design with centre points is carried out and a linear model is fit. In case of a good fit, we are still far from the maximum and, hence, the ascent direction will be corrected and we continue looking for the maximum.
4. In case the previous model does not fit well, the maximum has probably already been reached. We then add more experiments to be able to estimate the quadratic terms.

→ Step 1

We start with a 22 design with 3 center points, with the low and high levels for pH and temperature that are shown in the following table

Level − Level +
pH 3,0 4,0
Temperature 20 25

The design matrix with the obtained results:

pH Temp [oC] Rate [·10-2 min-1]
3.0 20.0 1.56
4.0 20.0 2.55
3.0 25.0 2.30
4.0 25.0 3.20
3.5 22.5 2.45
3.5 22.5 2.31
3.5 22.5 2.31

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