3. In an experiment on the ammoniation of 1,2-propanediol, the chemical reaction

Question

3. In an experiment on the ammoniation of 1,2-propanediol, the chemical reaction yields primar- ily 1,2-propanediamine and 2,5-dimenthylpiperazine. The factors were ammonia concentra- tion (A), maximum temperature (B), water concentration (C) and initial hydrogen pressure (D). The design matrix and response data appear below see ammonia.dat. The planning matrix can be recovered by multiplying by a scaling factor and adding a centering factor: A (51,102), B (20,250), C (200,300) and D (350,850), where the numbers in parentheses rep- resent scaling and centering constants, respectively. For example, for factor A, multiply by 51 and then add 102, so that coded level +1 corresponds to (+1)(51) 102 171. The re- sponse is percent yield of 2,5-dimenthylpiperazine (DMP), where high DMP yield is desirable. are the star points to complete the are for initial first-order design and runs second-order design.

Explanation / Answer

Ans Minitab answer

The design is Box-Behnken design.

factors=4

no of runs=25

Box-Behnken Design

Factors: 4 Replicates: 1
Base runs: 25 Total runs: 25
Base blocks: 1 Total blocks: 1

Center points: 1

Response Surface Regression: DMP versus A, B, C, D

Analysis of Variance

Source DF Adj SS Adj MS F-Value P-Value
Model 4 2061.30 515.32 2.75 0.057
Linear 4 2061.30 515.32 2.75 0.057
A 1 45.48 45.48 0.24 0.628
B 1 32.85 32.85 0.18 0.680
C 1 1521.28 1521.28 8.12 0.010
D 1 461.69 461.69 2.46 0.132
Error 20 3746.96 187.35
Total 24 5808.25

Model Summary

S R-sq R-sq(adj) R-sq(pred)
13.6875 35.49% 22.59% 0.00%

Coded Coefficients

Term Effect Coef SE Coef T-Value P-Value   
Constant 29.67 2.74 10.84 0.000
A -3.02 -1.51 3.07 -0.49 0.628
B 2.57 1.28 3.07 0.42 0.680
C -17.48 -8.74 3.07 -2.85 0.010
D 9.63 4.81 3.07 1.57 0.132

Above R-sq(adj) =22.59% so the design is good.

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