Worksheets/Week6

Part 1

Case study: Achieve a stability value of 50 days or more, for a new product. We had a full factorial set of experiments in 3 factors:

Factor name	Description	Low value	High value	Type of factor
A	Enzyme strength	20%	30%	Numeric factor
B	Feed concentration	75%	85%	Numeric
C	Mixer type	R	W	Categorical

We will show what we loose out if we pretend we only did half the experiments. In other words, we actually have 8 experiments, but we will see what happens if we only use 4 of them.

# This is the half-fraction, when C = A*B A = c(-1, +1, -1, +1) B = c(-1, -1, +1, +1) C = A * B # The response: stability [units=days] y = ... model_stability_poshalf model_stability_poshalf = lm(y ~ A*B*C) summary(model_stability_poshalf) # Uncomment this line if you run the code in RStudio #library(pid) # Comment these 2 lines if you run this code in RStudio source('https://yint.org/paretoPlot.R') source('https://yint.org/contourPlot.R') paretoPlot(model_stability_poshalf) # This is the other half-fraction, when C = -A*B A = c(-1, +1, -1, +1) B = c(-1, -1, +1, +1) C = -1 * A * B # The response: stability [units=days] y = ... model_stability_neghalf = lm(y ~ A*B*C) summary(model_stability_neghalf)

Part 2

Data from a bioreactor experiment is available, were we were investigating four factors:

Factor name	Description	Low value	High value	Type of factor
A	Feed rate	5 g/min	8 g/min	Numeric factor
B	Initial inoculant amount	300 g	400 g	Numeric
C	Feed substrate concentration	40 g/L	60 g/L	Numeric
D	Dissolved oxygen set-point	4 mg/L	5 mg/L	Numeric

The 16 experiments from a full factorial, 2^4 = 16, were randomly run, and the yields, y, the outcome variable were given in standard order: [60, 59, 63, 61, 69, 61, 94, 93, 56, 63, 70, 65, 44, 45, 78, 77]

base = c(-1, +1) design = expand.grid(A=base, B=base, C=base) A = design$A B = design$B C = design$C D = A * B * C # These are correct, but confirm that you can find these 8 runs yourself: y = c(60, 63, 70, 61, 44, 61, 94, 77) model_bio = lm(y ~ A * B * C * D) summary(model_bio) # Uncomment this line if you run the code in RStudio #library(pid) # Comment these 2 lines if you run this code in RStudio source('https://yint.org/paretoPlot.R') source('https://yint.org/contourPlot.R') paretoPlot(model_bio)