Worksheets/Week6
Part 1
Your group is developing a new product, but have been struggling to get the product’s stability, measured in days, to the level required. You are aiming for a stability value of 50 days or more.
- A: enzyme strength: -1 == 20%; +1 == 30%
- B: feed concentration: -1 == 5%; +1 == 15%
- C: mixer type: -1 = R mixer; +1 = W mixer
# 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 <- 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:
- A = feed rate: 5 g/min or 8 g/min
- B = initial inoculate amount: 300 g or 400 g
- C = feed substrate concentration: 40 g/L or 60 g/L
- D = dissolved oxygen set-point: 4 mg/L or 5 mg/L
The 16 experiments from a full factorial, 24, 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
# 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)