Worksheets/Week6

From Statistics for Engineering
Revision as of 09:36, 17 October 2019 by Kevin Dunn (talk | contribs) (→‎Part 2)
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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

See the link full case study, and to help you, there is a table you can fill out.


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)