Design of experiments

Question 1

DoE definition 2

Answer 1

1. Planning, in advance, what data to collect, and what tools to use for their analysis
2. A systematic approach for planning experiments so that the data obtained can be analysed to yield statistically valid and objective conclusions

Question 2

inputs and outputs

Answer 2

factors and responses

Question 3

system studied

Answer 3

process model

Question 4

examples of factors

Answer 4

inlet temperature
inlet pressure
reactants
inlet flow rate

Question 5

examples of responses

Answer 5

outlet temperature
outlet pressure
products
outlet flow rate

Question 6

main effects

Answer 6

How strongly the “level” of a single factor (input) affects a given response (output)

Lines with shallow slopes correspond to weak main effects - factor (on x axis) not very important

Lines with steep slopes correspond to strong main effects
- factor (on x axis) important

Question 7

interaction plots

Answer 7

Near-parallel lines suggest the interaction does not affect the response
Non-parallel lines suggest an effect
More non-parallel = stronger effect!

Question 8

coded variables

Answer 8

Putting all variables on the same scale allows us to compare them & their effects more easily
-1 – 1
min max

Question 9

code a given temperature

Answer 9

𝑇_𝑐𝑜𝑑𝑒𝑑=

(𝑇−0.5(𝑇_𝑚𝑎𝑥+𝑇_𝑚𝑖𝑛 )) /

0.5(𝑇_𝑚𝑎𝑥 − 𝑇_𝑚𝑖𝑛 )

Question 10

Quantitative

Answer 10

has a number value

Question 11

Qualitative

Answer 11

physical thing

Question 12

Interaction effect:

Answer 12

a factor’s effect on the response that depends on the levels of another factor(s)

Question 13

natural variable

Answer 13

a “normal” or “uncoded” variable

Question 14

experimental design 4

Answer 14

Aims of the study
All experimental factors to be tested and the relevant levels thereof
All responses which will be measured
The number of experiments to be carried out

Question 15

randomisation

Answer 15

Assign a random order to individual experiments (‘runs’)
Minimise issues relating to human error or equipment malfunction
bias

Question 16

replication

Answer 16

Repeat experiments – at least in triplicate (ideally more!)
Minimise errors
can average

Question 17

blocking

Answer 17

Perform experiments in distinct groups or “blocks” of similar runs
Help identify systematic errors, e.g. due to day-to-day or batch-to-batch variations
minimise variables

Question 18

randomisation example

why bother

Answer 18

Imagine you are performing an experiment involving an endothermic reaction in a stirred tank reactor
The viscous drag on the impeller acts to slowly but consistently heat the fluid
You systematically vary a parameter 𝑋 from 𝑋_𝑐𝑜𝑑𝑒𝑑=−1 to 𝑋_𝑐𝑜𝑑𝑒𝑑=1 and notice a small increase in reaction rate.
Can you be certain the increase is due to 𝑋?
What if instead the order had been randomised?
randomisation means pattern isn’t because of repeating T

Question 19

blocking example

why bother

Answer 19

Imagine you are performing a trial on a new vaccine and want to check its efficacy.
You could group your trials, for example, by age and/or gender to ensure that any variations or patterns you see are solely due to the drug and not gender, age etc.
can give false negative or positive

Question 20

replication why bother

Answer 20

more repeats = better statistics = more trustworthy data

Question 21

typical steps in doe

Answer 21

1. define aim
2. process and factors - choose reasonable input factors
3. response and measurements- choose relevant output responses
4. experimental design
5. experiments
6. check data
7. modelling
8. validation- verify predictions with experiments

Question 22

OFAT (one-factor-at-a-time) strategy for doe

Answer 22

– study each factor independently, one by one.
Pros: simple and easy to implement
Cons: inefficient – especially for many factors; does not account for interactions- not easy to see whats causing change

Question 23

Factorial design strategy for doe

Answer 23

Investigate multiple factors simultaneously, exploring all permutations of factors.
Pros: Efficiently identify factors with strong effects; study effect of interactions
Cons: complex when using many factors and/or levels; an error on a single data point can have significant consequences

Question 24

Response surface design strategy for doe

Answer 24

Aims to find the specific levels of relevant factors that produce the optimal response
Pros: A very direct and rigorous route to optimisation
Cons: Relies on fitting a suitable model; complex – especially if data cannot be fitted by a simple, smooth surface

Question 25

Screening design strategy for doe

Answer 25

Aims to find, for an experiment with many factors, those which dominate the system behaviour
Pros: Simple, straightforward, provides valuable information for further design/testing
Cons: In itself, not a complete strategy – mainly used as a precursor e.g. to response surface design