Coffee: Design of the Experiments (Part 2: RSO)

In Review

The results of my 4-trial fractional factorial experiment (main effects) showed that extraction time is the most important variable, and that temperature and C/W ratio are less important. In the interest of completeness this experiment will not simply vary extraction time, but rather seek to efficiently find the maximum.

Lessons from the Screening Experiment

I am accustomed to making my coffee with about 22 fluid ounces of water, which makes two nice cups for my morning. During the screening I used 22 fl oz as a baseline, and increased or decreased the amount of coffee accordingly. The result was that some experiments required 48.8 g of coffee. You can’t possibly imagine how much coffee that is. It almost completely fills a coffee cup with just the beans!

In subsequent experiments I will limit the amount of coffee beans to something more modest, perhaps about 20 g, and vary the amount of water. With this more cautious approach I may live to see the final results.

The Design

NIST offered three designs for response surface objective (RSO) experiments. Specifically there are two interpretations of the Box-Wilson central composite design, each of which requires 20 total runs. An alternative design reduces the number of experiments to 15, which is the reason I chose it.

Specifically, the Box-Behnken design provides an RSO approach for 3 factors in 15 experiments. That is the same number I originally suggested through my naïve approach, but without all the baggage. Effectively, my original 5 values for each factor get reduced to three, and those are shuffled about in a way that is well-suited to estimating their effects. In my case, the specific experiments would be:

Response Surface Objective

Actual Values

Statistics Jargon

Trial

r (g/ml)

t (sec)

T (F)

R

T

T

1

0.035

10

195

-1

-1

0

2

0.075

10

195

+1

-1

0

3

0.035

300

195

-1

+1

0

4

0.075

300

195

+1

+1

0

5

0.035

55

185

-1

0

-1

6

0.075

55

185

+1

0

-1

7

0.035

55

205

-1

0

+1

8

0.075

55

205

+1

0

+1

9

0.055

10

185

0

-1

-1

10

0.055

300

185

0

+1

-1

11

0.055

10

205

0

-1

+1

12

0.055

300

205

0

+1

+1

13, 14, 15

0.055

55

195

0

0

0

This set will take me about three weeks. With luck by the time you read this I will have trickled out previous articles, and you will have results in two weeks or less. Sorry for the suspense.

Oh yes, I’m interested in other people’s Q functions too, so if you want to run my exact experiments, please post your data and I will post your results. Public or anonymous, at your discretion.

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One thought on “Coffee: Design of the Experiments (Part 2: RSO)

  1. Pingback: Coffee: Analysis & Results of the Response Surface « Park.

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