{"id":122,"date":"2009-02-23T20:58:10","date_gmt":"2009-02-24T03:58:10","guid":{"rendered":"http:\/\/inkofpark.wordpress.com\/?p=122"},"modified":"2009-02-23T20:58:10","modified_gmt":"2009-02-24T03:58:10","slug":"coffee-design-of-the-experiments-part-2-rso","status":"publish","type":"post","link":"https:\/\/www.inkofpark.com\/?p=122","title":{"rendered":"Coffee: Design of the Experiments (Part 2: RSO)"},"content":{"rendered":"

In Review<\/h1>\n

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.<\/p>\n

Lessons from the Screening Experiment<\/h1>\n

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!<\/em><\/p>\n

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.<\/p>\n

The Design<\/h1>\n

NIST offered three designs<\/a> 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.<\/p>\n

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 na\u00efve 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:<\/p>\n

\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n\n
Response Surface Objective<\/td>\n<\/tr>\n
<\/td>\n\n

Actual Values<\/p>\n<\/td>\n

\n

Statistics Jargon<\/p>\n<\/td>\n<\/tr>\n

Trial<\/td>\n\n

r<\/em> (g\/ml)<\/p>\n<\/td>\n

\n

t<\/em> (sec)<\/p>\n<\/td>\n

\n

T<\/em> (F)<\/p>\n<\/td>\n

\n

R<\/em><\/p>\n<\/td>\n

\n

T<\/em><\/p>\n<\/td>\n

\n

T<\/em><\/p>\n<\/td>\n<\/tr>\n

1<\/td>\n\n

0.035<\/p>\n<\/td>\n

\n

10<\/p>\n<\/td>\n

\n

195<\/p>\n<\/td>\n

\n

-1<\/p>\n<\/td>\n

\n

-1<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n<\/tr>\n

2<\/td>\n\n

0.075<\/p>\n<\/td>\n

\n

10<\/p>\n<\/td>\n

\n

195<\/p>\n<\/td>\n

\n

+1<\/p>\n<\/td>\n

\n

-1<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n<\/tr>\n

3<\/td>\n\n

0.035<\/p>\n<\/td>\n

\n

300<\/p>\n<\/td>\n

\n

195<\/p>\n<\/td>\n

\n

-1<\/p>\n<\/td>\n

\n

+1<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n<\/tr>\n

4<\/td>\n\n

0.075<\/p>\n<\/td>\n

\n

300<\/p>\n<\/td>\n

\n

195<\/p>\n<\/td>\n

\n

+1<\/p>\n<\/td>\n

\n

+1<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n<\/tr>\n

5<\/td>\n\n

0.035<\/p>\n<\/td>\n

\n

55<\/p>\n<\/td>\n

\n

185<\/p>\n<\/td>\n

\n

-1<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n

\n

-1<\/p>\n<\/td>\n<\/tr>\n

6<\/td>\n\n

0.075<\/p>\n<\/td>\n

\n

55<\/p>\n<\/td>\n

\n

185<\/p>\n<\/td>\n

\n

+1<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n

\n

-1<\/p>\n<\/td>\n<\/tr>\n

7<\/td>\n\n

0.035<\/p>\n<\/td>\n

\n

55<\/p>\n<\/td>\n

\n

205<\/p>\n<\/td>\n

\n

-1<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n

\n

+1<\/p>\n<\/td>\n<\/tr>\n

8<\/td>\n\n

0.075<\/p>\n<\/td>\n

\n

55<\/p>\n<\/td>\n

\n

205<\/p>\n<\/td>\n

\n

+1<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n

\n

+1<\/p>\n<\/td>\n<\/tr>\n

9<\/td>\n\n

0.055<\/p>\n<\/td>\n

\n

10<\/p>\n<\/td>\n

\n

185<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n

\n

-1<\/p>\n<\/td>\n

\n

-1<\/p>\n<\/td>\n<\/tr>\n

10<\/td>\n\n

0.055<\/p>\n<\/td>\n

\n

300<\/p>\n<\/td>\n

\n

185<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n

\n

+1<\/p>\n<\/td>\n

\n

-1<\/p>\n<\/td>\n<\/tr>\n

11<\/td>\n\n

0.055<\/p>\n<\/td>\n

\n

10<\/p>\n<\/td>\n

\n

205<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n

\n

-1<\/p>\n<\/td>\n

\n

+1<\/p>\n<\/td>\n<\/tr>\n

12<\/td>\n\n

0.055<\/p>\n<\/td>\n

\n

300<\/p>\n<\/td>\n

\n

205<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n

\n

+1<\/p>\n<\/td>\n

\n

+1<\/p>\n<\/td>\n<\/tr>\n

13, 14, 15<\/td>\n\n

0.055<\/p>\n<\/td>\n

\n

55<\/p>\n<\/td>\n

\n

195<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n

\n

0<\/p>\n<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<\/div>\n

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.<\/p>\n

Oh yes, I’m interested in other people’s Q<\/em> 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.<\/p>\n","protected":false},"excerpt":{"rendered":"

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 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[4],"tags":[23,31,48],"class_list":["post-122","post","type-post","status-publish","format-standard","hentry","category-coffee","tag-coffee","tag-food-cooking","tag-statistics"],"_links":{"self":[{"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=\/wp\/v2\/posts\/122","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=122"}],"version-history":[{"count":0,"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=\/wp\/v2\/posts\/122\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=122"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=122"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.inkofpark.com\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=122"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}