arraysalgorithmstatisticscombinatoricsblack-box-testing

How to create Orthogonal array?


Suppose we have following three factors:

Factor A: 5 possible values
Factor B: 4 possible values
Factor C: 2 possible values

How can I construct an Orthogonal array for these?

Main thing which I don't understand is making the combinations. I remember we used to follow '11112222', '11221122', '12121212' this kinda combinations, but it seems everyone has different approach for filling the values in array. Is there any standard approach?


Solution

  • There isn't a single neat algorithm that generates orthogonal arrays to order. Instead there are a variety of constructions that have been discovered in a host of different areas of mathematics, and some techniques for modifying orthogonal arrays to change their parameters in some way or another. For instance see http://www.itl.nist.gov/div898/handbook/pri/section3/pri33a.htm and http://www.win.tue.nl/~aeb/preprints/oa3.pdf. Many statistics packages have an orthogonal array design utility which uses these rules and a list of known orthogonal arrays to try and find an orthogonal array that will satisfy the requirements it has been given.

    In your case I can find nothing closer at the moment than the six five-level factors design at http://www.york.ac.uk/depts/maths/tables/l25.htm using 25 runs. You can certainly discard three columns. Where you have e.g. five levels in the design and only 4 (or 2) levels in the experiment I would be inclined to consistently relabel e.g. {1,2,3,4,5} -> {1,2,3,4,4} and {1,2,3,4,5} => {1,2,1,2,1} but I have no clear idea of what this does to the experimental properties.