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?
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.