Tiaris, I think that is the hard way of going about it. Admittedly this is only theoretical as I have never had the space to try it, but here it goes.
If you have a decent sized set up say 12 flights. I would pair a yellow bird with a red bird in each flight. All offspring are at least spilt yellow and can be sold that way. After a season where no yellow chicks (you would probably need to breed at least 6 - 8 birds to be sure) are produced in the flight you would call the red parent bird "probable pure". I would then pair up the probable reds and breed them til their done. With some of their offspring you could also test breed these back to yellow to be sure no spilt birds have slipped through.
Doing it this way you have much more confidence of no mutation birds being in your flock and if there are you can identity them much more quickly. It doesn't however guarantee that your line isn't spilt for fawn or another mutation
Multiple mutations in a species makes it much more difficult, such as gouldians.
Do you agree that this might work?
Cheers Ian
Ian's strategy is certainly valid, but I have two problems with it.
The major concern is that you are generating a whole lot of split birds is the process, which seems contrary to the aim of increasing "pure" stock. This may not be an issue for the individual, but I think it is an issue for the hobby as a whole.
Second point is that despite your efforts you are still not guaranteed of getting "pure" birds. In the examples given, if you accept 6 red offspring as "proof" there is still a 1/32 chance of the bird being split. 8 red offspring, 1/128 chance of still being split. No number of normal offspring can provide a 100% guarantee. It is just not possible to totally eradicate recessive traits.
My own view is that I try to not get too fixated on a single trait, like breast color. Each bird has its own unique characteristics, and if you can breed a strain that has the characteristics that you want, whether it is "wild-type" or something else, then that is an accomplishment to be proud of. If an occasional bird "throws back" to something different then cull it from your stock.
Cheers
Brett