THERE ARE NO INDUSTRY TOLERANCES

Each mill use their own limits. This is testament to how good they can manufacture their products. The lower the tolerance, the better they believe they can make the products.
It is important to check for pattern run off BEFORE making the first cut. The entire shipment must be checked at various spots throughout all the rolls. The pattern run off can then be corrected if it is within stated tolerances.

It seems to me, that the most often used numbers for out of tolerance, are:
I in. in 12' for pattern elongation
3/4 in. in 12' for pattern bow
1 2 in. in 12' for skew.

To check for pattern run off the first thing you need is a square line chalked across the width of the carpet. This line needs to be at a 90 degree angle to the pattern, not necessary to the side of the carpet. Measure from a like point in the pattern on both sides, the difference will give you your skew in 12'.
Next, find a like point in the pattern on both sides of the carpet, using a chalk line or a dry line, hold each end on the pattern. Where the pattern varies the most across the width is your bow in 12'.

The most important is pattern elongation. To find this measurement, count down a certain amount of pattern repeats on one side and measure the distance, following the same procedure,  using the same point of the repeat on the other the of the carpet, measure the distance, this is the elongation. it is always a good idea to try to measure a distance that will be close to your seam lengths. This procedure must be repeated at different intervals throughout the roll as the difference could change, effecting your cuts.
Elongation Is important because it dictates which cut you will begin with. You MUST start with the panel that has the most elongation, then the adjacent cuts need to be the ones with the next longest elongation and so forth. Remember, you can always stretch a short pattern to a long pattern, however, it is almost always impossible to shrink a longer pattern opposed to stretching a shorter one

There are other pattern problems that will effect installation such as length bow, (this is where the pattern bows along the length of the carpet) the trueness of the edge ( the pattern looks like a wavy line down the length)  This problem is the most prominent and should ALWAYS be checked before cutting.

Is there any wonder that installing pattern carpets should require additional
compensation?
On a side note, should you encounter a carpet that is defective due to being out of tolerance, document your findings prior to cutting the material. Contact the Mill and explain the problems that you have encountered. If you think that you
can make the job work, you should be compensated by the MILL for the additional work NOT THE RETAILER. Remember, the mills have tech people that most probably have installation backgrounds, if you try to gouge them or get rich based upon the situation, you will probably wind up with nothing. BE FAIR with your requests, and most mills will be willing to cough up additional $$$$$ for your time to correct their mistake.