Some 5 piece bonuses do not improve regardless of the quality of the set.

You should be able to see what the fully improved stats would be when you are in the upgrade menu (before you upgrade). The actual stats that you get will be a weighted average based on the quality of all the gear. To get the maximum you would need to have all 5 pieces upgraded to gold, whereas if you had 3 purple and 2 gold, you would get a combination of the two.

I'm not familiar enough with the Eagle Eye set to know if it's one that has a static 5 piece or not (but the 2-, 3-, and 4- piece bonuses should definitely increase)

Drunkensot wrote: »

I bought three eagles eye jewelry, and improved the necklace to chromium, but got not benefit of any improved stats. If I improve all three will I get any better stats?

Take off all 3 pieces. Look at each piece in your inventory. A gold piece of Eagle Eye should be 833 Weapon Critical and
1829 Weapon Critical. Is that what the necklace says? Do the purple rings show slightly lower stats? Upon re-equipping the jewelry, does each piece now show an identical number somewhere between the un-equipped gold and purple jewelry? Equipped jewelry auto-calculates a weighted value of each active set bonus. So if you have one piece of 833 Weapon Critical and two pieces of 811 Weapon Critical, once equipped, all three pieces will show something like 820 Weapon Critical.