While they are separate campaigns, it is possible that a poor quality score on a keyword in one of your campaigns will affect the same keyword in a totally separate campaign. Quality scores are assigned to keywords within your account, so a poor Quality score history in one campaign will affect the starting Quality score in any new campaign. Additionally, there is a Quality Score for your overall account which affects any new keywords that you add to a campaign.
It is important to note that your Quality Score is based primarily on your historical keyword CTR as compared to your competitors, and is weighted toward your most recent performance so it will rapidly change based on how your ads perform. If you are writing compelling ads, testing, and managing them properly, you should have no problem overcoming any historical bias on your keywords.