This is for testing the accuracy of OCR conversion of a document. If I want to be certain I have a positive match of a word or phrase containing 15 characters, how many correct characters do I need to match? For example, if I can only match 5 characters in the proper sequence, what is the probability this is a positive match? The same test would go for a number sequence with 15 numbers.

How about using the following.

The quick brown fox jumped over the lazy dogs back 1234567890 times.

Repeat it a number of times... and it contains every letter and number in the alphabet. Long used as a test to catch garbling of transmitted messages.

I'm not sure what you are asking here. OCR uses algorithms to try and determine what the actual text is. Those algorithms are proprietary secrets of the software vendor.