Overall Equipment Effectiveness is a metric that is the product of three measures: 1) Percent of acceptable product, 2) Percent of expected cycle time actually achieved, and 3) Availability, or up-time percentage.
For example: If your product is running 5% defects (95% acceptable), the actual cycle time is 55 seconds when it should be 60 (92% of expected), and the line is down for 20 minutes in a typical 480 minute (8 hr) day (or 95% uptime), THEN the OEE = .95 x .92 x .96 = 84%.
Run @ Rate, according to QCI's Quality Dictionary is "
verification that a production process is capable of producing the desired quality at quoted rates ." That seems to indicate a combination of two of the above three factors - quality and production rate - and does not include uptime.
Postscript:
Also, a simple Cove search (for OEE & Run at rate) shows good threads and attachments. GM-1960 and GP-9 cover the run-at-rate requirement.
Hope that helps.