Actually, the goal is to provide the functionality to prevent the app firing the server and putting it down by excessive quering. Despite on the wrong app's coding or DOS attacks.

needs some logic to inform DBA's that something is going wrong, and needs to work with to prevent the server down. The query You provide gives the average value of number of executions per second. When the plan is in cache for a long period, the avg will not reflect to peaks of N/per sec

my thoughts were to gather executions of SPs grouping the numbers by hour. Then compare the particular measurement with the average of the same day(days) of week with the same hour.

certainly, I'll try to use your query.