When I was working reviewing reliability numbers at an airline, there were 5 numbers that we used.
A14: Arrival within 15 minutes of scheduled arrival time for all flights.
D0: Airplane parking brake is released at departure time, which is filtered to remove weather, airport operations, passenger loading, catering, etc
D15: Airplane is within 15 minutes of scheduled departure time (filtered as above)
D120: Airplane is within 120 minutes of scheduled departure time (filtered as above)
Cancellations: Canceled for airplane maintenance and mechanical reasons including crew time out due to airplane maintenance, but not weather or lack of crew availability
The reason for so many metrics is that each of them is evaluated for different reasons.
The metric reported to the public is A14 and shows the overall health of the airline. This metric can be used to measure performance of all divisions from crew operations to maintenance to dispatch. It also shows delays caused by cascading problems in the schedule. Padding the schedule helps this number, but padding the schedule comes at the cost of paying higher crew rates and lower fleet utilization.
D0 is the goal from an aircraft availability point. The airplane is ready to fly with no mechanical problems. Airport operations delays can happen, but the airplane should be ready to go.
D15 is important because items causing mechanical delays less than 15 minutes are understandable. They typically are for deferring a part or cycling power quickly to a system. They do not require intensive maintenance and show that the airline is healthy at addressing a maintenance problem from the second the plane blocks into the gate rather than waiting until departure is imminent.
D120 is useful because it shows overall how reliable are the airplanes. Poorer reliability can be fixed by improving maintenance programs. D120 are delays that usually result from a genuine mechanical problem and not about simple deferral items.
Cancellations are about maintenance but also spares availability, dispatch's ability to swap airplanes and crew, etc.
If you have never designed an airplane part before, let the real designers do the work!