In what cases are the roughness values Rt and Ra used?

The average roughness, Ra, effectively gives a smoothed value of roughness. The best indication of roughness is the distance between the peaks and the troughs, Rt.

If one item has peaks at 6 and troughs at 4, the average value is 5, but range of roughness is 2.

If another item has peaks at 9 and troughs at 1, the average value is again 5, but range is 8. The second item is rougher.

Theoretically talking, the peak to peak value let us to estimate the worst case scenarios. Here is an example, A shaft fixed inside a conical coupling.

How we make sure if the coupling can transmit the required torque? We need to calculate it using this pk-pk value. I'm not going further into details.

In production serie of a specific component , people are less interested about how much really this peak to peak value is, but rather they are interested in the average. This average is not sensitive to strong deviations, and is an indicator of your machining tools health and lifetime. Strong deviations in average value means worn cutters ... .

But that's not all, sometimes the average value plays very important rule in theoretical calculations as wel, for instance designing the thrust bearing requires always the average value, and the peak to peak value here dose't make sense.