Which one of these processes would have the least amount of measurements go out of spec if the process mean shifted towards the upper spec limit?

The process with the least amount of measurements going out of spec when the process mean shifts towards the upper spec limit is the one characterized by a narrower specification range and a more favorable distribution of process data. In the context of this question, a process that originally has a mean closer to the center of its specification limits may exhibit fewer out-of-spec measurements if the mean shifts upward compared to a process that has a wider distribution or is already closer to the limits.

In this case, choosing Process C suggests that it is strategically positioned such that it can accommodate shifts in the mean without quickly exceeding the upper specification limit. This would indicate that Process C has a more controlled variability or tighter standard deviation in relation to its specifications, allowing it to operate effectively even with shifts.

Processes with less favorable distributions might already be at risk of exceeding their limits under normal operations, making them more vulnerable to further shifts. Thus, the configuration of Process C—likely benefiting from a well-centered mean and constrained variability—contributes to fewer instances of out-of-spec measurements when faced with a mean shift. This aligns with the principles of process capability and control in quality management practices.