Al,
Your logic is right on target IMHO. Cp does not take into account the process centering. Once you look at Cpk you have to consider the process centering and the process can be out of control. The fact that the X-bars are within limits does not speak to individual x's or to the overall spread of the subgroups. I suspect, as you do, that the range chart, or sigma chart as the case may be, is not in control.
raghuraman,
With regard to CPK of 1.33, that is an arbitrary value that basically allows the process some wiggle room with in the specification limits while still being in control. As the CPK goes up the wiggle room gets greater. Keep in mind that process variation and process centering are two separate process characteristics that are conveniently measured together by Cpk. They should be understood separately from each other. Remember, the process does not know what the specifications are. The process can be statistical control and capable or not capable depending on how we arbritrarily set the specification.
Rick