Interpretation & Calculations
Process capability attempts to answer the question: can we consistently meet customer requirements? The number one limitation of the process capability index is that it is meaningless if the data is not from a controlled process. The reason is simple: process capability is a prediction, and you can only predict something that is stable. In order to estimate the process capability index, you must know the location, spread, and shape of the process distribution. These parameters are, by definition, changing in an out of control process. Therefore, only use Process Capability charts if the process is in control for an extended period.
The same argument holds for a Histogram. If the purpose of creating a histogram is to see the "shape" of the process, it will be very misleading if the process is not stable. For example, a process that is stable could very well have the same histogram as a process undergoing a trend, since the only difference in the data would be the order of the points. Since the histogram does not consider the sequence of the points, you would see no difference between histograms.
Learn more about the SPC principles and tools for process improvement in Statistical Process Control Demystified (2011, McGraw-Hill) by Paul Keller, in his online SPC Concepts short course (only $39), or his online SPC certification course ($350) or online Green Belt certification course ($499).