The number one limitation of process capability indices is that they are 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 process capability, 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 indices 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.
Upon further investigation, however, it is apparent from the control chart of this process data (shown below) that the process is not in statistical control. Thus, while we can assert the sample data is Normally distributed, we can make no assertions about the more general (and relevant) process behavior, including its Process Capability index.
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