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Process capability attempts to answer the question: can we consistently meet customer requirements? 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.

For example, the data shown in the Histogram below would appear to come from a process whose behavior may be characterized by the Normal distribution. This is further indicated by both the K-S Goodness of Fit value =0.5 (shown beneath the Histogram in the stats display) and the Normal Probability Plot shown below at right.

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.

If this data represented a 100% sampling of a particular batch from the process, then we could assert with reasonable comfort that the process output for this period in time was normally distributed. We could also calculate relevant Process Performance indices for the batch. If the data was not a complete (100%) sample from the batch, assertions about the batch properties are limited to our comfort that the sample was representative of the batch. This is difficult to estimate if the process is not in control. We can make no reasonable assertions, including Process Performance, about the remainder of the batch if the process that generated the batch is not in statistical control. If it occurs to you that this seems to contradict prevalent industry behavior, you are right!! It is too common that statistical inference tests for means, variances or proportions ignore the basic assumptions of Normality and independence.