Process capability (Cp, Cpk, Pp, Ppk) deceptions and resolution

It has been said that Cpk can be used to short term capability and Ppk used to long term performances. However, is there more to the story?

Process capability indices, Cpk and Cp, are a function of how the data are collected and can be very deceiving.  For example, if data are collected using an x-bar and R chart, standard deviation for these process capability indices is determined from within subgroup variability.  However, if an individuals chart is used, standard deviation for these process capability indices is determined from between the “individual-value subgroupings”.  The implication of this is that Cpk and Cp are a function of how the data are sampled, which is not a good thing.

Ppk and Pp, process performance indices, are better form of reporting relative to getting a more consistent answer; however, their interpretation can be confusing.  Because of this, I prefer to report the expected percentage non-conformance rather than a process capability or performance index using a probability plot, which can easily handle non-normal situations as well as normally distributed data.

Also, it is important that the process is in control (or stable) before the calculations are made.  But then the question becomes how do we determine if the process is in control or not?  If an x-bar and R chart is used a process may be considered out of control; however, if an individuals control chart is used for the same situation it might not be considered out of control.  Why is this?

The x-bar and R chart can be deceiving because variability between subgroups is not a part of the calculation of the upper and lower control limits for an x-bar and R chart.   To illustrate the implication of this, consider that daily a new batch of raw material is received and these batches do affect the response of the process, but not necessarily an out of spec condition.  In my classes and lectures, I ask the question whether this raw-batch input should be considered a source of common-cause variability or special.  Invariability the consensus is that this input should be considered a common-cause input variability source.  Because of this desire, an individuals control chart should be used to assess process stability/control, as opposed to an x-bar and R chart.

Once the data are shown via an individuals control chart to be stable then process performance can be reported using a probability plot with the inclusion of the calculation of a best estimate for the percent non-conformance.  Note how this is a report-out in terms that everyone can easily understand, as opposed to Pp, Ppk, Cp, and Cpk.

A published article that describes the about 30,000-foot-level metric reporting and the advantages of individuals control charts over x-bar and R charts can be obtained through the link, Issues with x-bar and R charts and an alternative .

If the percent non-conformance is larger than desired, this metric improvement needs “pulls” for the creation of an improvement project.  Success of the project is demonstrated when the individuals control chart shifts to a new-improved level of performance.