Key Points

• Short-term standard deviation is best used for Cp and Cpk.
• When calculating Pp and Ppk, the long-term standard deviation is your best choice.
• These measurements are commonly confused, even by skilled practitioners.

One must necessarily understand that the short-term standard deviation reports on the “instantaneous reproducibility” of a process whereas the long-term standard deviation reflects the “sustainable reproducibility.” 

To this end, the short-term standard deviation is comprised of the “within group” sums of squares (SSW).  The long-term standard deviation incorporates the “total” sums-of-squares (SST).  Of course, the difference between the two constitutes the “between group” sums-of-squares (SSB).

Breaking It Down

By employing a rational sampling strategy it is possible to effectively block the noises due to assignable causes from those due to random causes.  In this context, we recognize that SST = SSW + SSB.  By considering the degrees of freedom associated with SST and SSW, we can compute the corresponding variances and then establish the respective standard deviations. 

In the case of a process characterization study, we note that the short-term standard deviation is given by the quantity Sqrt(SSW / g(n – 1)).  The long-term standard deviation is defined as Sqrt(SST / ng– 1).

When computing Cp and Cpk, it is necessary to employ the short-term standard deviation.  This ensures that the given index of capability reports on the instantaneous reproducibility of the process under investigation. 

To reflect the sustainable reproducibility of the process, the long-term standard deviation must be employed to compute Pp and Ppk.  Oddly enough, many practitioners confuse these two overlapping sets of performance indices.

Further Reading

For more information on this topic, reference Harry, M. J. “The Vision of Six Sigma: A Roadmap for Breakthrough” located at http://www.tristarvisual.com/sixsigma2/index.mgi2.  Also see Harry, M.J. and Lawson, R.J. (1988). Six Sigma Producibility Analysis and Process Characterization. Publication Number 6s-3-03/88. Motorola University Press, Motorola Inc., Schaumburg Illinois.

Using the Right Tool for the Job

The purpose of today’s article isn’t so much to serve as a comprehensive look at things. Instead, it is a means of analyzing common issues and picking the right tool. You don’t cut a board with a hammer after all. As such, learning the right calculations to use for your indices is going to go a long way in yielding relevant data.

Other Useful Tools and Concepts

Looking for some other ways to bolster your business? You might do well to look at implementing the likes of trend analysis tools in your workflow. This is a great way of looking into future events.

Further, you might want to take a closer look at the 7 QC tools. If you’re hitting snags in your production, then these tools can help you get down to what matters most.

More Food for Thought

As an additional post to your question, let us consider how the shift factor figures into the larger scheme of things.  Generally speaking, the shift factor is added to an estimate of long-term capability to remove long-term influences, thereby providing an approximation of the short-term capability.  Conversely, the shift factor is subtracted from an estimate of the short-term capability to inject long-term influences, thereby providing an approximation of the long-term capability. 

For example, if the long-term capability of a process was known to be 4.5s, and we seek to approximate the short-term capability, then 1.5s would be added to 4.5s, therein providing the short-term estimate of 6.0s.  Conversely, if the short-term capability was known to be 6.0s, and we seek to approximate the long-term capability, then 1.5s must be subtracted from 6.0s, therein providing the long-term estimate of 4.5s.