Hello all;
I have a problem with SPC manual. In the first edition (chapter 2, section 5, page 86) and under the title of "applications of process measures" the manual says:
"…particularly for unstable processes, it might be helpful to also graph or plot inherent process variation versus total process variation to gain an appreciation for a rough perception of the gap between the process "capability" and "performance" and to track improvement. Generally, the size of this gap is a measure of the degree to which the process is out of control."
My questions are:

1-Suppose that we calculated Cpk and Ppk for an unstable process and Cpk>Ppk. What should I learn from the gap between Cpk and Ppk?

2-For an unstable process, is it possible that Cpk>Ppk?

Thanks all.

My interpretation of the passage is that in an out-of-control process, Cpk/Ppk should only be used for noting general improvement, not to perform the improvement process. (As a rule, these indicators are for in-control processes.) The passage tells us we shouldn't rely on them, but to "also graph or plot inherent process variation versus total process variation" which means use individual charts to do the improvements with, because Cpk is the "total" process indicator. Does that help?

If my understanding is right,

CpK should be calculated ONLY when the process appears the process is stable, while

PpK is calculated ONLY for chronically unstable processes with predictable special variation

Therefore, for stable processes, you can not apply PpK

I guess it is fair warning to be careful how you identify if a process is unstable. More often than not, it seems, you need to understand your total variation equation before jumping to conclusions. :cool:

A bit more explanation here:

Cpk is the capability of the process without subgroup to subgroup variation. It is calculated using the within subgroup variation. It is always* greater than Ppk.
Ppk is the capability of the process including all sources of variation. It is calculated using the total standard deviation of all of the data points. Even a homogenous, Normal distribution that is randomply samples with replacement will have some subgroup to subgroup variation due to natural sampling 'error' or variation. In this case Ppk will be slightly smaller than Cpk
*If you have 'chunky' data - very little resolution, only 3-4 possible values in your data range - AND you use the Range method to calculate the within subgroup variation, you may over calculate the within subgroup standard deviation and thus you will have a Cpk that is mathematically greater than your Ppk value. This is a formula selection error, not a true difference in the capability.


The presence of an assignable cause does not mean the process is unstable or out of control - either in a statistical sense or in a practical sense. When an assignable cause is systemic (you see it in the data and know exaclty what causes it and it recurs or occurs on a regular and predictable basis) your process is essentially stable and predictable. examples of systemic causes are: tool wear, machine to machine differences, vendor lot to vendor lot differences, etc. These differences can be seen as trends or shifts.

IF these differences are acceptable - all data are sufficiently within spec - then there may be no need to 'eliminate' the assignable causes. we only need to deal with them in our control plans and SPC chart selection / rational subgrouping schemes.

Plot your data using a multi vari format. (NOT multi variable. Multi Vari was first proposed by Leonard Seder. Google it, you'll find some articles) You will see your largest components of variation. If your process is not capable (outside of the calculation of the indexes, they are too easy to get wrong mathematically) look to inprove the largest component of variation first...

Thanks all.
Dear Bev D, here are other two questions arised from your explanation.
1- Suppose that there is a stable process. In principle, Cpk and Ppk should be equal. Now an assignable cause comes into the process and makes the spread tighter. What will be the relation between Cpk and Ppk for this new process?
2- How can I calculate process capability in the presence of systematic assignable cause such as tool wear?:)

Thanks all.
Dear Bev D, here are other two questions arised from your explanation.
1- Suppose that there is a stable process. In principle, Cpk and Ppk should be equal. Now an assignable cause comes into the process and makes the spread tighter. What will be the relation between Cpk and Ppk for this new process?
2- How can I calculate process capability in the presence of systematic assignable cause such as tool wear?:)

As far as Issue 2: If you have a precision machining process, which means the fundamental variation is tool wear, I recommend reading Statistical process control for precision machining (http://elsmar.com/Forums/blog.php?b=79) . You should have a non-normal distribution which Cpk and Ppk do not apply. If you do have a normal distribution, then you are likely out of control. But, the above link also explains how you must control the process to get it to the correct continuous uniform distribution, and the correct calculation for capability at that point. :cool:

Thanks all.
Dear Bev D, here are other two questions arised from your explanation.
1- Suppose that there is a stable process. In principle, Cpk and Ppk should be equal. Now an assignable cause comes into the process and makes the spread tighter. What will be the relation between Cpk and Ppk for this new process?
2- How can I calculate process capability in the presence of systematic assignable cause such as tool wear?:)

Let me answer your questions in reverse order:

2. How you do the calculation depends on why you or you Customer wants to do with the process capability. There are three basic purposes:

To truly understand your process capability; what are the largest components of variation, within piece, piece to piece, cavity to cavity, vendor lot to lot, set up to set up, time to time, etc. This helps us improve the variation, determine how to apply statistical process control and/or mistake proofing devices, how to establish inspection lots among other control and improvement activities.
To understand the yield of the process (the classical method of translating the Ppk index to a ppm or %yield value). This enables us to know how many parts to start in order to get the required number yielded to make our delivery commitments. It also enables us to make informed decisions when prioritizing our improvement activities.
To understand the process spread vs. the tolerances. When tolerances have not been well engineered, it can be advantageous to not allow the process to consume the entire tolerance to ensure better reliability – this is particularly true when dealing with sub components that must fit together, avoiding tolerance stack-up problems or wear due to poor fits, etc. Additionally some believe – erroneously – that if the process spread is less than the tolerances there is a ‘buffer’ that allows some process movement before you manufacture out of tolerance parts.


If you are performing a capability study for the first reason – good for you! In this case, you don’t need to calculate a capability index at all. They are only a summarized index that enables your customer or someone else in your organization to quickly look at the number and check a box. They have very little value add. You should determine your Yields of course but this is a simple ratio. This value should be tracked and charted on a control chart over time – in addition to other critical parameters of the process - and used to monitor the performance of your process.

If you are performing the study for the second reason and you need to report a capability index to someone, you can perform a simple ‘reverse calculation’ by determining the Z score from the yield ratio: in Excel, normsinv(yield). The Ppk score is Z/3. The Cpk value for shifting systemic causes is calculated in the traditional way as it is just the within subgroup variation without the systemic variation. If you have a systemic cause that trends such as tool wear Cpk is more difficult to calculate as it has no practical meaning that is different from Ppk. They are essentially the same index.

If you are performing the study for the third reason, you can simply calculate the indexes using the actual physical range of the process instead of the standard deviation.

Most standards and Customer requirements allow for alternate calculations if you don’t have a Normal distribution…

Please note that I am notorious for my dislike of Ppk/Cpk. I believe that to reduce our knowledge of a process’s variation to a single number is absurd. It is diametrically opposed to the study of variation, SPC and Process improvements. They are not statistically sound and enable organizations to avoid the hard work of real and practical process analysis. I do not use them, my organization does not use them and our suppliers are not required to report them.

1. I’m not sure what your question is? I am not sure what you mean by making the spread tighter? Which spread?

Let me address your first statement: In theory, Cpk and Ppk are equal for a stable process that is composed of independently and homogenously distributed results. However: “In theory, there is no difference between theory and practice. But, in practice, there is.” (Jan L.A. van de Snepscheut)

As I said before, even a perfect Normal distribution composed of independent data that is homogenously distributed and randomly sampled will have sampling error. Sampling ‘error’ is the standard deviation of the sample averages. It always exists if you are sampling: SDaverages = SDtotal/sqrt(n). Since Cpk is the capability index calculated using ONLY the within subgroup standard deviation (it excludes the between subgroup variation) it will ALWAYS be larger than Ppk which includes both within and between subgroup variation. They may be close enough to not matter much but they will be: Cpk > Ppk.

When we add in real life processes which are never homogenously distributed*, rarely completely independent and often have some level of shifting and drifting, the difference between Ppk and Cpk will ensure that they are never the same.

*Unless we create the homogeneity by true random samples or by physically mixing the parts together like shuffling a deck of cards.