In the Six Sigma quality methodology, process performance is reported to the organization as a sigma level. The higher the sigma level, the better the process is performing.

Another way to report process capability and process performance is through the statistical measurements of *C*_{p}, *C*_{pk}, *P*_{p}, and *P*_{pk}. This article will present definitions, interpretations and calculations for *C*_{pk }andÂ *P*_{pk} though the use of forum quotations. Thanks to everyone below that helped contributed to this excellent reference.

**Jump To The Following Sections:**

- Definitions
- Interpreting
*C*_{p},*C*_{pk} - Interpreting
*P*_{p},*P*_{pk} - Differences Between
*C*_{pk}and*P*_{pk} - Calculating
*C*_{pk}and*P*_{pk}

**Definitions**

Â *C*_{p}= Process Capability. A simple and straightforward indicator of process capability.

Â *C*_{pk}= Process Capability Index. Adjustment ofÂ *C*_{p} for the effect of non-centered distribution.

Â *P*_{p}= Process Performance. A simple and straightforward indicator of process performance.

Â *P*_{pk}= Process Performance Index. Adjustment ofÂ *P*_{p} for the effect of non-centered distribution.

**Interpreting C_{p}, C_{pk}**

“

*C*

_{pk}is an index (a simple number) which measures how close a process is running to its specification limits, relative to the natural variability of the process. The larger the index, the less likely it is that any item will be outside the specs.”

*Neil Polhemus*

“If you hunt our shoot targets with bow, darts, or gun try this analogy. If your shots are falling in the same spot forming a good group this is a high *C*_{p}, and when the sighting is adjusted so this tight group of shots is landing on the bullseye, you now have a high *C*_{pk}.” *Tommy*

“*C*_{pk} measures how close you are to your target and how consistent you are to around your average performance. A person may be performing with minimum variation, but he can be away from his target towards one of the specification limit, which indicates lower *C*_{pk}, whereasÂ *C*_{p} will be high. On the other hand, a person may be on average exactly at the target, but the variation in performance is high (but still lower than the tolerance band (i.e., specification interval). In such case alsoÂ *C*_{pk} will be lower, butÂ *C*_{p} will be high.Â *C*_{pk} will be higher only when you r meeting the target consistently with minimum variation.” *Ajit*

“You must have aÂ *C*_{pk} of 1.33 [4 sigma] or higher to satisfy most customers.” *Joe Perito*

“Consider a car and a garage. The garage defines the specification limits; the car defines the output of the process. If the car is only a little bit smaller than the garage, you had better park it right in the middle of the garage (center of the specification) if you want to get all of the car in the garage. If the car is wider than the garage, it does not matter if you have it centered; it will not fit. If the car is a lot smaller than the garage (Six Sigma process), it doesn’t matter if you park it exactly in the middle; it will fit and you have plenty of room on either side. If you have a process that is in control and with little variation, you should be able to park the car easily within the garage and thus meet customer requirements.Â *C*_{pk} tells you the relationship between the size of the car, the size of the garage and how far away from the middle of the garage you parked the car.” *Ben*

“The value itself can be thought of as the amount the process (car) can widen before hitting the nearest spec limit (garage door edge).

*C*_{pk }=1/2 means you’ve crunched nearest the door edge (ouch!)

*C*_{pk }=1 means you’re just touching the nearest edge

*C*_{pk }=2 means your width can grow 2 times before touching

*C*_{pk }=3 means your width can grow 3 times before touching” *Larry Seibel*

**Interpreting Pp, Ppk**

“Process Performance Index basically tries to verify if the sample that you have generated from the process is capable to meet Customer CTQs (requirements). It differs from Process Capability in that Process Performance only applies to a specific batch of material. Samples from the batch may need to be quite large to be representative of the variation in the batch. Process Performance is only used when process control cannot be evaluated. An example of this is for a short pre-production run. Process Performance generally uses sample sigma in its calculation; Process capability uses the process sigma value determined from either the Moving Range, Range or Sigma control charts.” *Praneet*

**Differences Between C_{pk} and P_{pk}**

“

*C*

_{pk}is for short term,Â

*P*

_{pk}is for long term.”

*Sundeep Singh*

“*P*_{pk} produces an index number (like 1.33) for the process variation.Â *C*_{pk} references the variation to your specification limits. If you just want to know how much variation the process exhibits, aÂ *P*_{pk} measurement is fine. If you want to know how that variation will affect the ability of your process to meet customer requirements (CTQ’s), you should use *C*_{pk}.” *Michael Whaley*

“It could be argued that the use ofÂ *P*_{pk} andÂ *C*_{pk} (with sufficient sample size) are far more valid estimates of long and short term capability of processes since the 1.5 sigma shift has a shaky statistical foundation.” *Eoin*

“*C*_{pk} tells you what the process is CAPABLE of doing in future, assuming it remains in a state of statistical control.Â *P*_{pk} tells you how the process has performed in the past. You cannot use it predict the future, like with *C*_{pk}, because the process is not in a state of control. The values forÂ *C*_{pk} andÂ *P*_{pk} will converge to almost the same value when the process is in statistical control. that is because sigma and the sample standard deviation will be identical (at least as can be distinguished by an F-test). When out of control, the values will be distinctly different, perhaps by a very wide margin.” *Jim Parnella*

“*C*_{p} andÂ *C*_{pk} are for computing the index with respect to the subgrouping of your data (different shifts, machines, operators, etc.), whileÂ *P*_{p} andÂ *P*_{pk} are for the whole process (no subgrouping). For bothÂ *P*_{pk} andÂ *C*_{pk} the ‘k’ stands for ‘centralizing facteur’Â â€“ it assumes the index takes into consideration the fact that your data is maybe not centered (and hence, your index shall be smaller). It is more realistic to useÂ *P*_{p}Â andÂ *P*_{pk} thanÂ *C*_{p} orÂ *C*_{pk} as the process variation cannot be tempered with by inappropriate subgrouping. However,Â *C*_{p} andÂ *C*_{pk} can be very useful in order to know if, under the best conditions, the process is capable of fitting into the specs or not.It basically gives you the best case scenario for the existing process.” *Chantal*

“*C*_{p} should always be greater than 2.0 for a good process which is under statistical control. For a good process under statistical control,Â *C*_{pk} should be greater than 1.5.” *Ranganadha Kumar*

“As for *P*_{pk}/*C*_{pk}, they mean one or the other and you will find people confusing the definitions and you WILL find books defining them versa and vice versa. You will have to ask the definition the person is using that you are talking to.” *Joe Perito*

“I just finished up a meeting with a vendor and we had a nice discussion ofÂ *C*_{pk} vs. *P*_{pk}. We had the definitions exactly reversed between us. The outcome was to standardize on definitions and move forward from there. My suggestion to others is that each company have a procedure or document (we do not), which has the definitions ofÂ *C*_{pk} andÂ *P*_{pk} in it. This provides everyone a standard to refer to for WHEN we forget or get confused.” *John Adamo*

“The Six Sigma community standardized on definitions of *C*_{p}, *C*_{pk}, *P*_{p}, andÂ *P*_{pk} from AIAG SPC manual page 80. You can get the manual for about $7.” *Gary*

**CalculatingÂ C_{pk} and P_{pk}**

“

*P*

_{p}= (USL – LSL)/6*Std.dev

*C*

_{pl}= (Mean – LSL)/3*Std.dev

*C*

_{pu}= (USL – Mean)/3*Std.dev

Â

*C*

_{pk}= Min (

*C*

_{pl},

*C*

_{pu})”

*Ranganadha Kumar*

“*C*_{pk} is calculated using an estimate of the standard deviation calculated using R-bar/d2.Â *P*_{pk} uses the usual form of the standard deviation ie the root of the variance or the square root of the sum of squares divided by *n – 1*. The R-bar/D2 estimation of the standard deviation has a smoothing effect and theÂ *C*_{pk} statistic is less sensitive to points which are further away from the mean than is *P*_{pk}.” *Eoin*

“*C*_{pk} is calculated using RBar/d2 or SBar/c4 for Sigma in the denominator of you equation. This calculation for Sigma REQUIRES the process to be in a state of statistical control. If not in control, your calculation of Sigma (and hence Cpk) is uselessÂ â€“ it is only valid when in-control.” *Jim Parnella*

“You can have a ‘good’Â *C*_{pk} yet still have data outside the specification, and the process needs to be in control before evaluating *C*_{pk}.” *Matt*