Process Capability (Cp, Cpk) and Process Performance (Pp, Ppk) – What is the Difference?

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 Cp, Cpk, Pp, and Ppk. This article will present definitions, interpretations and calculations for Cpk and Ppk though the use of forum quotations. Thanks to everyone below that helped contributed to this excellent reference.

Jump To The Following Sections:

 Cp= Process Capability. A simple and straightforward indicator of process capability.
 Cpk= Process Capability Index. Adjustment of Cp for the effect of non-centered distribution.
 Pp= Process Performance. A simple and straightforward indicator of process performance.
 Ppk= Process Performance Index. Adjustment of Pp for the effect of non-centered distribution.

Interpreting Cp, Cpk
Cpk 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 Cp, and when the sighting is adjusted so this tight group of shots is landing on the bullseye, you now have a high Cpk.” Tommy

Cpk 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 Cpk, whereas Cp 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 also Cpk will be lower, but Cp will be high. Cpk will be higher only when you r meeting the target consistently with minimum variation.” Ajit

“You must have a Cpk 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 requirementsCpk 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).
Cpk =1/2 means you’ve crunched nearest the door edge (ouch!)
Cpk =1 means you’re just touching the nearest edge
Cpk =2 means your width can grow 2 times before touching
Cpk =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 Cpk and Ppk
Cpk is for short term, Ppk is for long term.” Sundeep Singh

Ppk produces an index number (like 1.33) for the process variation. Cpk references the variation to your specification limits. If you just want to know how much variation the process exhibits, a Ppk 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 Cpk.” Michael Whaley

“It could be argued that the use of Ppk and Cpk (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

Cpk tells you what the process is CAPABLE of doing in future, assuming it remains in a state of statistical control. Ppk tells you how the process has performed in the past. You cannot use it predict the future, like with Cpk, because the process is not in a state of control. The values for Cpk and Ppk 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

Cp and Cpk are for computing the index with respect to the subgrouping of your data (different shifts, machines, operators, etc.), while Pp and Ppk are for the whole process (no subgrouping). For both Ppk and Cpk the ‘k’ stands for ‘centralizing facteur’ – 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 use Pp and Ppk than Cp or Cpk as the process variation cannot be tempered with by inappropriate subgrouping. However, Cp and Cpk 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

Cp should always be greater than 2.0 for a good process which is under statistical control. For a good process under statistical control, Cpk should be greater than 1.5.” Ranganadha Kumar

“As for Ppk/Cpk, 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 of Cpk vs. Ppk. 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 of Cpk and Ppk 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 Cp, Cpk, Pp, and Ppk from AIAG SPC manual page 80. You can get the manual for about $7.” Gary

Calculating Cpk and Ppk
Pp = (USL – LSL)/6*
Cpl = (Mean – LSL)/3*
Cpu = (USL – Mean)/3*
 Cpk= Min (Cpl, Cpu)” Ranganadha Kumar

Cpk is calculated using an estimate of the standard deviation calculated using R-bar/d2. Ppk 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 the Cpkstatistic is less sensitive to points which are further away from the mean than is Ppk.” Eoin

Cpk 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 useless – it is only valid when in-control.” Jim Parnella

“You can have a ‘good’ Cpk yet still have data outside the specification, and the process needs to be in control before evaluating Cpk.” Matt

Comments 79

  1. Walt Crompton

    Excellent summary!

  2. tool maker

    Very useful article on CP And CPK.
    Have better understanding after reading this article, Thanks.

  3. Allan117

    Very Useful Article.. It helps me a lot in understanding the meaning and concept of Process Capability…Now I can start explaining this to all..Thanks a lot

  4. Victor

    I asked the below question of a software provider hoping he could explain why his software was giving me a Cpk greater then 1.0 while having points out of spec? Can any one out there help me better understand ?

    “…I still do not understand how Cpk can be greater than one with a point out of spec. your template must be wrong. There is no way that you can have a CPK (not CP) greater than one with point (s) out of spec???????

    His reply: “Your question is incorrect”

    “Cp and Cpk do not take into account where the process mean is located relative to the specifications. It simply measures the spread.”
    Montgomery Intro to SPC 4th.

    Cp and Cpk answer the question “should it fit”, not “does it fit.”

  5. Ben


    Technically, your software provider is right (although not very helpful). The Cp & Cpk calculation is based on the process mean & range and has nothing to do with how many points are in or out of spec. In actual practice, this shouldn’t happen very often. The Cpk is an indicator of how centered your process is (use Cp and Cpk together to evaluate this).

    The Cpk calculation assumes that the data is normally distributed. From the sounds of it, your data may not be. A skewed distribution would throw off the range. If you haven’t checked for normality, I’d start there.

  6. victor

    i have a big doubt, in calculation of cpk does it matter if the process acts like no-normal process or normal process, wich curve should i take weibull, longest side, etc then if my process is unilateral how do i need to calculate the procees performance???

  7. LitSong

    very good explaination..


    the information given is very useful

  9. B. C. Biswal

    very good explanation

  10. Ashish


  11. anuragkhari

    What is difference between Standard Deviation and Estimate Standard Deviation. Why Estimate Standard Deviationcalculated in SPC.?

  12. jasonw

    how can you calculate Pp or Ppk when your standard deviation is 0?

    You typically wouldn’t calculate Pp or Ppk when st. dev. is 0. Pp/Ppk would be infinitely large. Either your process is so good, any actual variation is small as compared to the specification or your inspection/measurment method is invalid. Ensure measurement system analysis rules are followed.

  13. jasonw

    What is difference between Standard Deviation and Estimate Standard Deviation. Why Estimate Standard Deviationcalculated in SPC.?

    I think this answers your question:
    Standard Deviation = Population and Estimate Standard Deviation = Sample

    Estimate St Dev is used in SPC because that’s what you are calculating for, a sample of the actual population.

  14. bharat100

    Hello all,

    I am new to this forum. I have some question regarding capability metrices.

    USL – 1.35
    LSL – 1.11

    Observation Results – 1.15, 1.15, 1.16, 1.15, 1.15, 1.16, 1.15, 1.15, 1.16

    Mean – 1.1533
    Std Dev – 0.005

    Cp = (1.35 – 1.11/ 6 * 0.005)
    = 8

    CpK = Min (1.35 – 1.1533/ 3 * 0.005, 1.1533 – 1.11/ 3 * 0.005)
    = Min (13.11, 2.88)
    CpK = 2.88

    After reading materials for capability index, it was clear that value above 2 for Cp and CpK is great. Process has achieved 6 sigma capability.

    But as we see my results are towards Lower Specification Limit. All are skewed to left of the plot.

    Does still my process is known as 6 sigma capable?
    My calculation is wrong?

    Please clarify.


  15. Khaja Mohinuddin

    I have a process for Incident Management ,Which handles different Customers and different Customers has different SLA like 240Mins .300Mins,480Mins ,720Mins etc…..
    Can anyone please help me in calculating the Cp and Cpk of this Process.
    USL=? i am confused what is the USL bcoz it has different SLA’s.
    Plese help me in resolving this its urgent……..

  16. ano


    think ur sd calculation is wrong.

  17. bharat100


    SD calculation is right.

    I did it in Excel (0.005) as well as using math formula (0.0047).


  18. ano


    0.005 is variance. SD is square root of variance=0.070711
    and cpk =min(0.92,0.204) = 0.204

  19. bharat100


    Sorry for late response.

    There is some confusion…

    Let me show my calculation for standard deviation. I know Std.Deviation is Sq Rt of Variance.

    Observation Results – 1.15, 1.15, 1.16, 1.15, 1.15, 1.16, 1.15, 1.15, 1.16

    Mean – 1.1533

    Std Dev = Sq.Rt [ (1.15 – 1.1533)^2 + (1.15 – 1.1533)^2 + (1.16 – 1.1533)^2 + (1.15 – 1.1533)^2 + (1.15 – 1.1533)^2 + (1.16 – 1.1533)^2 + (1.15 – 1.1533)^2 + (1.15 – 1.1533)^2 + (1.16 – 1.1533)^2/ 9]

    6 observations of 1.15 and 3 observations of 1.16

    (1.15 – 1.1533)^2 = 0.00001089 X 6 = 0.00006534
    (1.16 – 1.1533)^2 = 0.00004489 X 3 = 0.00013467
    Total = 0.0002000.1/9
    = 0.0000222
    Std Deviation = Sq rt (0.0000222)
    Std Deviation = 0.0047

  20. Andy


    I agree, I think your calculations are correct

    I think the problem is your small sample size.

    If i do a minitab calculation of

    Power and Sample Size

    Test for Two Standard Deviations

    Testing (StDev 1 / StDev 2) = 1 (versus not =)
    Calculating power for (StDev 1 / StDev 2) = ratio
    Alpha = 0.1
    Method: Levene’s Test

    Size Power Ratio
    9 0.9 4.55704
    9 0.9 0.21944

    The sample size is for each group.

    This means that with only 9 samples, your 90% confidence limit for your standard deviation is a ratio between
    0.2 and 4.5

    I.E your actual standard deviation could be between
    0.001 and 0.0225

    worst case (0.0225), your CP values come out at
    Min(2.91, 0.64)

    If it was my process, I would take more samples
    Size Power Ratio
    50 0.9 1.59061
    50 0.9 0.62869

    I would also try to increase the precision of your measurements, as you could expect the difference between 1.15 and 1.16 to be measurement error….

    So in short, the issue probably lies in your SD figure, not in your calculations but your method.

  21. A S. Kaplan

    The analogy we used at Motorola in the mid-eighties when Six Sigma was devloped:
    Imagine we are the road crew painting a series of white stipes that form dotted lines down the center of the highway.
    With just a sampling of as little as three stripes, CP calculates the consistency of one stripe to another, meaning – “How exactly alike are they?”
    And CPK measures how centered we are making the sequence of stripes that constitutes our dotted line – “Is it exactly up the center?” In the manufacturing business this would mean “How centered is each piece between its + and – tolerances.
    CP – The more the slight variations, meaning the looser our process control becomes (people fatigue in the hot sun, or because the machine occasionally sputters and splatters) the more likely the stripe will soon become unacceptably long, short, or wide, thereby creating a statistical number of rejects per thousand, or per million, etc. And…
    CPK – The less centered we are, (as our vision starts to blur, or the truck wobbles to one side) the sooner we can expect to reduce the lane size so that it is too small for cars to fit, or maybe we will even run off the road!
    Hope this helps explain it to non-QA’ers.

  22. Ankur

    Really good description of Cpk & Ppk

  23. Scott

    I highly recommend all of you to quit using software. You need to understand the fundementals of this to even being to know what any answer means. All mathematical calculations should be performed by hand only using a calculator. By doing this you will understand what the answer means.

  24. Suresh Rawal

    Very useful informations.
    Thanks and regards.
    Suresh Rawal

  25. Sam Mathews

    Very apt articulation of the subject matter – the concept has been explained quite lucidly. Thanks a ton

  26. B.P.Sharma

    good conclusion to understand cp/cpk fundamental.

  27. Periwan

    To sum it up…
    There are NO definitions for Cp, Cpk, Pp and Ppk stated that is valid everywhere and accepted by all.
    What is NORMAL definitions in Automotive Industry is whats in AIAG handbooks.
    Short version of this is

    Pp = (USL – LSL)/6*
    Cp = (USL – LSL)/6*

    Ppl/Cpl = (Mean – LSL)/3*
    Ppu/Cpu = (USL – Mean)/3*
    Ppk/Cpk= Min (Cpl, Cpu)

    Difference between Cp and Pp indexes are HOW TO CALCULATE THE SIGMA.

    Sub groups over time = Cp indexes / All data available = Pp

    Special case for Cp; NO sub groups (individual data points/sub group size equal to “1”) BUT not “long term” evaluation. In this case You use table approximations of the estimations of SIGMA.

    Then it is up to You to define what is long term, short term and if to use subgroups or individual data points.
    Criterias for these descisions are time, destructive/non-destructive testing for the data, price of parts etc.

    So if You collect data one Monday morning, say one sample every 15 min for 4 hours You will get 13 samples.

    If the parts are expensive You might just collect one measurement in the case of destructive testing or just one since the measuring is time/cost consuming. In this case You will get an estimate of the SIGMA within the “sub group” by assuming process in control and stable and using table values (this is done automatically by most software such as MINITAB with sample size set to 1). The OVERALL Sigma is calculated as any normal SD.

    If You have sampled say 5 data point each time then You can calculate a WITIN subgroup Sigma (datapoint vs sub group mean for each sub group).

    So now we have an estimated WITHIN subgroup SIGMA and an OVERALL SIGMA.

    Sigma within (based on table values or sub group calculations) is used for Cp and Cpk calculations.
    Sigma overall is used for the Pp and Ppk calculations.

    The same goes for if You would have collected the data for a whole week, say one sample on Monday one on Tuesday and so on. Same calculations but different analysis.

    So, what is “long term” and what is “short term” has to be defined.

    And logically the meaning of the four different capability indexes are;
    Ppk is what the customer sees.
    Pp is what Ppk would have been if the process were centered.
    Cpk is what the Ppk will be if the process is stable (no change between subgroups mean).
    Cp is what Ppk will be if the process is stable AND centered.

  28. Peter

    Sorry to tell, but definition of Cpk and Ppk is wrong, it´s just the other way round:
    Ppk is a short term analysis (mostly done with 50 or 100 samples measured)
    Ppk is Process Potential Capability
    Cpk is long term analysis and is Continous Process capability

    i.g. Automotive Industrie requires a Ppk better than 1,67 and Cpk better than 1,33
    or Ppk better than 2,0 and Cpk better than 1,67 (f.e. daimlerfor safety criterias)


    its good and easy to understand.

  30. Jaydip Kanzariya

    Very good summary


    Very good summary

  32. Raju Pramanick

    Very Useful Article.It helps me a lot in understanding the meaning and concept of Process Capability.Thanks a lot

  33. Santosh.k. Rawariya

    Very Useful Article.It helps me a lot in understanding the meaning and concept of Process Capability.Thanks a lot

  34. engr.aimes

    explanations are good.. thanks :)

  35. Ramesh

    In six sigma, histogram indicates specification limits are kept 6 standard deviations of both side. But normally distribution of process with in 3-sigma level. Please explain this doubt.

  36. gangaram

    Good artical. It was really useful info. I got good understanding on cp &cpk

  37. Cuong

    Thank for your sharing and explain about Cp and Cpk. it really heplful for me and everybody.

  38. John

    Great explanation. Thanks

  39. Desiree Rice

    Was really happy to come across this article while doing a bit of research. Well done! I especially like the variety of quoted interpretations.

  40. Nagaraj.D

    Simply and excellent explanation of process measuring methodology. It explains clearly each and every stage. Good.

  41. Júlio Magno

    Congratulations for this content! I’m a production engineer for Vale (world’s biggest ire ore minning company) and the text below really helped me to define some instructions that will compose a tranning wich will be minitrated to thounsands of people! You just can’t imagina how you helped me! Thank you a lot!

  42. shantilal parmar

    it is very good explanation. Useful

  43. reddy

    very good explanation

  44. Raghuram Singh

    It is very good and has very clear/simple explanation.

  45. Kedar Sahebrao

    It is good practice as an employ need to update & check process stability on portal through this media. Thanks for it .

  46. Rohit

    How can I used of CP as placed CPK?

  47. ENSiTE

    Is it possible for Cp = Cpk ?

  48. I want example of non normal capbility analysis.

    If non normal capability analysis is there & only one limit is there then cpk value will come . But I want one example with distribution .

  49. Nancy Hall

    I have to measure 3 runs (30 samples / each run) for the validation . Do the cpk of 3 runs must have the same value?
    If I have cpk of run 1 = 1.00 / cp = 33.72 / pp = 35.67
    run 2 = 0.45 / cp = 24.23 / pp = 26.95
    run 3 = 0.07 / cp = 20.84 / pp = 18.16
    What’s that mean?
    Are they acceptable?
    What I have to do to correct if that is not acceptable?

    Please advice

    Best Regards,

    Nancy Hall

  50. Bala

    Very nice useful information.

  51. Ravi Kant Kumar

    How should I get the value of D2 in calculation of sigma.

  52. Cesar Vasquez

    Another way to see the difference is Cp and Cpk use the within group variation and Pp and Ppk use total observed variation in their calculations.
    To refresh the concept: Total variance = Within group variance + Between group variance

  53. Kuldeep

    Very usefull article now i understand my confident

  54. Tracye

    Thank you for this summary.

  55. Sandhya

    Excellent explaination

  56. Hai

    Cpk should not be over 2 value.
    If it is over 2 , have to check n review again the specification vs actual results


  57. Layce

    I am wondering what sest stands for or how it is figured in a CPK study.

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