# cp and cpk

Viewing 44 posts - 1 through 44 (of 44 total)
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• #27585

TLawson
Member

Is there a simple definiton for cp and cpk ?

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#67784

mcintosh
Participant

There’s a great thread on Cp and CpK here:https://www.isixsigma.com/forum/showmessage.asp?messageID=2035

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#67813

Participant

Cp is the capability of the process to delivery the requirements within the specifications.
Cp is calcuated as (USL – LSL)/6*Std.Dev.
Cp should always be greater than 2.0 for a good process which is under statistical control.
Cpk is the critical process capability something similar to the Cp but the difference is that Cpk looks at both the specification limits, USL and LSL.
Cpk is calculated as below.
Cpl = (Mean – LSL)/3*Std.dev
Cpu=(USL-Mean)/3*Std.dev
Cpk=Min(Cpl,Cpu)
For a good process under statistical control, Cpk should be greater than 1.5
Cp, Cpk defines the capability of a particular process.

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#67841

Elsa
Participant

The formulas given by the first person that reply to this message are correct. Both indexes need the specifications. The difference between them is that Cp is a “process potential index” because assumes that the process is centered between the specs or that can be centered. Cpk is a process capability index that measures the proportion of natural tolerances between the center of the process and the nearest spec.

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#67825

TLawson
Member

Thanks that is what I was looking for!!!!!!!!!!!

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#67859

Participant

cp is a one time measuring process
ex:  measuring 150 item at one time
whereby Cpk required to take measurment at specific time frame
ie.: every 1 hr

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#77175

Gus
Participant

Why would my customer specify that Ppk is required over Cpk? We have to acheive a Ppk of 1.67 or greater before they will approve a line for production. I have never used Ppk and I find that it is very difficult to get to a 1.67 value in some cases.

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#77176

Gabriel
Participant

I don’t know your specific case, but ussually is not that Ppk is required OVER Cpk, but some oranizations do not accept the result of a Cpk based on a few consecutive sample from the trial run (what usually happens in a short study for the initial submition) just because in such a short time there is no oportunity to prove stability, what is a prerequisite of Cpk. I support this possition. That’s the same reason (I think) why a Ppk of 1.66 (instead of a Cpk of 1.33) is required (it is a safety margin due the low confidence in such a study). Note that, in such a case, if you dont reach a Ppk of 1.66 you will be allowed to supply anyway, but it will be requested that you take some containment action for the potential non conforming parts while you implement the corrections to reach to a Cpk of 1.33. All that is if your process is a new one. If you have your process already working and with history recorded to show, a Cpk of 1.33 based on those records will be probably accepted. That’s at least my experience.
This topic was widely (and wildly) discussed also in the following threads:
Cp, Cpk, Pp and Ppk
Cp & Cpk against Pp & Ppk

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#95939

rich barber
Member

What does USL an LSL mean and how are they calculated or determined.

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#95956

tottow
Member

Rich,
USL and LSL are Upper Specification Limit and Lower Specification Limit.  They are not claculated.  They are determined by your customer (internal or external).
UCL and LCL on the other hand are your Upper Control Limit and Lower Control Limit on Control charts.  These are calculated Using different methods depending on the specific type of chart you use.
A good quick reference to use for these is “The Memory Jogger II” from GOAL/QPC.  You can contact them at 1-800-643-4316.

I am not now nor have I ever been associated with GOAL/QPC in any way.

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#95980

Dr. Steve W.
Participant

You can have a process with Cp > 2 but all your parts or service are out of spec.! Cp fails to recognize that your process mean has to be in the spec. in order to have a good process. Cp only tells you how good your process can potentially be and it will reach its entitlement only when your process mean is at the middle of the spec. limits. That is why we need Cpk. The difference between Cp and Cpk is not that the latter looks at both spec. limits—-Cp looks at them too —you look at the formula you provided. The difference is that Cp ignores process average but Cpk uses it as a key element of its calculation, recognizing the process average has to be within the spec. in order for the process to even have a chance to be good.

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#96073

MEH
Participant

Flatness is critical to a part my company uses. I have flatness specification of 0-.010″. I need to assess capability of the supplier providing the part within that range. How is the best way I can chart my measurement results? I will be taking 3 measurements lengthwise and two widthwise for each part.  Since I have a one sided specification, where I want the curve skewed towards the lower side, what is the appropiate way to determine capability. I could always use .005 +/- 0, but that might lead to incorrect analysis results.

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#100980

bhavin
Participant

please send  me information about cp,cpk used in statistical process control with example and control charts.

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#100982

Mike Clayton
Participant

USL and LSL are the upper and lower SPECIFICATION limits used in Cp and Cpk.  And they are the Achilles heel of this whole metric.   Often they are “American style” limits, which tend to be simply 10% of nominal.  Useless in many cases, but common.  So Cp and Cpk can be >5 for example in computerized testing, but parts can cause field failures if distribution shifts by many sigmas and are still “in spec.”  I recommend no Cpk > 3 allowed!  Guardband to that value or tighter to assure that your test system catch big shifts.  Your SPC systems can warn at 3 sigma, but are often ignored for containment.  Japan used TARGETS for inline SPC and CONTROL limits (calculated from the data, not given by engineers as economically sound guesses).  And they used Cpm which does not require SPEC limits, just target and deviations from that.

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#100983

Mike Clayton
Participant

Single sided specs that originate at ZERO are usually best handled using  Cp = Cpk by definition, then if the data looks symmetrical just use the Cpk = Mean/3 sigma of raw data….which is the distance between the Mean and Target (0) divided by 3 standard deviations.  Report Cp as the same if required, addding a footnote that Cp is really undefined for single sided limits, but for computer and  reporting purposes can be so stated.  But if the data is highly skewed, you may need to do some transformation to get more symmeterical distribution (perhaps the logx) then find sigma and mean and transform back again.  Most texts show many ways to do this.  But remember that increading the sample size may change your results greatly, especially if the extra sites measured are highly correlated.  That’s another story.

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#102242

skip
Member

Can the cpk ever be greater than the cp?

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#102243

mjones
Participant

No.
Cp assumes the process is perfectly centered — and it rarely is.
Cpk is measured to the closest spec limit.
At best, Cpk is = Cp.

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#111995

sam1tim315
Member

Cp = (USL-LSL)/6(sigma) = Design_Tolerance/Process_Capability
From the above formula, Cp ONLY tells us whether we have enough tolerance in our design to accomodate imperfection in the manufacturing process. Product design engineers control the numerator while process design engineers control the denominator. Cp DOES NOT tell us if the process is centered within the Design_Tolerance. Thus the need for Cpk which compares the average to the Target Center as shown by the formula below
Cpk = Cp * (1-k)
where k = (Target – Process Average)/[(USL-LSL)/2]
Cpk is the ACTUAL capability index. It takes into account the actual location of the process mean relative to the specification target.
Ideally k = 0, meaning process is centered at target. Thus it follows that ideally, Cpk = Cp. Now as to the question on whether Cpk can be greater than Cp, i think YES because if you look closely at the formula, k can assume a negative value if Target < Process Average – meaning the process (distribution) is shifted right from the target. I am coming from the assumption that k formula is not enclosed in absolute value operator.
Thus, if k can go negative, we can say that ideally Cpk should be slightly less or slightly more than Cp. We know that process has shifted left or right from target depending on whether Cpk is less than or greater than Cp.
Now i go back to my assumption, and ask anyone to please confirm if –
k = ABSOLUTE VALUE of (Target – Process average)/[(USL-LSL)/2] ?

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#112053

Loehr
Member

Hi Sam,
The k formula does include the absolute value operator, meaning that k is always positive or zero. Thus, Cpk will always be less than, or equal to, Cp.
Cpk = Cp ( 1 – k )
Hope this helps.

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#112057

sam1tim315
Member

Hi Ross,
Thanks a lot for your confirmation. Now i understand the other definition/formula of Cpk (i.e. the lesser of USL – Mean/ ..or  Mean – LSL/….).
sam

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#112075

Brian.P.M.
Participant

OK Lets try this again…
Cp=(USL-LSL)/6*sigma hat
Cpk=min (USL-x bar bar)/3*sigma hat OR (x bar bar-USL)/3*sigma hat
Where sigma hat is the estimated standard deviation arrived at using the formula r bar/d2, d2 being a constant based on subgroup size.
The formulas given so far have used the actual sigma in the calculations which would give Pp & Ppk
The proccess must also be in statisical control in order for these indexes to be meaningful.
Because Cp & Cpk use estemates of the standard deviation based on the average range of the subgroups, proccess with small within variation but large between variaton will show a fair index. But if the same data are put in the Pp & Ppk formulas the index will drop like a stone.
If anyone is interested, I have a small data set that shows a Cp of ~1.7 but a Pp of ~.66
It also shows the importance of being in control as the data would show out of control points if charted.
My \$0.02
Brian.P.M.

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#141653

Desmond
Participant

Cp is calcuated as (USL – LSL)/6*Std.Dev.
Cpl = (Mean – LSL)/3*Std.dev
Cpu=(USL-Mean)/3*Std.dev
Question:
What’s explanation behind the “6” used in Cp and the “3” used in Cpl/Cpu?
Appreciate someone can enlighten me on that.
Cheers and thx!
Rgrds,
Desmond.

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#141654

RP
Member

Cp looks at the entire spread of the normal curve (both sides) which is why it uses 6x.
Cpk is the comparison of the two sides of the normal curve of which it takes the smaller (i.e Cpk = smaller of Cpu or Cpl).  Cpu and Cpl are one-sided which results in the 3x.

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#141655

Hans
Participant

Difference between UCL and LCL = 6 standard deviation (total range)
Mean to LCL = 3 standard deviations, lower part of the range (Mean cuts the UCL and the LCL in half if distribution is normal)
Mean to UCL = 3 standard deviations, upper part of the range
I hope this helps.

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#141658

villageidiot
Member

In any 6S improvement you only do 2 things:  either reduce the variation of process and/or center it.  This allows you to move the distribution of your process within your specification limits (hopefully well within) and thus determines the degree to which it is capable of meeting your customers requirements.
All Cp and Cpk do is give you a basic comparison between what error is allowed by your customer (Tolerance) and what error is found in your current process (std deviation).  That’s it.   Cp tells you if it is even mathmatically possible for your process to be capable.  Cpk tells you more realistically how capable your process is by taking into account how well it is centered around your target.
At Cp = 1.0 your process is theoretically possible of being fully capable, but not practically, as your process output will shift (long term variability, 1.5 shift, etc).  Interpret the ratio accordingly.  At Cpk of 1.33 (I believe), conventional wisdom tells you that your process is repeatable, in control, and thus, predictable.  This is app. a 4 sigma level process and takes into account shifting of your process over time.
Verify this.  It has been awhile since I have used it.  Good luck.

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#141664

S. Praveen
Member

detais and graphs

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#141667

villageidiot
Member

I have no idea what that means.

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#141679

Pip
Participant
#144221

Jeff
Participant

I am using Cp and Cpk when testing production semiconductor chips.  I use Cpk when running a reliability study running 1 part 100 times.  Is Cpk still valid if I run 50 parts 1 time each?  Is that a valid distribution?  If not, what would be a correct quantity to run?
Jeff

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#146456

vishal Bhardwaj
Member

Dear Sir,
Pls. send me the detail of Cp & Cpk.
I am very thanks full to you.
Thanks & Regards
Vishal Bhardwaj

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#146457

vishal Bhardwaj
Member

Dear Sir,
Pls. send me the detail of Cp & Cpk.
I am very thanks full to you.
Thanks & Regards
Vishal Bhardwaj

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#148071

Jay Arthur
Participant

Your post describes Cp and Cpk as calculated using stdev. However Pp and Ppk are calculated with stdev, but Cp and Cpk use sigma estimator the average of the ranges over the constant d2 (Rbar/d2). For correctness, your post should read:
Calculating Cpk and PpkCp = (USL – LSL)/6*SigmaEstCpl = (Mean – LSL)/3*SigmaEstCpu = (USL-Mean)/3*SigmaEstCpk = Min(Cpl,Cpu)
Pp = (USL – LSL)/6*Std.DevPpl = (Mean – LSL)/3*Std.devPpu = (USL-Mean)/3*Std.devPpk = Min(Cpl,Cpu)
AIAG standard formulas are available at: http://www.qimacros.com/formulas.html#histogram

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#148073

Savage
Participant

Jay – no self promoting.  Thank you.

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#148075

Ward
Participant

When calculating Pp and Ppk for a process capability study, overall standard deviation is typically adjusted by the bias correction factor c4, so there will be a slight difference in the overall standard deviation calculation for the smaller sample sizes.

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#148084

The Force
Member

Cp – can it fit the spec
Cpk – does it fit the spec

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#148087

TVI
Member

Before getting wrapped around the axle on this one, consider why you are using it….I am not a big fan of this particular metric…lots of reasons…talk to someone smarter than me to determine if you even want to get into this metric….can be misleading, confusing, and just plain wrong….good luck.

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#148101

SPC
Member

Cpk < 1.0  … can still be 100% in spec !
The process MUST be stable for a process to be capable.

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#149143

Participant

Dear Sir,
hello,
how are you ?
sir first pls explain me cp/cpk value,how to use.
regards!
lokesh
mobile no:9811511103

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#153771

Sorour
Participant

It is written as:
Cpl = (Mean – LSL)/3*Std.dev
Cpu=(USL-Mean)/3*Std.dev
But shouldn’t it be
Cpl = (Mean – LSL)/(3*Std.dev)
Cpu=(USL-Mean)/(3*Std.dev)
Notice the final parenthesis.

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#153800

Sunil Agrawal
Member

Cp gives how much process variation is fitting between specification limits. For example Cp=1 indicate that 99.73 % of process variation in fitting between specification limits.
While Cpk gives closeness of process mean to mean of specification limits in addition to information given by Cp.
For example your Cp=2 and your Cpk=1.5. It indicate that your 99.999998% of variation is fitting between specification limits but your process mean is away for specification mean 1.5 time of Std. deviation.

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#154485

Prashob Jacob
Participant

Sir
I would like to know how the formulas for Cmk and Cpk has ben derived? What is the basis if the formulas and who was the one who proposed the formulas. Ths is a part of my project.
With Regards
Prashob

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#157169

Siva
Member

Cp – can be simply defined as process capability mean how much a process can deliver good results.
Cpk – is process capability indiex.

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#158636

V ASHOK KUMAR
Member

Please let me know what values should be considered for USL and LSL. My concern is whether the USL & LSL of the standard average weight should be considered or the actual average weight ‘s USL & LSL should be considered.
For Ex.
Standard WT: 700 mg. + / – 5%
USL : 735
LSL: 665

Actual Average Weight observed durng the run is 704 mg.
USL: 739.2
LSL: 668.8

PLease let me know which one is the right value

It would of great help if u cansolve my concern

V Ashok kUmar
Cipla
Patalganga

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#158637

Bhupendra Nema
Participant

Dear Mr. Ashok,
By Cp and Cpk we would always try to measure the process capabilities with respect to our specification(standard).
Thats why, always we should consider the standard specifications for the USL and LSL in Cp and Cpk calculation.
In your case standard spec is 700+5% and actual mean is 704 mg, So for Cp and Cpk calculation,
Average = 704 mg(Actual)
USL = 735 mg(standard)
LSL = 665 mg (standard)
Formule for calculation:
Cp=(USL-LSL)/(6*Standard Deviation of mesured values)
Cpk=(USL-Avg)/(3*Standard Deviation of mesured values) or
(Avg-LSL)/(3*Standard Deviation of mesured values) whatever is lower.

Regards,
Bhupendra Nema
Crompton Greaves Ltd.
Bhopal (India)

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