# Why do we need to calculate Cp and Cpk

Six Sigma – iSixSigma Forums Old Forums General Why do we need to calculate Cp and Cpk

Viewing 34 posts - 1 through 34 (of 34 total)
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• #39080

Alok Vyas
Participant

Hi ,
I am new to Six Sigma Concepts. I have 2 questions
1) Why do we calculate Cp and Cpk when we are anyways calculating Process Sigma ?
2) Can we deduce Process Sigma value from Cp?
Can any one guide me on this . Thanks in advance.
Alok

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#118077

Whitehurst
Participant

The answer to the first question Cp gives the actual process capability is your process is centered and Cpk or Ppk calculates the process capability using the short term and long term process capabilty the general rule to get the z value from from Cp or Cpk is 3 * Cpk and for Ppk the Zst is = (3 * Ppk )+ 1.5

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#118078

Alok
Participant

Hi Joe,
Thanks for the quick response. if Cp gives me the process capability then why do i calculate Process Sigma in the first place. will appreciate if you can give some insight on this.
Alok

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#118082

Whitehurst
Participant

Cp gives the process capability but it doesnot give u the Zst or Zlt value it gives u the USL-LSL / 6 sigma value Cpk and Ppk gives the value consdering the one sided specification thats the reason the formulae is USL – mean / 3 sigma Cpk uses the short term calculation and Ppk uses the long term calulation and thats the reason we add 1.5 to 3Ppk to get the Zst value.
Hope this helps !  Dont worry too much about Cpk and Ppk or Cp just remember Zst = 3 Cpk or 3Ppk + 1.5 .

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#118086

Mikel
Member

Wrong. Who teaches this?

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#118087

Mikel
Member

Why do we calculate process sigma when the world speaks Cp / Cpk?
Process sigma = 3 * Cp

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#118088

Whitehurst
Participant

Well Stan All the GE materials says that

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#118089

Mikel
Member

Thats quite a statement Joe – you know what ALL of the GE materials say? Go read the original material from Motorola if you want the right answer.

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#118091

Markert
Participant

Hi everybody,
I m phil and want to understand how Cpk for on sided distribution and % defect are related

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#118093

Whitehurst
Participant

BS is a nice word to use but Stan Motorolla considers Ppk as a short term capability do you know that!!!
3*Cp =Zst
3*Cpk=Zst
you have to accept it , and again it depends how your process is centered.

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#118096

Mikel
Member

You don’t know what you are talking about.You claim to know about ALL GE materials and also what Motorola teaches wrong? What actual training/education do you have?

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#118098

Alok
Participant

Hi Joe,
Thanks again for the answer, i will definately think more on it.
Stan,
Request you to stop using those words and provide a real solution (if you have one). we are not here to fight or prove others wrong. we are here to share whatever little we know with others. Hope you will appreciate that.
Anyone has any more intresting insights to share?

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#118099

Deep
Participant

Hi Joe:
thanks
Deep

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#118103

Anonymous
Guest

Dear Alok,
Chilli is hot, sugar is sweet, garlic is pungent, fish source is salty, and lemongrass is sour. Where would we be without the ‘five flavours?’ I know you appreciate this – don’t ake offense: just add some spice to your life!
Andy

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#118104

Mikel
Member

Alok,
This is not about insights. I gave you the right solution with my original post to you – read it.

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#118106

Markert
Participant

Hey guys there,
not sure whether what I m gonna say is dealt already or not:
1. Cp Cpk are to process what mean and SD are to data. Cp is akin to SD and Cpk is to mean.
2. Cp tells us the ability of the process to perform whereas Cpk tells us where it is actually performing. we can derive ppm directly if we know Cpk.

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#118107

Whitehurst
Participant

I think Stan you are just disturbed because you didnt know this ? so its OK ! I am not a Statistician  like you but what little knowledge I had I tried to share I think thats the real purpose of this forum so it doesnt matter whether you liked the answer or not.
Hope this cools you down !! take care pal !

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#118109

Mikel
Member

Its not a matter of what I like, its a matter that your answer is wrong. To bad you are not taking the time to understand this.

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#118206

FTSBB
Participant

Why calculate Cp and Cpk? – because everyone else does; it’s statistical jargon that has been around forever
Process sigma – YACK!
Process sigma from Cp – sure, but why bother?
Personal insight: What is the spec width in terms of process variation (sigma), and how far is your process centered from the target value and the nearest specification limit (in sigma)?  The end.

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#118223

Mikel
Member

So you advocate using Cpm over all other measures?

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#118227

FTSBB
Participant

Nope.  I don’t really like any of the C___metrics.  Dimensionless numbers scare me…
I prefer advocating a check for assignable cause, see where your process is, and fix it.  Chopping it into a dozen different statistics isn’t always necessary or even helpful.

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#118586

param
Participant

Hi All,
To understand process capability to customers specification we use Cp. Note Cp stand for  Capability Potential.
Cp = Voice of Customer / Voice of process = (USL – LSL) / 6* Standard Deviation.
Cpk = minimum (Cpl, Cpu)
Cpl = (mean – LSL) / 3* standard deviation
Cpu = (USL – mean) / 3 * standard deviation
In general  Cpk <= Cp.
Note: When your mean and the goal/target is equal , Cp = Cpk

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#118588

Ashok
Participant

Cp is the ratio of the specification spread (upper spec – lower spec or US – LS) to the process spread (six standard deviations of the process data, i.e., 6 sigma).  So, Cp contains more information than just the process standard deviation.  It tells you whether or not the process variations are well accommodated within the specification limits, i.e., it gives you info about the capability of the process to deliver sepcs.  Through simple statistical formulae, you can convert a given Cp value into the process rejection rate – which you can’t, if you know only the process sigma.  Finally, Cpk, simply tells you if your process is skewed from the center of the specs so that just by readjusting (resetting) the process center, you can reduce the process rejections. Cpk is the smaller of the two ratios: (US – process aveaage)/ 3 sigma) and (process average – LS)/ 3 sigma.  You can see that it represnts the conservative value of Cp and equals Cp when the process is centered at the specs center.
Hope this helps – please feel free to ask me if you need more explanation.   Ashok

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#118615

chew
Participant

This is my personal comments on the above:First of all, Cp is an index of process capability based on given tolerance, what I meant is that there are two variables in the formula the determine the result; Tolerance and Sigma.*Tolerance is the expectation of customer or requestor on that particular process.
*Sigma is the resultant of computation of data collected.Hence, Cp is a index that can give the customer or requestor a feel of how capable the process is respect to the tolerance given.

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#118726

OP
Participant

Hi,
Attaching somwe insite for ur refe….
Process Capability (Measuring conformance to customer requirements)
Objective:
To determine whether a process, given its natural variation, is capable of meeting established requirements or specifications of the customers.
1)      Helps a team answer the question, Is the process capable?
2)      Helps to determine if there has been a change in the process
3)      Helps to determine percent of product or service not meeting customer requirements.
Steps to arrive at Process Capability.
Step 1.
Collect the performance data of the process. Determine the process grand average, X (Double Bar) and the average range, R Bar.
Use a stable Control chart, which means the process is stable and normally distributed.
Step 2.
Calculate the Upper Specification Limit (USL) and the Lower Specification Limit (LSL)
The USL and LSL are based on customer requirements. Recognize that specification limits are based solely on customer requirements and do not reflect the capacity of the process.
Step 3.
Calculate the process standard deviation
Process capability is based on individual points from a process under study. Information from a Control Chart can be used to estimate the process average and variation (standard deviation, s).
s  is a measure of the process (population) standard deviation and can be estimated from information on the Control Chart by

s = R bar / d2               or             s = s bar / C4
Where R bar and s bar are the average of the subgroup ranges and standard deviation, and d2 and C4 are the associated constant values based on the subgroup sample size. See the Table of Constants in Control Charts.
The process average is estimated simply by X double bar and X bar.
Step 4.
Calculate the process capability
To measure the degree to which a process is r is not capable of meeting customer requirements, capability indices have been developed to compare the distribution of your process in relation to the specification limits.
A stable process can be represented by a measure of its variation- six standard deviation. Comparing six standard deviation of the process variation to the customer specifications provide a measure of capability. Some measure of capability includes Cp and its inverse Cr, Cpl, Cpu, and Cpk.
Cp (simple process capability)

Cp = USL  LSL
6s
Note:
While Cp relates the spread of the process relative to the specification width, it DOES NOT look at how well the process average is centered to the target vlue.
Cp is the ratio of the specification spread (upper spec – lower spec or US – LS) to the process spread (six standard deviations of the process data, i.e., 6 sigma).
So, Cp contains more information than just the process standard deviation.  It tells you whether or not the process variations are well accommodated within the specification limits, i.e., it gives you info about the capability of the process to deliver sepcs.  Through simple statistical formulae, you can convert a given Cp value into the process rejection rate – which you can’t, if you know only the process sigma.
Cpk, simply tells you if your process is skewed from the center of the specs so that just by readjusting (resetting) the process center, you can reduce the process rejections.
Cpk is the smaller of the two ratios: (US – process aveaage)/ 3 sigma) and (process average – LS)/ 3 sigma.  You can see that it represnts the conservative value of Cp and equals Cp when the process is centered at the specs center.
Regards
Om Sharma is working for GTL Limited, India, he is B.Sc. Com Sc.), Masters in Total Quality Management, PGDQM from World Quality Council, UK, Persuing Doctorate in Quality Management and Operational Research from Portsmouth University UK. He posses ISO 9000:2000 & ISO 14000:1996 Lead auditor Certifica ion from IRCA UK, Six Sigma Black Belt, COPC Regd Coordinator from COPC Inc USA, Has implementation Experience on ISO 9K, ISO 14k, QS 9000, CMM, GPNQA, Six Sigma, QC,QA,QM etc. He has performed numerous quality audits on Quality Management Systems, Six Sigma, TQM Business excellence etc, He is a lead Six Sigma practitioner at GTL for Six Sigma implementation. Om can be reached at [email protected]

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#118757

BB in Fortune 500 Company
Participant

Does anyone work at a company that uses Six Sigma (BB/MBB) Part-time.  If so how successful is this approach? Or is my company just wasting money and time?

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#118759

Heebeegeebee BB
Participant

no.
hell no.
Why bother?
Would you use you relegate finance to a part time status?

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#121947

K
Participant

How does LSL and USL hard limits affect the Cp and Cpk values and why?
If my LSL is zero and my process is best at zero ,USL has no hard limit then how will it affect the CP and Cpk values?
How do I calculate considering the hard limits?

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#127860

mariappan
Participant

Why do we need to calculate cp and cpk?
why don’t we calculate cp for unilateral tolerance dimensions?

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#127875

Jorge
Participant

It is very simple.
Cp is the short term capability index (rational subgroup sigma or R/d2) and tells you how capable your process is. Cp = USL-LSL/6*Sigma hat as you can see in this formula it does not take into consideration if the process is centered, just takes into consideration the ratio of tolerance spread to process spread.
Cpk is the same concept but incorporates the process average
Cpk = min[USL-Mean/3*Sigma hat, Mean-LSL/3 sigma hat]
So we tend to say that for a process to be capable (One that follows a Normal Curve) the product falling outside the tolerance spread should be less than 0.0027 (or 3sigma) or in mathematical terms
P(X USL) <= 0.0027 (this number can be change if you want 4sigma, 5sigma, or 6sigma)
Working this equation leads to the ratio
USL – LSL /6 Sigma Hat >= 1 (This is the Cp index)
And thats why we say that if it is greater than 1 the process is capable (but we are referring to 3sigma)
For Example,
If Cp is 2 and your Cpk is 0.87 and I ask you can this process be fixed?. The answer is yes, since the process has very litte variability compare to the tolerance spread (high Cp). However it is not well centered and that is why you have a small Cpk. In other words the process has potential to perform better than it is currently doing.
If Cp is less than 1 there is nothing you can do since that is the best your process can perform, no matter if it is right in the middle your Cpk will not be greater than 1. So being less than 1 your only options are to buy a new machine, improve your process, reduce variability, etc.
I hope these helps,
Jorge

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#127926

mariappan
Participant

Dear Jorge,
Thank you. I had the doubt is cleared with the discussion of you. Thank you so much.

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#142995

sathish kumar
Member

I need a brief note about cp,cpk.

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#166045

hari
Participant

cp & cpk

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#171427

lama
Participant

Wow. You take statistics a little too seriously. Get a hobby, hit the town, get a life

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