Hi,

I will like to understand :

1. How do we translate Process Capability into Sigma Level and vice-versa ?

2. What is the difference between Cpk and Ppk ?

 

Dear Sandeep,

There is a more complex formula and explanation that goes with your first question, but let me just say that as a rough guideline 3 * Process Capability = Sigma Level. So, if Process Capability = 2, then Sigma Level = 6 etc.

Cpk stands for short term (within) process capability and Ppk stands for long term (overall) process capability.

SJ

It is a complex question.  To explain in simple terms, to under process capability, first the process has to be stable and predictable.  This is used more for diagnostic purposes.  USL- LSC = Voice of customer, and Process behavior chart is the voice of process.

When the data you are analysing is of attribute, then it is calculated in terms of dpo, dpmo and referred to sigma table for conversion.  If it of variable data, then we talk in terms of VOC, VOP and mentioned as cp, cpk, pp, ppk.

cpk is called as process performance and cp is process capability. if cp<1, the process is not capable and cp=2,then it is a 6s process.

cp =  tolerence width / short term process spread.

 

 

 

Dear Sandeep,

As mentioned by SJ, the Cpk is a short term capability and Ppk is the long erm capability.Fro simplicity you could create a small table where in Cpk=0.5=3 sigma and Cpk=1.5=6 sigma. In the table increase Cpk by 0.1 and increase Sigma by 0.3, from the base value of 0.5 and 3.0 correspondingly. If required you could also add ppm as 66810 at 3 sigma,  down to 3.4 at 6 sigma.

Sripathy

Dear Suresh/Srini/Sripathy,

Thanks a lot for all your inputs on the same...

SG

Process capability is more accurate to establish and control precise in the machine related processes. We can control with various devices and automation, process steps designed accurate to meet the tolerances. Cp and Cpk gives the natural process capability after establishing statistical process control. We can more or less say with accuracy it is machine capability to produce the quality products to the tolerance. It is normally accepted in the industries to expect Cpk>1.33 for a very capable process.

In the case of Six Sigma, sigma levels we use it combining with DPMO to look for continual improvement projects. Variability if it occurs, and  if there is an opportunity need to be identified with performance data, rejections  and evaluation of financial impact of type of scra/waste produced. In the case of Cpk, Ppk, SPC provides a wider varrieties of knowing the established causes, detect and control along with hourly chasrts established, then and there if we had established a long-range capability.

Both have different purpose and should not be mixed with any short-cut formulae .

 

 

hi

confused the conspt six sigma & process capability. pleas clarification different between them by point of comparator

Shimaa,

Both the concepts of sigma level and the process capability are related.

The formula for sigma level is

sigma level = (Upper spec.Limit - Lower Spec.Limit)/(2 * sigma)

Thus, the sigma Level = 6 means, the total specification range (USL-LSL) is equal to 12 Sigmas (Standard deviations)

The Process Capability is defined through two different formulae Cp and Cpk.

The Cp value tells only about variation, using the formula

Cp = (USL-LSL)/(6 *Sigma)

Thus we can see that Sigma level and Cp are related

Sigma Level = Cp * 3

If Cp=1, then Sigma Level =3 &  If Cp =2, then Sigma Level = 6

Next, Cpk value tells not only about variation, but also tells us, how close the data is to the target, using the formula

Cpk = Minimum of (USL-mean)/(3*Sigma) and (mean-LSL)}/(3*Sigma)

Now, we can see that Cp and Cpk will be equal, only if the mean is matching with the target. If the mean deviates from the target then Cpk will be lower than Cp

Thus the difference between Cp and Cpk is an indicator for the deviation of the data from the targeted value.

Hope that helps.

thanks a lot (bala Dr)

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AbhishekM

Hi,

Thanks this was indeed useful, could you please help me understand what does MIN denote in the CPk formula.

Prabhu,

As explained in my post above, Min stands for minimum.

See the formula

Cpk = Minimum of (USL-mean)/(3*Sigma) and (mean-LSL)}/(3*Sigma)

Thanks Dr Bala

then why not directly look at CPk when its inclusive of CP, I mean we do give a lot of importance to CP as well where as CP will increase if the process width is high where process owners don't have control and i client specified. and also I wanted some more clarity on how we calculate K which is the shift in the process and why isn't that a part of CPk calculation

I hope by now you would have understood the following.

Cp is the absolute measure of variation in the process ignoring whether the target is actually achieved or not.

Cpk is the measure of how close the process was aimed at the target.

Now coming back to your question, why look at Cp first and then Cpk - here is the answer.

it comes from the primary focus of the six-sigma methodology.

The primary objective of a six-sigma practitioner is to reduce variation first.

Only After reducing the variation, one must look at the location (achievement of targeted value)

The assumption here is that the target can easily be achieved by "shifting" the appropriate control variable which is already known and within the control of the operator.

If the variation is too large (say Cp<<1) then of course Cpk will be far too small too....

Then where do you focus??? If you are a six-sigma practitioner, you must first focus on Cp to bring it up to be atleast Cp>1 (note six-sigma requirement is Cp>2).

then Cpk can be looked at by appropriately "tuning" the process towards the target.

If the process is centered on "target', then Cpk=Cp or Cp-Cpk is close to zero.

Prabhu,

regarding your question about how Cpk is related to the "shift" in the target, may be you could not figure it out from the expression in terms of the USL and the LSL.

So, you better use the following formula (which is equivalent to the expression given by me earlier. You can do the maths and find out how these two are equivalent).

Cpk = Cp - |m-μ|/3σ

Here you know what is Cp already.

m is the mean achieved by the process and μ is the target required by specs.

σ is the standard deviation observed in the process.

Note: The vertical lines around m-μ denote that you must take only the absolute value of the difference. that is m-μ is m is greater and μ-m if m is smaller.

I hope the above expression clears your doubt about how Cpk is related to Cp and also how it is related to the "shift" in the mean. See the same equation rewritten below.

Cp - Cpk = |m-μ|/3σ

Do you see the relationship clearer now?

sorry for the typo in the abvoe post... here is the correction.

that is m-μ if m is greater and μ-m if m is smaller.

Dr Bala,

Truly appreciate and thank you for your help.

I know have another doubt which is pertaining to attribute RnR, what is the acceptable rnr result in service sector

Thanks

Prabhu

Dear Prabhu, it is not clear what exactly you wanted to know about the attribute R&R.

What is "acceptable" obviously depends on the "cost" of the error.

If you are looking at ppm levels of error then nothing less than 100% is acceptable.

Even 99% would mean 10000 defects escaping detection out of a million.

so, it is left for you to decide, what is "acceptable"

Yeah, it is quite obvious that Inspection by Attributes is very very subjective and achieving 100% overall screen effectiveness vs standard is practically impossible.

So, the best you can try is go as near to 100% as is practically possible.

If it is not possible to improve it beyond say 90% and if the "error" is not tolerable (remember, the question of whether it is tolerable or not is decided from the business point of view and not from statistical point of vew) then you need to figure out alternate ways of measurement - (say implementation of automation, quantification etc...)

Hello Prabhu, it is usually 70% and above....

hello

about DPU,DPO,DPMO

DPU ( DEFECT PER UNIT)=TOTAL NO. OF DEFECTS OBSERVED /TOTAL NO. OF UNIT PRODUCED.

DPO(DEFECT PER UNIT OPPORTUNITY)=DPU/m where m is no. of opportunity

DPMO (defect per million oppurtunity)=DPU/m*1000000

for example

If m=8

DPU=1

DPO=1/8=0.125

DPMO=DPO/M*1000000=125000

regards

anil gupta