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  Statistical Techniques and 6 Sigma
  Cp and Cpks

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Author Topic:   Cp and Cpks
john allen
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posted 16 July 2001 12:06 PM           Edit/Delete Message   Reply w/Quote
When I did a X bar R chart with subgroup size of 5 and total lot size 50, except one X bar value which was below LCL, all other points are within Control limits. Interestingly, when I calculated Cp was 1.5 and Cpk was 1.38. Also, 7 individual X values are out of UCL and LCL limits.

Could some body explain how is it possible to have a good Cp and Cpk values in this condition.

Regards....

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dWizard
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From:Normandy, TN 37360
Registered: Mar 2001

posted 16 July 2001 02:29 PM     Click Here to See the Profile for dWizard   Click Here to Email dWizard     Edit/Delete Message   Reply w/Quote
…except one X bar value which was below LCL, all other points are within Control limits

Could some body explain how is it possible to have a good Cp and Cpk values in this condition.

From Cpk.pdf in the FTP portion of this site:

Calculation of predictable process capability indices is dependent on the statistical control of the process. If the process is not in statistical control, then the results of the study are subject to fluctuate unpredictability.

Regards,
dWizard

------------------
I was better but I got over it.

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KenK
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From:Northbrook, IL, USA
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posted 17 July 2001 09:18 AM     Click Here to See the Profile for KenK     Edit/Delete Message   Reply w/Quote
Regarding "7 individual X values are out of UCL and LCL limits"

That is not so unusual since the raw X values follow an entirely different probability distribution (with larger variation) than that of the means. The control limits are based upon that distribution of the means, not of the individual X values.

With a sample size of 5, 18% of the individual data values would be expected to fall outside of +/-3 standard deviations OF THE MEAN. Of your 50 data points, 18% is 9, so you actually did better than expected.

For sample sizes of 10, 15, & 20, the respective percentages that might exceed the control limits are 34%, 44%, and 50%.

Ken K.

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QEgirl
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posted 17 July 2001 11:07 AM           Edit/Delete Message   Reply w/Quote
The Cp and Cpk are independent of the control chart....they are measures of the ability of the process distribution to stay within the product specifications, and they are not related to the control limits. Therefore, it is perfectly possible to have a "good" Cp and Cpk and yet have an out of control process. The only problem is, as mentioned before, that you can't really predict what your process is going to do unless it is in statistical control (i.e. within control limits).

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AJLenarz
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From:Princeton, IN, USA
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posted 17 July 2001 04:52 PM     Click Here to See the Profile for AJLenarz   Click Here to Email AJLenarz     Edit/Delete Message   Reply w/Quote
quote:
Originally posted by QEgirl:
The Cp and Cpk are independent of the control chart....they are measures of the ability of the process distribution to stay within the product specifications, and they are not related to the control limits. Therefore, it is perfectly possible to have a "good" Cp and Cpk and yet have an out of control process.

I believe a CPK is an indicator for a stable process and should not be used to report on processes that are out of control. Be carefull on the use and application of "CPK"

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Al Dyer
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From:Lapeer, MI USA
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posted 17 July 2001 05:48 PM     Click Here to See the Profile for Al Dyer   Click Here to Email Al Dyer     Edit/Delete Message   Reply w/Quote
If you have the time and the software a good experiment is to input all of your data into your program and and print our the Cp/Cpk values using different sample sizes, 2,3,4,5,6 etc... and review the data. This could give you a good mental picture of the relationship between Cp/Cpk and process control.

ASD...

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Ajay
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posted 19 July 2001 12:47 AM           Edit/Delete Message   Reply w/Quote
Measurement of Cp or Cpk, without the process being under Statistical Control is useless. One point on the X bar char bellow LCL indicates a presence of assignable cause of variation in the process. This cause needs to be identified and prevented from recurring. Recalculate the control limits omiting this data for which assignable cause has been identified. Possibly some other point may lie outside the new control limits. Repeat the process till no point lies ouside the control limits. Then the process would be under statistical control. Cp and Cpk can be evaluated under such a condition.

In case of bilateral tolerances, a different values of Cp and Cpk indicate the process average is not centered but near to either of the specification limits, there by resulting in either oversize or undersize products.

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QEgirl
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posted 19 July 2001 09:51 AM     Click Here to See the Profile for QEgirl     Edit/Delete Message   Reply w/Quote
Agreed, Ajay. The Cp and Cpk are dependent upon a normal distribution. There are some conversion factors which can be used to approximate capability indices if you have an inherently skewed (e.g. stamping - tool wear) or kurtic process distribution.

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john allen
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posted 19 July 2001 11:45 AM           Edit/Delete Message   Reply w/Quote
QE girl,

Could you elaborate further.

Regards....

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QEgirl
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posted 19 July 2001 03:00 PM     Click Here to See the Profile for QEgirl     Edit/Delete Message   Reply w/Quote
John Allen-

Pearson distribution curves can be used to calculate capability for just about any shape of distribution. As long as you can determine the skewness and kurtosis of your process distribution, you can calculate a capability index by consulting a table containing the "standardized tails of Pearson curves". I've got a worksheet for calculating them, along with copies of the tables, copied from an old Quality Progress article. You might check the ASQ website and see if they have any info.

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QEgirl
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posted 19 July 2001 03:26 PM     Click Here to See the Profile for QEgirl     Edit/Delete Message   Reply w/Quote
I went ahead and checked on ASQ's website and found a link through which you can purchase a copy of the article I have. They also have several others which might be interesting. Here's the link, and good luck.
http://qic.asq.org/perl/search.pl?item=14059

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john allen
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posted 21 July 2001 10:27 AM           Edit/Delete Message   Reply w/Quote
Thanks for your efforts

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MSAFAI
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Posts: 42
From:Tehran - IRAN
Registered: May 2001

posted 04 August 2001 04:12 AM     Click Here to See the Profile for MSAFAI   Click Here to Email MSAFAI     Edit/Delete Message   Reply w/Quote
quote:
Originally posted by Ajay:
Measurement of Cp or Cpk, without the process being under Statistical Control is useless. One point on the X bar char bellow LCL indicates a presence of assignable cause of variation in the process. This cause needs to be identified and prevented from recurring. Recalculate the control limits omiting this data for which assignable cause has been identified. Possibly some other point may lie outside the new control limits. Repeat the process till no point lies ouside the control limits. Then the process would be under statistical control. Cp and Cpk can be evaluated under such a condition.

May I ask this question from our SPC practitioners:

is the procedure described above is acceptable for calculating Cpk?

In other words, is it just enough to take corrective action, delete the out of control points, and then calculate Cpk based on the remaining data?

Shouldn't we run the process for ANOTHER 25 subgroup or so, to make sure the assignable causes are removed and the process is under control, THEN calculate Cpk?

Any thoughts?

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Rick Goodson
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From:Wuakesha, Wisconsin, USA
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posted 13 August 2001 09:21 AM     Click Here to See the Profile for Rick Goodson   Click Here to Email Rick Goodson     Edit/Delete Message   Reply w/Quote
Once a process has been 'fixed' by removing assignable cause the control chart limits should be recalculated and the process monitored for a period to determine if the process is in control given the new limits. Then you should calculate process capability

Regards,

Rick

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KenK
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From:Northbrook, IL, USA
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posted 13 August 2001 03:04 PM     Click Here to See the Profile for KenK     Edit/Delete Message   Reply w/Quote
Earlier someone had said that Cp & Cpk are independent of control charts, and specifically, that they are independent of the control limits.

I agree, but I have learned through experience that whereever possible, calculation of a capability index should be accompanied by the display of an appropriate control chart (X-bar, individuals,...).

These charts provide an excellent temporal look at the process.

In addition the user should also provide some assessment of the process distribution, such as a histogram, normal probablity plot, or test of normality. Regardless of opinions on the importance of normality for control charts (I lean toward requiring normality), this assumpion must clearly be considered in order to use these process capability indices.

I have found MINITAB software's Capability Sixpack to be a very well laid out tool for a first look at process capability. If problems are apparent from either the metrics or the graphics, other methods can be used to assess their impact.

If you haven't seen it, check it out at http://www.minitab.com

(I'm not associated with Minitab in any way other than being a VERY satisfied and somewhat vocal user.)

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AJLenarz
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posted 13 August 2001 05:09 PM     Click Here to See the Profile for AJLenarz   Click Here to Email AJLenarz     Edit/Delete Message   Reply w/Quote
quote:
Originally posted by KenK:
... Earlier someone had said that Cp & Cpk are independent of control charts, and specifically, that they are independent of the control limits.

I agree, ...


Whoa...

CPK is an index that should be applied to a stable process.

How can you calculate capability (CPK) if you first don’t have a control chart to determine if the process is in control? Why do you have to provide an assessment of process distribution if you have a stable process?

I don’t understand the logic of separating CPK’s from control charts. Please straighten me out if my understanding is twisted.


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Rick Goodson
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From:Wuakesha, Wisconsin, USA
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posted 13 August 2001 05:50 PM     Click Here to See the Profile for Rick Goodson   Click Here to Email Rick Goodson     Edit/Delete Message   Reply w/Quote
Regarding Cpk, Control Chart Limits, chickens, eggs, Catch 22, etc.

Cpk is an indice of the capability of a process with relationship to the specification limits, that is the specification limits divided by the 6 sigma of the process. This 'sigma' is actually sigma cap, or an estimate of the population sigma developed usually from the average range, R-bar, divided by the d2 factor. To that end the capability indice has nothing to do with the control chart limits. However, for the 6 sigma cap estimate to be usuable, it must come from a process that is in statistical control. Keep in mind, all things being equal, that the sample distribution from a process in control will always be normally distributed regardless of the population distributional shape (Central Limit Theorem). A process that is in statistical control may be capable or may not be capable. The process does not care what the specifications are. In fact a process that is capable can be made to be incapable by changing the specs.

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