# Cp and Cpk - Cpk is an index that should be applied to a stable process

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#### Don Winton

<font color=#0011dd>…except one X bar value which was below LCL, all other points are within Control limits </font>

<font color=#0011dd>Could some body explain how is it possible to have a good Cp and Cpk values in this condition.</font>

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,

Don
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I was better but I got over it.

J

#### john allen

Cp and Cpks

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....

K

#### KenK - 2009

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

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

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

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

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

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.

J

#### john allen

QE girl,

Could you elaborate further.

Regards....

Q

#### QEgirl

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.