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#### Leigh

I am fairly new to the world of Capability Analysis. My problem at the moment is the more I read the more my head spins. I’m slowly getting a hold on the concepts involved but I need help on a specific issue.

A customer of ours manufactures an electronic component for us. This component (an IC or integrated circuit) must meet over 150 parameters within well defined limits. (Each lot consists of about 2500 pieces). Therefore the supplier tests the IC prior to shipping and provides, as part of the test report, the capability analysis results for each parameter. The test processes are quite stable and the measured test results are generally centered within the limits. Below is his description of Cp and Cpk. To my understanding he is using actual standard deviation rather than estimated std as is required by Cp /Cpk formulas, and therefore I think are really descriptions of Pk and Ppk..

My question is: 1) Is his interpretation of Cp and Cpk below correct and relevant? 2) Is below actually a description for Pk and Ppk? and 3) Should he be using Cp or Pp in determining out process capability, and if so how?

Many thanks for any help offered…. Leigh

Definition of Cp

===========

Cp, the capability of a process, is determined by the width of the process distribution

relative to a set of limits. For a test program, this means the width of a distribution of

test results relative to the test limits. The standard measure of the width of a

distribution in statistics is the standard deviation (std_dev), so Cp must somehow

relate the standard deviation to the test limits:

Cp = min{ ((HTL-nominal)/(3*std_dev)) , ((nominal-LTL)/(3*std_dev)) }

with:

HTL = Higher Test Limit

LTL = Lower Test Limit

nominal = nominal value = (HTL+LTL)/2

std_dev = standard deviation of measured value

As the equation suggests, Cp is the number of standard deviations that will fit between

the upper and lower limits of a test. A standard convention is to scale the number of

standard deviations by multiplying by 6. This makes it easier to interpret the Cp value

in terms of 6 sigma quality goals. The correct interpretation of Cp is "the number of 6

sigma distribution which can be fit between the high test limit and low test limit".

In actually calculating Cp, Test Insight uses the distance between the nominal value

and the closest test limit. Because this distance covers only half the distribution, it

divides the distance by 3 sigma’s, not six. The end results, however, correspond to the

number of 6 sigma distributions that can fit between the limits.

Definition of Cpk

============

This measures the shift in the mean of a test away from its ideal position. If Cp is a

measure of the potential yield of a perfectly centered distribution, then we should

diminish Cp for every unit the mean deviates from the center of the test limits. It is

this combination of Cp and k which yields the Cpk statistic.

Cpk = Cp (1 - k)

with:

k = (nominal-mean) / (HTL-LTL)/2

mean = mean of measured value