I would like to respond to dragonmasters original question.
As Don Winton notes: Cp is just the inverse of Cr. Cp is known as process capability. It is simply the ratio of two numbers: A and B.
The numerator in the ratio (number A) is simply the difference between the upper spec and lower spec limits. Obviously I am assuming a two-sided spec limit.
Referring to Sam's post, a +/- spec limit of 0.005 is equivalent to
0.005 - (- 0.005)
or a value of 0.01 for the numerator, not "0."
The denominator (number B) is 6 times the short term estimate of sigma. Lets not get into long-term and short-term estimates of sigma, even though the difference is important. For dragonmasters simple question lets keep it simple.
So we have A/B = 0.01/(6*sigma)= Cp.
Cr = (6*sigma)/0.01
In either case, the answer is not zero.
Cpk is another matter. Cp is a capability index since it measures a processes potential for performance. It is the best one could expect if the process were centered directly between the upper and lower spec limits.
Cpk assumes the process is not centered. In such a case you must calculate two values for Cpk, and use the lesser of the two resulting values.
First we measure Cpk relative to the upper spec limit (USL). Then we measure Cpk relative to the lower spec limit (LSL). The smaller of the two values is the Cpk for the process. The two equations are:
Cpk = (USL - Xbar)/ 3*sigma
Cpk = (Xbar - LSL)/ 3*sigma
Pick the smaller.
If you want to read everything there is to know about measuring process capability suggest Davis R. Bothe's MEASURING PROCESS CAPABILITY, McGraw-Hill, ISBN 0070066523. It runs about $100, so I hope you really want to know this stuff.
Cheers.
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