My esteemed colleagues: I believe that you missed the question. It was, for two processes with identical Cpk, one perfectly centered, the other 1/2 way to the spec limit, which is producing more defects. The answer is easy (assuming a normally distributed process), since Cpk is only calculated based on the closest spec limit, the centered process is producing twice the number of defects as the non-centered process. This can be observed by simply drawing the distributions. For the off-center process you will see that the width of the distribution is considerably narrower than the perfectly centered distribution. You will also observe that the other side of the off-center distribution has gone so close to zero as to be considered zero. For the centered process, the defects for Cpk are only counted on one side, but exactly the same number will exist on the other side! So, in reality, the effective Cpk is much lower. Although not the question, as others have indicated, the off-center process is also likely to be much easier to improve, as it is usually an easier task to adjust settings to affect the mean than to reduce the variation.
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