Ron, your statement The idea is to have both measurements [Cp=Cpk] equal is well taken, however, it is a good general statement, particularly, when you are focusing only on a single domain, such as quality by reducing defects.
It may NOT be a good generalization when we are characterizing (concurrently) in more that just one domain. Quality is one domain, but there are other domains, such as speed, cost, etc.
Lets state some underlying assumptions, so the readers dont derail.A1 – The Cp can never be smaller than the Cpk.
A2 The Cp and Cpk cannot be negative.
A3 Knowledge exists on how to control the average and the variance.
A4 Dealing with variable data under the Ratio scale of measurement.
A5 Maximizing a domain does not imply maximizing its value.
A6 A domain may have multiple responses.
In the quality-domain, having the Cp equal to the Cpk, implies that the average is centered in the middle of the specification limits, and this in turn minimizes the probability to produce outside the specification limits (below the lower spec. limit and above the upper spec. limit). However, when now, we introduce a second domain, the general idea of having the Cp=Cpk, may not be the way of maximizing for both domains. When dealing with two domains, quality and cost, a better choice may be to maximize the Cp and not maximize the Cpk. Maximizing Cp may work best for quality and cost. However, maximizing the Cpk may be best for quality but not cost. As a matter of fact, maximizing the Cpk may be detrimental in the cost-domain. A good example is Gold Plating, particularly at a spot price of 750 USD per oz. In a gold plating process, I may want to maximize the Cp, but I may want to have a Cpk that meets the standard but with an average as close to the lower specification limit as I can get. This in turn guarantees that I am maximizing under the quality-domain (less probability of producing beyond the specification limits) and maximizing under the cost-domain (by providing the minimum gold or less cost, thus more earnings), and still meeting customer satisfaction.
When we characterize processes under the MPCpS Methodology we are working on maximizing five domains.
So, the statement of Cp=Cpk is good, but it may depend on the process and under how many domains I may be characterizing that process.
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