Fig. 4 Process variation and sigma values
Notice that one on the curve is where it transitions from concave to convex. It was determined that this process, for the material being used, had a of 0.005mm or 0.0002in. When a process approximates the normal distribution, about 68.7% of the parts are found between + and - one from the average. About 95% of the parts are found between + and - 2 from the average. About 99.73% of the parts are found between + and - 3 from the average. 
Notice that in this example, as is true in most processes, the average is not exactly on the goal. This is where accuracy and the Cpk index will come into play. 

Imagine that the mean of the process was always centered on the goal. The design engineer comes up with a terrific new design that requires a tolerance on a critical diameter be held within ±0.005mm or a total of 0.01mm. 

Cp for this design would be: 

This would mean that, if the process was centered on the goal, roughly 68% of the parts produced would be in tolerance, about 16% would be oversize (could possibly be reworked) and about 16% would be undersize (scrap). The wise approach would be to reject the design and send the design engineer back to the CAD system until a more robust design (one not requiring such a tight tolerance) could be created. Had the design engineer concocted a design requiring a tolerance of ±0.01, which is ±2s, approximately 95% of the parts would be in tolerance. Or, there would be a 5% chance of parts being out of tolerance. 

A tolerance of ±0.015, ±3s, would yield approximately 99.73% in spec parts or roughly 3 discrepant parts per 1000 produced. 

Keep in mind that there is an assumption that the process will always be centered.

When is the design robust enough? Historically Cp = 1 was considered good enough. This is a ±3s design. Today, however, most companies claim to be trying for ±6s. In our example the design engineer would have to create a design that would function if the critical diameter had a tolerance of ±0.03mm or ±6 times the standard deviation of 0.005mm. 

A major reason why care must be taken is due to the fact that processes do not remain centered. Tools wear, machines heat up and cool down, raw material is not consistent, etc. That is where Cpk comes in. 

Cpk is the index used to describe the float or drift of the distribution of parts relative to the design specifications. It is a measure of the accuracy of the process. Cpk describes how close the process mean is to the nearest limit and compares that distance to the dispersion of parts about the mean. 

Using our target rifle example, accuracy is determined not by how close the average of the shots is to the center of the target but rather by how close the average is to the nearest edge of the target (Fig. 5). If the marksman stays well clear of the edge of the target, the shots will land close to the center.