The only surefire method to eliminate waste is to design a product and its process so that the parameters of interest to consumers are brought close to the target value or design center. There is no other way to get 100% yields or to achieve zero defects. Once this is done, production becomes a breeze, and manufacturing can put products together without the necessity of inspection tests, which are no value-add whatsoever.

Before the variation in a parameter can be reduced, however, it must be measured. Two yardsticks, Cp and CpK, have become standard terminologies. Process capability, Cp, is approximately defined as a specification with divided by the process width. Is a measure of spread. The “Cp as a Measure of Variation” figure depicts six frequency distributions comparing the specification with(always 40-20=20) to the process width.

Cp as a Measure of Variation

Process A in the “Cp as a Measure of Variation” figure has a process width of 30, is defined by traditional three Sigma limits, to give a Cp of 0.67. It is a process that is out of control, with the 2 ½% rejection tails at both ends. For such an out-of-control condition only brute force sorting, scrap, and rework can produce product suitable for shipment to customers.

Process B has a process width equal to the specification width to give a Cp of 1.0. Although somewhat better than Process A, it too can be considered almost out-of-control because any slight change or ripple cause rejects.

Process C has a Cp of 1.33, showing a margin of safety between the tighter process limits and the specification limits. This is a good standard for important parameters in scale-up and early production runs.

Process D, with a Cp of 1.66 is better, with an even wider safety margin. Process E, with a Cp of 2.0 is an important milestone in the march towards variation reduction. Here the process width is only half the specification width. Most companies today have established a Cp of 2.0 as a minimum standard for their own, as well as their suppliers, important quality characteristics.

Process F, with the Cp of 8.0 is not only much better; it is also attainable and at a lower overall cost. In fact, there’s no limit to higher and higher Cp numbers, so long as no reoccurring costs are added to the product or process, and only the cost of design of experiments, is incurred.

Process Capability Equations

Taking process capabilities a bit further, the use of CpK allows an even better measure variation and process control. This is because see P does not take into account any non-centering of the process relative to the specification limits of the parameter. Such non-centering reduces the margins of safety, and therefore has a penalty imposed, called the K correction factor. The “Process Capability Equations” figure shows the calculations involved for these factors.

CpK as a Measure of Process Capability

When the process average, and the design center or target value, coincide, the correction factor K is reduced to zero, making Cp and CpK equal. If however, the process average is skewed towards one end or the other of the specification limit, away from the design center, the value of K increases, causing a decrease in CpK relative to Cp. This effect is shown in the “CpK as a Measure of Process Capability” figure. For example sub-figure A has a wide spread, with the Cp of 0.71. Since is the design center and its average, coincide, the Cp, and CpK values are the same at 0.71. Sub-figure B has a narrow spread, with a respectable Cp of 2.5. However, because it is located close to the lower specification limit, the K factor penalizes it to give it a poor CpK of 1.0. Sub-figure C has a broader spread than sub-figure B, with the lower Cp of 1.67. But it is closer to the design center, than is sbu-figure B, and so the K factor is less of a penalty, resulting in a CpK of 1.33, which is better than sub-figure B. Sub-figure D is ideal, with both a very narrow spread and a centered process to give a Cp and CpK of 5.0.

CpK is an excellent measure of variability and process capability because it takes into account both spread and non-centering. In process control, centering a process is much easier than reducing spread. Centering typically requires only simple adjustments, whereas spread reduction often requires the patient application of design of experiments techniques. As with Cp, the objective should be to attain higher and higher CpK values, with a CpK of 2.0 considered merely as a passing milestone on the march pass zero defects to near zero variation. CpK is also a convenient and effective method of specifying supplier quality.