Quality Scan: Cpk and Continuous Improvement of Quality
Although Cpk is an effective means of determining process stability, the use of Cpk alone does not lead to continuous improvement of quality.
Take a look at Figure 1. In this illustration, you see upper specification limit, lower specification limit, nominal, and plots of two different sets of processed components. Using the data in Figure 1, we calculate Cp and Cpk as follows:
Thus, in Case 2, the process capability is twice as good as it is in Case 1, and the company is losing out on a tremendous quality improvement of their manufacturing process. That is, the company should move the Case 2 process to nominal, and possibly have an actual six-sigma manufacturing process.
The cost of not being on the nominal of 15.0 would be shown by Professor Genichi Taguchi's Loss Function. Taguchi's Quadratic Loss Function states that "the quality of a product is the (minimum) loss imparted by the product to society from the time the product is shipped." The idea is that a great loss occurs not only when the product falls outside of the specifications, but also that the loss continually increases as the part dimension deviates further from the nominal.Taguchi uses a simple quadratic function to approximate the behavior of this loss to society.
The Quadratic Loss Function is L = k(x-T)2.
|L = Loss in dollars
||X = Value of quality characteristic
|k = Cost coefficient
||T = Target value
Furthermore, the Taguchi loss function recognizes the customer's desire to have products that are more consistent, part to part, which leads to a low-cost product. The loss to society is composed of the costs encountered during use by the customer (e.g. repair, lost time, and lost business). To minimize the loss to society, the strategy is to encourage uniform products at nominal, and thus reduce costs at both the point of manufacturing and at the point of use.
Both quality improvement methods make a very important assumption—that the manufacturing process is stable with minimum variability. That is, the proper control charts show that, first, the process variability given by the R-chart is consistent, and that the chart is also in statistical control; that is, the process is stable in variability and location.
Another critical concept is that the R-chart has to be in statistical control before you can check the chart, because the control limits on the chart are a function of , which would not be valid if the chart was out of statistical control. The latter assumption is also true for a control chart for individuals, i.e., it should be MR-X control charts for continuous improvement of quality and customer satisfaction.
This article was first published in the July 2007 edition of Manufacturing Engineering magazine.