## 2019

by Davis R. Bothe

There are times when the results of several capability studies must be reported to top management or a customer. The report can be a comparison of the capabilities for several machines producing the same characteristic, the outputs from multiple process streams, various part numbers run on the same process or even several characteristics of the same part produced on different processes.

Simply listing all characteristics studied, their actual capabilities (expressed here in terms of their Cp indexes) and their corresponding capability goals can be rather confusing, especially if their goals are substantially different (see Table 1). How well does each characteristic meet its goal? Which characteristic is doing best in relationship to its goal? Which is in the most need of help? Finding the answers to these questions is a daunting task.

One easy way to enhance the analysis of this information is to display the ratio of actual capability to its goal on a circular radar graph (see Figure 1). The plot points are calculated with this formula:

 Plot point = Cp actual Cp goal

With a Cp index of 1.68 and a goal of 1.33, the plot point for characteristic A is 1.26. This value is plotted near the top of the radar graph in Figure 1.

A ratio of 1.26 means characteristic A exceeds its Cp goal by 26%. A ratio of 1.00 would indicate the feature just meets its goal. If the ratio is less than 1.00, the characteristic's actual capability is less than its associated capability goal.

Once calculated, the ratio for each characteristic is plotted on a separate spoke radiating from the center of the radar graph to its outermost circle. There are as many spokes as there are characteristics, with equal angles between spokes. In this example, there are five characteristics, so there are five corresponding spokes on the radar graph, each being 72º apart (360 / 5 = 72).

Every spoke has an identical scale that begins at 0.5 on the outermost circle and increases to 2.0 at the graph's center. The concentric circles denote ratio levels of 0.5 (only 50% goal attainment), 1.0 (100% goal attainment) and 1.5 (150% goal attainment). The closer a point is to the center of the graph, the better the characteristic's capability is in relationship to its goal.

After plot points have been computed for all characteristics (see column four of Table 1), they are plotted on the radar graph. A polygon is created by drawing a line that connects these five separate plot points (see Figure 2).

The points for characteristics B (ratio = 1.35) and E (ratio = 1.46) are inside the 1.0 circle, indicating the process capability for these features surpasses their respective capability goals of 1.67 and 1.50. The plot point for C (ratio = 1.00) falls directly on the 1.0 circle of the radar screen, revealing that the capability for this characteristic (Cp = 1.33) matches its requirement of 1.33.

Points outside the 1.0 circle identify characteristics not achieving their Cp goal. Because its ratio is only 0.77, the process variation for characteristic D (Cp = 1.54) must be significantly reduced if it will ever meet its desired capability level of 2.00. Traditionally, a manager would direct his or her attention to those characteristics having the lowest capability indexes. The radar graph, however, focuses a manager's attention on those features failing to satisfy their capability goals.

In this example, characteristic C has a Cp index of 1.33, the lowest of the five being studied. Nevertheless, with a Cp goal of 1.33, its ratio for the radar graph is 1.00, meaning C just meets the customer's requirement. At 1.54, the Cp index for characteristic D is greater than that for C. However, with a Cp goal of 2.00, D's ratio is only 0.77. Therefore, to bring about the biggest increase in customer satisfaction, a manager should concentrate improvement efforts on D rather than C.

DAVIS R. BOTHE is director of quality improvement at the International Quality Institute in Cedarburg, WI. He has a master's degree in business administration from the University of Wisconsin-Milwaukee. Bothe is an ASQ Fellow, a certified quality engineer and reliability engineer and author of the ASQ Quality Press book Measuring Process Capability.

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