The Circular Safety Region: a Useful Graphical Tool in Capability Analysis

When measuring the capability of a manufacturing process some form of process capability index is often used. To assess the capability, using a random sample, confidence intervals or hypothesis tests on the index are frequently used. Here, an alternative approach is presented. A process is usually defined to be capable if the capability index exceeds a stated threshold value, e.g. Cpm > . This inequality can be expressed graphically as a region in the plane defined by the process parameters (μ, σ). This graphical region, or safety region, similar to a confidence region for (μ, σ), can be plotted to test for capability. Under the assumption of normality a circular safety region for the capability index Cpm is constructed that can be used to draw conclusions about the capability at a given significance level. This simple graphical approach is helpful when trying to understand if it is the variability, the deviation from target or both that need to be reduced to improve the capability. Using circular regions several characteristics can be monitored in the same plot. Copyright © 2005 John Wiley & Sons, Ltd.