Safety Regions in Process Capability Plots

Abstract

A process is usually defined to be capable if the process capability index exceeds a stated threshold value, e.g., Cpm > 4/3. This inequality can be expressed graphically as a region in the plane defined by the process parameters (μ,σ). In the obtained plot special regions can be plotted to test for process capability. These regions are similar to confidence regions for (μ,σ). This idea of using regions in process capability plots to assess the capability is developed further for the capability index Cpm. A new circular region is constructed that can be used, in a simple graphical way, to draw conclusions about the capability of the process at a given significance level. Using circular regions several characteristics with different specification limits and different sample sizes can be monitored in the same plot. Under the assumption of normality the suggested method is investigated with respect to power as well as compared to other existing graphical methods for drawing inference about process capability.

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