A Graphical Method to Control Process Capability

Abstract

We suggest that one should focus on the process parameters (y, a) instead of the capability index alone by using process capability plots, both when defining what is meant by a capable process and when deciding whether a process can be considered capable or not. First we introduce the so called the (S, y)-plot, to define a capability region. The (S, y)-plot is based on a capability index but focuses on the parameters (µ, a). We have earlier defined a class of capability indices, containing the indices C 13 , C pk , C pm , and C pm k. By varying the parameters of the class various indices as well as various capability regions with different properties are obtained.Under the assumption of normality we suggest two process capability plots to be used when interpreting the results of the estimated indices in the above mentioned class for deciding whether a process can be considered capable or not. One of these plots is the so called (b“, ÿ)-plot, which is based on the estimated index and is a generalization of the (S, y)-plot. The other is the so called confidence rectangle plot. This plot is based on a confidence region for (S, y), which is plotted in the (S,y)-plot. These plots are compared and discussed from different aspects. An advantage with using a process capability plot, compared to using the capability index alone, is that we will instantly get visual information, simultaneously about the location and spread of the studied characteristics, as well as information about the capability of the process. When the process is non-capable, the plots are 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. In this way the proposed graphical methods give a clear direction for quality improvement.KeywordsGraphical MethodProcess CapabilityConfidence RegionCapability RegionProcess SpreadThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.