Leaderboard

Benchmark Six Sigma Expert View by Venugopal R To fully understand the explanation to this question, one has to be clear on the principles of XBar–R chart and also about the variations related to Gage R&R. While many of the ambassadors would have given good explanations, I will express my points briefly. Please be cautioned that this write-up will not give a full education on these topics and hence I request the readers who seek further clarity to read and develop more understanding of the two topics as mentioned above. How does an XBar–R chart work? XBar–R chart is constructed based on several groups of small samples processed under nearly similar conditions. Each such group is termed as “Rational sub-group”. The Range chart shows variation within these samples and the control limits for Range chart are statistically derived from the sample data. A reasonable time gap is allowed to pick the successive groups of samples, intending to bring out any process variations. The X-Bar represents the mean value of each of the sub-groups. It is to be noted that the control limits of the X-Bar chart are also derived using the average range values. How is the X-bar R chart interpreted? If all the X-Bar values are falling within the control limits, the variation between the subgroups cannot be distinguished from the variations within the sub-groups. This could mean that the Process variations are very low and do not show up over and above the ‘within’ group variations. It could also mean that the ‘within’ group variations are so high that the process variations are not being distinguished. If more values of X-Bar fall outside the control limits, then the process is considered to be influenced by assignable causes, whose influence is over and above the ‘within-group variations’. On the whole, more points falling within control limits is a desirable situation here. Now let’s examine the X-Bar R chart used for interpreting Gage R&R Here, each sub-group is represented by the readings taken by the same appraiser on the same part, assuming the range chart is made for each appraiser. The control limits for the X-Bar chart, being based on these R values, depict the variation of the measurement system. Each point on the X-Bar chart represents the average of the readings by each operator. The variations between X-Bar values are considered as due to Part to Part variation. Now, if most of the X-Bar values fall within the control limits of the X-Bar chart, it means that the Part to Part variation is not distinguishable from the Measurement system variation. It either means that the Measurement System Variation is too high or the choice of the parts is not representative enough to bring out the Part to Part variation, or a combination of both. If most of the X-Bar values fall outside the control limits, it means that the variation due to Measurement System is low enough to show up the variation due to Part to Part. In other words, here, we would like to have the relative variation of the measurement system to be low compared to the Part to Part variation that the system is expected to assess. Hence more points falling outside the control limits is a desirable situation here.