Methods of Quality Improvement - Statistics Project Example

Furthermore, the R-chart shows no points outside the upper control limit or lower control limit. Therefore, the process is under statistical control and we can say that from the perspective of process variation, the process is in control. x-bar chart measures the central tendency (accuracy) of a process and indicate whether changes have occurred. R-chart measures the variability (dispersion) of a process. R-chart indicates that a gain or loss in uniformity has occurred. R-chart is independent from process mean.

x-bar chart and R-chart are used together to monitor variables in process are in control (or not). R-chart is monitored before the x-bar chart. This is because the x-bar chart limits rely on the average range and if process variability is not stable and is affected by special causes, then is not a reliable estimate of variability, and thus the x-bar chart limits are less meaningful (Moore et. al., 2011). The R-chart indicates that the process variability is in control, as all the ranges for the subgroup are in-between upper and lower control limits and there is no unusual pattern, as we move from left to right on the R-chart.

However, the x-bar chart indicates that the process accuracy is not in control, as not all the means for the subgroup are in-between upper and lower control limits. Rational sub-groupings are used in constructing control charts so that the individual observations within the subgroups have been measured under similar process conditions. The main idea behind rational sub grouping is that if the individual observations within the subgroups are as homogeneous as possible, then any special causes disrupting the process will be reflected by greater variability between the subgroups.

When special causes are present in the process, rational sub-grouping attempts to maximize the likelihood that subgroup statistics will signal that the process is