In Statistic control Process, to analyze Variable Data, we need to use mean, range and standard deviation. Control charts are used to Monitor these Parameters to study whether the process is out of control or not. Any of the Parameter outside the Control limit means special cause variation is present in the process.
When we deal with any Variable, it is necessary to control the mean and dispersion for process stability. For Average we have X bar chart however to check the variability either Range (MR, R Chart) or Standard deviation (S Chart) to be calculated based on rational Subgrouping of Sample Data.
Hence two charts required to check the process means and variation over a time.
I-MR is chart is used when there no subgrouping in the Data. Following is chart depicts Sample of 500 ML size Bottle Filled over a period.
From the above I-MR chart analysis, MR chart is stable, however Individual chart is out of control. MR chart must be analyzed before analyzing I-Chart as I-chart control limits are calculated based on MR charts variation and average. MR chart depicts the variation of range calculated from consecutive data points. If MR chart is out of control, then it is irrelevant to Analyze the I-Chart as control limits for I chart will be incorrect.
X bar R (X bar R chart is required to calculate average and Range when Rational Subgroup Size is 2 to 8.)
The following charts (Average Call Handling time for 5 Calls for 30 Days) for X bar and R show the process is in control. R-chart should be in control before analyzing the X bar chart because X bar control limits are derived from R control chart. If R chart is out of control, then X bar charts limits are inaccurate, and it is irrelevant to analyze the X bar chart. For process to be in control, Both X bar and R charts must be in control.
X bar S (X bar S chart is required when subgroup size is greater than 8. When number of subgroups are large, S chart (Standard deviation) is more efficient than R (range) chart as X bar S charts can provide more accurate depictions of small variation a process.
The following charts (Average Call Handling time for 12 Calls for 30 Days) for X bar and R show the process is in control. S-chart should be in control before analyzing the X bar chart because X bar control limits are derived from S control chart. If S-charts value are out of control, then X bar charts limits are inaccurate. For process to be in control, Both X bar and S-charts must be in control.