Welcome to this Statistical Process Control tutorial on Control Chart for Xbar. We will be constructing an Xbar chart from process data and then determine if the process is in statistical control. If you've seen the first video in this series on our chart, you know that a control chart comprises of a centerline, a lower control limit, and an upper control limit.
Well, The centerline for the X bar chart is X double bar, that is, the mean of the sample means. Now, if the standard deviation of the process is known, this formula is used to calculate the control limit. However, we will be using the range in this video. In our case, the upper control limit UCL is X double bar plus A2 R bar.
And the lower control limit LCL is X double bar minus A2 R bar. R bar is the average of the sample ranges, and A2 is found on the control chart factors table. We will be using this process data consisting of samples of size 5 collected every day for 10 days.
Our objective is to determine if the process mean is in statistical control. As required in the control limit formulas, we will first obtain The sample ranges and means. The range is largest minus smallest. So for the first day of first sample, the range is 509 minus 496 which gives 13. We do the same for the rest of the samples. The mean for the first sample can also be obtained by adding up the values and dividing by 5 and that gives 502. We do the same for the rest of the samples.
Next, we calculate rbar and xdoublebar. The sum of these ranges is 231. So rbar is 231 divided by 10 which gives 23.1. The sample means add up to 4978. So there mean xdoublebar is 497.8.
Looking again at the formulas for control limit here, we have everything but a2. To find A2, we simply go to the Control Limits Factor table and check under Sample Size 5. The corresponding A2 value is 0.577. Now we have A2, X double bar, and R bar.
So UCL equals 497.8 plus 0.577 times 23.1 which gives 511.1. And for LCL, we have 497.8 minus.577 times 23.1 which gives 484.5. For the chart, let's first draw the sample point for the data.
And then draw the control limits. And finally, draw out the run chart. The X bar chart is now complete. We can see that the sample mean for Day 5 is clearly below the lower control limit. Therefore, the process mean is not in statistical control or is out of control.
As a result, we would recommend that the activities of Day 5 be investigated to determine the special cause of variation and to take necessary corrective actions. And that's X bar chart. Thanks for watching.