Notation and Terminology Consider process data consisting of the amounts (oz) of Coke in randomly selected cans of regular Coke. The process is to be monitored with \(\bar x\)and R control charts based on samples of 50 cans randomly selected each day for 20 consecutive days of production. What are x and R control charts, and what do \(\bar x,\bar R\), UCL, and LCL denote?

The process data is recorded from 50 randomly selected cans containingcoke for 20 days. It is monitored using two control charts; \(\bar x,R\)-charts.

Control charts are visual depictions of certain statistical measure taken from all the samples over the time period.The control charts would include three other measures other than the observations:

• Centerline\(\left( {\bar R\;or\; \bar x} \right)\)
• Lower control limit (LCL)
• Upper control limit (UCL)

In case of \(\bar x\)-charts, the measure under study is sample mean and the corresponding centerline value \( \bar x\)is the mean of all sample means. The chart is used to monitor the means.

In case of \(R\)-charts, the measure under study is range of the samples and the corresponding centerline value \(\bar R\) is the mean of all sample range measures. The chart is used to monitor the variation.

The UCL and LCL are lower and upper control limits of the charts,, computed in a way that 99.7% of the observations fall within the range of two limits in any of the two control charts.