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The variables commonly charted are the mean and either the range or the standard deviation. The range is usually preferred over the standard deviation because it is simple to calculate. We will now make control charts for the mean and range, commonly called the XÂ Ì… and R charts.

Q. Make XÂ Ì… and R control charts for a sampling of the wattages of the lamps on a production line.

Step 1: Choose a sample size n and the testing frequency.

Use the sample size of 5 bulbs, checked daily for 21 days.

Step 2: Collect the data.

Step 3: Start the control chart by plotting XÂ Ì… versus time, also R versus time.

â†‘: Days versus average wattage

â†‘: Days versus average wattage

Step 4: Compute the average mean XÂ Ì¿ and the average range RÂ Ì….

XÂ Ì¿ means the average of averages, and is pronounced “x double bar”

Use:

(XÂ Ì¿=(Î£XÂ Ì…)/observations and RÂ Ì…=Î£R/observations)

Step 5: Compute the control limits for the mean and for the range.

For the mean: XÂ Ì¿Â±A_2 RÂ Ì…

For the range: D_3 RÂ Ì… and D_4 RÂ Ì…

Factors for computing control chart lines

(from the ASTM Manual on Presentation of Data and Control Chart Analysis)

Step 6: Choose a confidence interval.

Step 7: Draw a horizontal at p, and upper and lower control limits at pÂ±3âˆ™SEp.

Video “ðŸ“š How to make a process control chart (Question 2 – Continuous Variable)” Author: Study Force