Rulers. A company that traditionally made rulers and yardsticks is setting up a manufacturing process to make metersticks. Obviously, accuracy is important for their new product. The company runs a 24-hour production process.

Using a calibration set of data they found:

X = 1.000 R = 0.0016 They took a sample of 3 metersticks each hour and recorded the results in the following table.

Sample 1 Sample 2 Sample 3 Hour 1 0.9983 1.0007 1.0010 Hour 2 1.0005 1.0011 1.0014 Hour 3 1.0002 0.9995 0.9997 Hour 4 1.0004 1.0016 1.0007 Hour 5 1.0014 0.9994 1.0008 Hour 6 0.9990 0.9996 0.9984 Hour 7 1.0014 1.0010 1.0017 Hour 8 1.0017 1.0002 1.0002 Hour 9 1.0003 1.0008 0.9993 Hour 10 0.9998 1.0002 0.9992 Hour 11 0.9985 1.0002 1.0006 Hour 12 1.0003 1.0012 0.9994 Hour 13 0.9998 1.0013 0.9995 Hour 14 1.0000 0.9994 0.9992 Hour 15 1.0005 0.9999 1.0016 Hour 16 1.0019 1.0018 1.0010 Hour 17 0.9993 0.9994 0.9993 Hour 18 1.0020 1.0000 0.9978 Hour 19 1.0007 1.0005 0.9991 Hour 20 1.0009 1.0005 0.9999 Hour 21 1.0002 0.9998 1.0021 Hour 22 1.0019 0.9986 0.9996 Hour 23 1.0011 1.0003 0.9993 Hour 24 0.9993 1.0010 1.0001

a) Create an X chart based on the calibration data statistics for these 24 hourly samples.

b) Create an R chart based on the calibration data statistics for these 24 hourly samples.

c) Assuming that the process was in control during the calibration period, is the company’s process for making accurate meter sticks out of control?