Question:
The boards data on the website are from a line which cuts spruce, pine and fir (SPF) to produce general quality lumber that you could purchase at Rona, Home Depot, etc. The price that a saw mill receives for its lumber is strongly dependent on how accurate the cut is made. Use the data for the 2 by 6 boards (each row is one board) and develop a monitoring system using these steps.
1. Plot all the data.
2. Now assume that boards 1 to 500 are the phase I data; identify any boards in this subset that appear to be unusual (where the board thickness is not consistent with most of the other operation)
3. Remove those unusual boards from the phase I data. Calculate the Shewhart monitoring limits and show the phase I data with these limits. Note: choose a subgroup size of 7 boards.
4. Test the Shewhart chart on boards 501 to 2000, the phase II data. Show the plot and calculate the type I error rate (a) from the phase II data; assuming, of course, that all the phase II data are from in-control operation.
5. Calculate the ARL and look at the chart to see if the number looks about right. Use the time information in the raw data and your ARL value to calculate how many minutes between a false alarm. Will the operators be happy with this?
6. Describe how you might calculate the consumer's risk.
7. How would you monitor if the saws are slowly going out of alignment?