STAT 300W: Project 4

In many manufacturing processes, tooling holes are used as a referencefor the coordinates related to all subsequent machining. For example, in the chainsaw industry, lasers cut the bars from a sheet of steel and drill tooling holes in several locations. These holes fit over pins on the milling machines, which stabilizesand positionsthe bar for the cutting of the groove, etc. It is critical that the diameters of these holes fall within tight specification limits: too small and they won’t fit over the pins, too large and the bar will “wiggle” too much (so won’t be positioned accurately).

The company wishes to introduce control charts as a means of monitoring tooling hole diameter and ultimately decreasing variability in this key measurement. Two variables that may affect the diameter are the width of the steel (three sizes: .191, .201, and .236) and the lasers (there are four different machines). As a preliminary step, the company collects some data on tooling holes (one per bar) drilled with different combinations of these factor levels. The data, which will be used to construct the control charts, are given in the file P4data.txt. All diameters are quoted in ten thousandths of an inch.

The target tooling hole diameter is 3824, with a lower specification limit of 3820and an upper specification limit of 3828.

Historical data indicate that diameters are approximately normally distributed, and that the variance of the observed diameters is not a function of the mean (i.e. the target diameter can be changed without impacting the variance of the observed diameters).

The company then collects some additional data (available for Laser 1 in the file newP4data.txt)for plotting on the control charts to begin process monitoring.

GOAL:Using language understandable to non-statisticians, write a report for the company’s management team explaining how to use control charts in this context and the assumptions of the method. Justify why you would recommend using one chart for each laser, but not one chart for each material or material/laser combination.

For your proposed control chart for Laser 1:

  1. Based on the preliminary data, set up the control chart. What proportion of diameters are within the specification limits? Discuss whether the laser should be adjusted in order to make the average diameter closer to the target value.
  2. Plot the new data and the control and specification limits. Interpret any signals.

Other guidelines:

  • The basic outline is essentially the PPDAC framework, and your report should be broken into appropriately defined sections. However, since the report is for a client, it is appropriate to use different section headings. For example:
  • Introduction – Describe the general concept of control charts, their usefulness, and how they can be used in the context of this problem. This section will contain the Problem and Plan stages of PPDAC.
  • Data – Discuss the data that are available forcreating the control charts. This section corresponds to the Data stage of PPDAC.
  • Analysis– This section corresponds to the Analysis stage of PPDAC.
  • Analysis of preliminary data. Analyze the preliminary data, commenting on the effects of steel width and laser. Be sure to check all assumptions of your model.
  • Setting up a control chart. Set up and comment on the control chart for Laser 1.
  • Interpreting a control chart. Plot the new data from Laser 1 and interpret any signals.
  • Conclusions – Summarize your results/recommendations in the context of this problem and explain these to the client. This section corresponds to the Conclusion stage of PPDAC.
  • Note that calculations are not appropriate for the main body of a client report.Any calculations should go in an appendix. Theseare not part of your word count.
  • I will also be expecting a text file, separate from your report, of the code you used for your project. This should contain code that I can simply input into the appropriate program (R or S-PLUS most likely) to reproduce your plots and analyses.

MAXIMUM of 1500 words.

Draft DUE date: 11:59pm Wednesday, Mar. 4 (email to )
Final DUE date: 11:59pm Wednesday, Mar. 18 (email to )

NOTE: Your draft and final reports should include:

  • The data set number you used.
  • A page of references including all materials you read (textbooks, websites, journal articles,…) as well as any people who helped or proofread your project.
  • Your project should be double spaced with a font size of 12 pt.