It's your first day at the Jedi Temple, working as a lightsaber manufacturer. Your first task on the job is to analyze the control and capability of this process. Your main concern is to see if the lightsabers fit within the required length specifications set forth by the Jedi Council. The Jedi Council has provided you with 50 hours of data on newly crafted lightsabers. Each hour, 5 samples were measured.

A.) Create the appropriate set of X-bar control charts (use the Stat Menu). Are the mean and the variation both in control?
B.) In Control Chart options, enable all Tests. Are any of the Western Electric or Sensitizing Rules for control charts violated? Display the 2 sigma warning limits.
C.) If any out of control points correspond to assignable causes, omit them from the control limit calculation. What are the new control limits? Note that any out-of-control points should still be displayed on the control chart, with annotation to indicate why they were removed.
D.) A change to the process was made and 50 additional hours of data are reported. Create a control chart that shows both the old and new data in separate stages, with separate control limits calculated for each.
E.) Before assessing capability, it is important to determine whether your data follows a normal distribution. Using the Individual Distribution Identification tool, is this assumption reasonable? (Explain in terms of AD and P values).
F.) Is this system capable? Specification limits for lightsaber lengths are 2.75 and 3.25 ft. What do the Cp, Cpk, Pp and Ppk values indicate? Discuss in terms of the traditional benchmark value for a capable process, and indicate how well the process is centered between the specification limits. What sigma level is the process currently operating at, and what is the potential sigma level? What does this indicate about the variation WITHIN subgroups compared to the OVERALL variation?

Problem 2. Gage R&R
In a study to isolate both gauge repeatability and gauge reproducibility, two operators use the same gauge to measure 10 parts three times each. Minitab hint: the data are not given to you in the exact form needed, but unlike DOE, you do not need to create the study in Minitab before you can analyze it.
A.) What type of Gage R&R study is being performed (Crossed, Nested or Expanded)?
B.) Does the Gage R&R show this system to be repeatable?
C.) Is the system reproducible?
D.) If the specification limits are 50±10, what can you determine about the capability of this gauge?

Problem 3. Full Factorial Design of Experiments
The Jedi Council has instructed you to perform a Design of Experiments study to determine which factors effect lightsaber length. Their experience with this process has indicated that the following factors may have an effect on length: lightsaber color, plasma temperature, or the identity of the Jedi who manufactured it.
A.) Create a full factorial design with 2 replicates of each corner point and 1 replicate of each center point. Label the factor levels as Color (Blue and Green); Temperature: 800 (low), 1000 (high); Jedi (A and B). Disable the option to randomize runs (for ease of copying results data from Excel in Standard Order).
B.) Analyze the DOE Factorial Design. Include all interaction terms in the model. According to the Pareto chart, which terms are most significant? Which terms are not significant?
C.) Create Factorial Plots to observe the main effects and interaction effects. What do the slopes of the lines on the interaction effects plot indicate about these variables? What do the main effect plots indicate about these variables?
D.) Remove the insignificant terms from the model to create a simplified regression equation. What is this regression equation? How does the "predicted R-square" term for this equation compare to that of the full model?
E.) Using the Response Optimizer tool, what do you predict as the best settings for achieving the target length of 3 feet?

Problem 4. Paper Airplane DOE Activity
Work in groups of 3-4. Your group will be given two different weights of paper. Create two different paper airplane designs. Designate one person the "designer" - they will fold all 4 of your airplanes for consistency. Designate two people from your group as "pilots".
A.) Describe your paper airplane designs (basic shape, any distinct features) and give each design a name. Create a randomized full factorial design in Minitab. Perform your trials in this order and input the distance each plane flies (in feet).
B.) Which factors were significant to launch distance? Include all interaction terms in the model.
C.) What do the Factorial Plots show about the main effects and interaction effects?
D.) What is the regression equation for distance? What does the R-squared value indicate about the fit of your model to the observed data?