Using the data in the ‘Part 1’ sheet, select two variables and conduct a two-way ANOVA. Justify your selection and discuss how this model could be used to identify sources of low production rate. Then, identify a third variable that you believe should be treated as a nuisance variable and create a blocked ANOVA to control for the effect of this variable. Continuing your analysis of the ‘Part 1’ data run a general full factorial DOE model using the original five factors and their defined levels (a mixed-level design). Discuss the validity and fit of the model and interpret the results.

QUESTION

PART 1 – DATA ANALYSIS
NOTE: You are not required to resolve any validity issues with the following models (i.e., do not run transformations, Welch ANOVA, etc.). Instead, run the models as specified and comment on their validity as well as what the next steps would be to resolve any validity concerns.

Download the provided Excel data file and complete the following analysis using Minitab software:

1. Using the data in the ‘Part 1’ sheet, select two variables and conduct a two-way ANOVA. Justify your selection and discuss how this model could be used to identify sources of low production rate. Then, identify a third variable that you believe should be treated as a nuisance variable and create a blocked ANOVA to control for the effect of this variable.
2. Continuing your analysis of the ‘Part 1’ data run a general full factorial DOE model using the original five factors and their defined levels (a mixed-level design). Discuss the validity and fit of the model and interpret the results.
3. The data in the ‘Part 2’ sheet has been limited to four observations per treatment combination. Using this data, create a 2k factorial model by restructuring the Supplier factor as two, two-level factors and treating Line as a four- level block. Use Minitab to generate a 25-2 model with one block and extract the relevant data from the provided dataset to complete the analysis. Discuss the validity and fit of the model and interpret the results including addressing aliased relationships.
4. Identify the treatment combinations that would be needed to complete the full fold-over for this design and briefly discuss how the fold-over model would help to interpret the results from Part 2. Complete the full fold-over, discuss the validity and fit of the model, and interpret the results.

Submit a Technical Report that describes the problem and analysis approach (assumptions, limitations, etc.), summarizes the results of your analysis including screen shots from the Minitab output, discusses findings, and makes recommendations based on the analysis. Also, submit the final Minitab output file. There is no minimum page or formatting requirements but the report must be formal/professional and cannot exceed 10 pages.

PART 2 – SHORT ANSWER 

Address the following writing prompt as an appendix to the Technical Report (Appendix A).
1. Discuss the advantages and disadvantages of the DOE approach in general and specifically for your area of study. Evaluate the primary limitations of this approach including addressing common criticisms of DOE. Identify potential alternative approaches and discuss the relative contribution of each approach. Provide three to five references. (750-1000 words).

PART 3 – CONCEPTUAL FOUNDATIONS

Complete the following analysis by hand (showing complete work) and include a PDF copy of your hand-written work as an appendix of the Technical Report (Appendix B).  Book ( Design and analysis of experiments 10^th, 9^th or 8^th edition) Douglas C Montgomery

Consider Problem 10^th 6.42 (9th – 6.43; 8th – 6.39) from Chapter 6 in our textbook. Please note that, while you should show complete work, it is acceptable to show abbreviated calculations and/or provide an example to demonstrate the process for parts 2 and 3.

1. Construct a 25-2 fractional factorial model using the optimal generators (showing your design matrix and selected observed values). Comment on the alias structure and any concerns about interpreting the results.
2. Calculate the Estimated Effects for each of the five main factors (not for the interaction effects) and identify those with the strongest effects.
3. Calculate the Sum of Squares values and complete the ANOVA table. Comment on all significant effects and identify important alias relationships.

4. ANSWER