Practice Problem 4

Practice Exam 4 Department of Industrial & Systems Engineering, University at Buffalo IE 509 | Fall 2023 Six Sigma Quality Dr. Cecilia Martinez Leon, Ph.D. Sc.D., MBB Due Date: November 12, 2023 Name: Shihan Reza

Q1. I did a cube plot Geometric representation of this experiment. Performing, Factorial Regression: Dryability versus drying agent, Temperature From the Coded coefficient table, I can see the effect of Drying Agent, temperature and the combination of both. By changing Drying Agent, I got the highest effect on the Dryability. After that temperature which is less than half of the effect of drying agent. The p-values for the main effects of drying agent, temperature and drying agent and temperature are less than 0.05, indicating that all factors have a significant effect on Dryability.

From the normal plot we can tell Factor A (drying Agent) B (temperature) and Ab all of them are significant

Q2. Factorial Regression: Toll Life versus A, B, C. cutting speed (A), metal hardness (B), and cutting angle (C) as the factors. o Do any of the three factors affect tool life? metal hardness (B), and cutting angle (C) significant individual factors . we have a significant interaction effect between A and C (cutting speed and cutting angle), so the answer is 'yes', tool life is affected by some or all of these factors. o What combination of factor levels produces the most extended tool life? Look at the run totals: BC gives the best performance. that is use high levels for metal hardness and cutting angle and low level for cutting speed.

Q3. # Show the design with a cube plot. # Identify the significant factors and interactions (if any): From the coded Coefficient and pareto chart I can tell B: Account-opening fee; D: Long-term Interest Rate and A: Annual Fee are the significant factor Coded Coefficients Term Effect Coef SE Coef T- Value P- Value VIF Constant 177.3 * * * A 30.37 15.19 * * * 1.00 B -38.88 -19.44 * * * 1.00 C 18.875 9.438 * * * 1.00 D -37.37 -18.69 * * * 1.00 A*B -22.63 -11.31 * * * 1.00 A*C 0.12500 0.06250 * * * 1.00 A*D -8.125 -4.062 * * * 1.00 B*C -3.625 -1.812 * * * 1.00 B*D 7.625 3.813 * * * 1.00 C*D 11.875 5.937 * * * 1.00 A*B*C -3.875 -1.937 * * * 1.00 A*B*D 6.375 3.188 * * * 1.00 A*C*D 0.6250 0.3125 * * * 1.00 B*C*D -8.125 -4.063 * * * 1.00 A*B*C* D -3.875 -1.938 * * * 1.00

# You may want to refer to the ANOVA table or the appropriate graph to facilitate the interpretation. Analysis of Variance Source D F Adj SS Adj MS F- Valu e P- Valu e Annual fee 1 3691 3690. 6 10.9 4 0.00 7 Account openning fee 1 6045 6045. 1 17.9 3 0.00 1 Initial Interest Rate 1 1425 1425. 1 4.23 0.06 4 Long term interest rate 1 5588 5587. 6 16.5 7 0.00 2 Error 1 1 3709 337.2 Total 1 5 2045 7 Annual fee and Account opening fee and Long term interest rate has effect as p value is low.

 Lastly, conduct the residuals analysis to validate the ANOVA assumptions. Please comment and give insights. Since the P value is high .529, so we need better statistics to get the P value lower than .5