Question 2 (2+4+4 points) Breeze Toothpaste Company makes tubes of toothpaste. The toothpaste is produced and...

Transcribed Image Text:

Question 2 (2+4+4 points) Breeze Toothpaste Company makes tubes of toothpaste. The toothpaste is produced and then pumped into tubes and capped. The production manager is concerned whether the filling process for the tubes of toothpaste is in statistical control. The process should be centered around 7 ounces per tube. Samples of 5 tubes were taken and each tube was weighed. The weights are given in the table below. Guideline: Follow procedures for constructing control charts and use A2, D3, and D4 tables in Quality Management Lecture Sample Ounces of Toothpaste per tube Tube 1 Tube 2 Tube 3 Tube 4 Tube 5 X-bar R Sample 1 6.90 6.86 7.12 7.20 6.99 Sample 2 7.22 6.80 6.76 7.03 7.10 Sample 3 6.88 7.34 7.20 6.23 7.06 Sample 4 7.12 6.57 7.11 7.23 7.02 Sample 5 6.78 6.76 6.85 6.79 7.03 Sample 6 7.05 6.99 7.01 6.89 6.78 a) Find the sample average and range for each of the six samples as completing the table. (2pts) b) Construct the control limits of the X-bar chart. Is there any out of control sample? (4pts) c) Construct the control limits of the R-chart. Is there any out of control sample? (4pts) Question 2 (2+4+4 points) Breeze Toothpaste Company makes tubes of toothpaste. The toothpaste is produced and then pumped into tubes and capped. The production manager is concerned whether the filling process for the tubes of toothpaste is in statistical control. The process should be centered around 7 ounces per tube. Samples of 5 tubes were taken and each tube was weighed. The weights are given in the table below. Guideline: Follow procedures for constructing control charts and use A2, D3, and D4 tables in Quality Management Lecture Sample Ounces of Toothpaste per tube Tube 1 Tube 2 Tube 3 Tube 4 Tube 5 X-bar R Sample 1 6.90 6.86 7.12 7.20 6.99 Sample 2 7.22 6.80 6.76 7.03 7.10 Sample 3 6.88 7.34 7.20 6.23 7.06 Sample 4 7.12 6.57 7.11 7.23 7.02 Sample 5 6.78 6.76 6.85 6.79 7.03 Sample 6 7.05 6.99 7.01 6.89 6.78 a) Find the sample average and range for each of the six samples as completing the table. (2pts) b) Construct the control limits of the X-bar chart. Is there any out of control sample? (4pts) c) Construct the control limits of the R-chart. Is there any out of control sample? (4pts)