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MgtOp 340—Operations Management (Section 4) Washington State University Fall 2014 Problem Set #2—Handwritten Section Due: September 24, 2014
(The online portion of the assignment is found in MyOMLab)
Show your work!
1. (12 points) Suppose that a metal rod is supposed to be cut 31.5 mm. in length. The upper spec limit is set at 32.0 mm., and the lower spec limit set at 31.0 mm. A metal rod that is out of spec must be scrapped at a cost of $20.00. The company uses the Taguchi Quality Loss Function to estimate quality costs. Suppose that a sample of 4 units was taken, and the rod measurements were: 31.6, 31.8, 31.1, and 32.0 mm., respectively.
a. Bob believes that the Taguchi Quality Loss function is an appropriate measure for quality costs. What is the Taguchi Quality Cost of that sample of 4 units?
b. Jerry likes the Taguchi Quality Loss function, but he believes that a linear function would better represent the cost of quality. Specifically, Jerry prefers a loss function of the form: L = T×|D|, where L, D, and T have the same definitions as in the Taguchi model. What would be the quality cost of the sample of 4 units using Jerry’s model?
2. (13 points) Johnson Company produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (in.) from the last six samples are provided below.
BOTTLE
Sample
1
2
3
4
1
0.601
0.612
0.575
0.600
2
0.597
0.601
0.608
0.605
3
0.581
0.550
0.585
0.597
4
0.630
0.605
0.595
0.577
5
0.598
0.624
0.608
0.604
6
0.585
0.580
0.620
0.579
a. What are the control limits for the R chart?
b. What are the control limits for the x-bar chart?
c. Is the process in control?
(The online portion of the assignment is found in MyOMLab)
Show your work!
1. (12 points) Suppose that a metal rod is supposed to be cut 31.5 mm. in length. The upper spec limit is set at 32.0 mm., and the lower spec limit set at 31.0 mm. A metal rod that is out of spec must be scrapped at a cost of $20.00. The company uses the Taguchi Quality Loss Function to estimate quality costs. Suppose that a sample of 4 units was taken, and the rod measurements were: 31.6, 31.8, 31.1, and 32.0 mm., respectively.
a. Bob believes that the Taguchi Quality Loss function is an appropriate measure for quality costs. What is the Taguchi Quality Cost of that sample of 4 units?
b. Jerry likes the Taguchi Quality Loss function, but he believes that a linear function would better represent the cost of quality. Specifically, Jerry prefers a loss function of the form: L = T×|D|, where L, D, and T have the same definitions as in the Taguchi model. What would be the quality cost of the sample of 4 units using Jerry’s model?
2. (13 points) Johnson Company produces plastic bottles to customer order. The quality inspector randomly selects four bottles from the bottle machine and measures the outside diameter of the bottle neck, a critical quality dimension that determines whether the bottle cap will fit properly. The dimensions (in.) from the last six samples are provided below.
BOTTLE
Sample
1
2
3
4
1
0.601
0.612
0.575
0.600
2
0.597
0.601
0.608
0.605
3
0.581
0.550
0.585
0.597
4
0.630
0.605
0.595
0.577
5
0.598
0.624
0.608
0.604
6
0.585
0.580
0.620
0.579
a. What are the control limits for the R chart?
b. What are the control limits for the x-bar chart?
c. Is the process in control?