Homework SourseSuppose that a metal rod is supposed to be cut 316 mm in len
Suppose that a metal rod is supposed to be cut 31.6 mm. in length. The upper spec limit is set at 32.4 mm., and the lower spec limit set at 30.8 mm. A metal rod that is out of spec must be scrapped at a cost of $26.00. The company uses the Taguchi Quality Loss Function to estimate quality costs. Suppose that a sample of 5 units was taken, and the rod measurements were: 31.5, 32.3, 31.3, 33.1 and 31.1 mm., respectively. 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 5 units? Alternatively, 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 times |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 5 units using Jerry\'s model? Dakota 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 seven samples are provided below. What are the control limits for the R chart? What arc the control limits for the bar x chart? Is the process in control?
Solution
a) We have a sample of 5 units.
Metal rod that is out of spec has the cost, C = $26.
We are given with following information:
Now we will calculate K = C / d2
d = 5 units
K = 26 / 25 = $1.04 per unit
The quality cost for the given sample can be calculated as:
The metal rod is supposed to be cut 31.6 mm, let say, t.
Now we will calculate the average of (y - t)2 as follows:
Now calculate K * (y - t)2 where K = 1.04:
Therefore Total Quality Cost = Avg (y - t)2 * Sum(K * (y - t)2)
=> Total Quality Cost = 0.618 * 3.2136 = $ 1.9860048
| Sample | Rod Measurement |
| 1 | 31.5 |
| 2 | 32.3 |
| 3 | 31.3 |
| 4 | 33.1 |
| 5 | 31.1 |
