Suppose that a metal rod is supposed to be cut 316mm in leng

Suppose that a metal rod is supposed to be cut 31.6mm in length. The upper spec limit is set at 32.4mm, and the lower spec limit set at 30.8mm. A metal rod that is out of spec must be tossed at a cost of $26.00. The company uses the Taguchi Quality Loss Function to estimate quality losts. Suppose that a sample of 4 units was taken, and the rod measurements were: 31.5, 32.3, 31.3, and 31.1mm, respectively.

Jerry likes the Taguchi Quality Loss Function, but he belives that a linear function would be better represent the cost of quality. Specifically, Jerry prefers a loss function of the form: L=T x |D|, where L, D, and T have the same defintions as in the Taguchi model. What would be the quality cost of sample of 4 units using Jerry\'s model?

Solution

T = target value = 31.6

|D| = absolute deviation from target value = |31.6-31.5| + |31.6-32.3| + |31.6-31.3| + |31.6-31.1| = 1.6

Given model is, L = T |D| = 31.6 * 1.6 = 50.56