Problem 2. A thickness specification is 760+20 mm, and the loss (A) when a unit

Question

Problem 2. A thickness specification is 760+20 mm, and the loss (A) when a unit is out of specification is ¥ 300, A sample of 10 units exhibited the following deviation from target value. 5, 1,2,3, 4,8, 5,3, 6,0 Average deviation = (VM): 3.70 On-1-2.406 VarianceOn-1=5.79 Compare the two types of quality loss: 1) continuing with the present process 2) setting the mean to the target value, 3) narrowing the distribution to zero (sigma = 0). HINT use Loss Function (L) for part 1 = A * [0n-12 + (Y-M) 2] = 300/202 *(2.4062 + 3.72) For part 2, set Y-M-0 and for part 3 set o- 0; and calculate the Loss function (C)

Explanation / Answer

(1) Total loss when continuin with the present process that means we will have to book loss because Variance from the mean value and then deviation from specification value.

Here L = A * [2 n-1 + (Y - M)2 ] = 300/202 * [2.4062 + 3.72] = 14.61 pound

(2) In this case we set the mean to the target value so that will reduce the losses due to difference with specification value.

Here L = A * 2 n-1 = 300/202 * (2.406)2 = 4.3416 pound

(3) In this case we will narrow the distribution by giving variance = 0 and losses only due to mean difference shall be there

L = A * (Y - m)2 = 300/202 * (3.70)2 = 10.2675 pound

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