Pandra Manufacturing specifies the quality characteristic of one of its popular products to be 0.500 $\pm$ 0.020.An analysis of company records for the last two years suggests that the average cost for warranty repair or replacement is $125 per unit.The customer service manager is of the opinion that the product is likely to fail during the warranty period when the quality characteristic differs from the target by more than 0.020 in either direction.
Required: To gain a better understanding of the impact of quality variation,you,the product manager,would like to know the following values in a Taguchi loss function,L(x).
(1)Cost coefficient,k.
(2)Estimated losses,L(x),when the actual quality characteristic,x,is 0.505.
(3)Estimated losses,L(x),when the actual quality characteristic,x,is 0.510.
(4)The amount of change in the estimated losses when the deviation from the quality characteristic doubled.

Question

Pandra Manufacturing specifies the quality characteristic of one of its popular products to be 0.500  $\pm$ 0.020.An analysis of company records for the last two years suggests that the average cost for warranty repair or replacement is $125 per unit.The customer service manager is of the opinion that the product is likely to fail during the warranty period when the quality characteristic differs from the target by more than 0.020 in either direction.
Required: To gain a better understanding of the impact of quality variation,you,the product manager,would like to know the following values in a Taguchi loss function,L(x).
(1)Cost coefficient,k.
(2)Estimated losses,L(x),when the actual quality characteristic,x,is 0.505.
(3)Estimated losses,L(x),when the actual quality characteristic,x,is 0.510.
(4)The amount of change in the estimated losses when the deviation from the quality characteristic doubled.

Quizplus · Accepted Answer

Feedback: (1)Cost coefficient,k = Total quality cost/(Tolerance allowed)² = $125/0.020² = $125/0.004 = $312,500 (2)The loss function is: L(x)= $312,500 [(x - 0.500)²].When the actual quality characteristic is 0.505,the departure from target is 0.005,and the estimated loss is L(0.505)= $312,500 [(0.505 - 0.500)²]= $7.8125 (3)When the actual quality characteristic is 0.510,the departure from target is 0.010,and the estimated loss,L(0.510)= $312,500 [(0.510 - 0.500)²]= $31.25 (4)The loss function,L(x),is a quadratic function.As shown below,the estimated loss when the actual quality characteristic is 0.510 is four times of the amount when the actual quality characteristic is 0.505: 11ea6e70_bd58_8992_8f54_1f0f7a985fa8_TB1699_00

Pandra Manufacturing Specifies the Quality Characteristic of One of Its ±\pm±

Pandra Manufacturing Specifies the Quality Characteristic of One of Its $\pm$