North Platt Machinery Company manufactures a shaft that must fit inside a sleeve

Question

North Platt Machinery Company manufactures a shaft that must fit inside a sleeve. The firm has just received an order of 44,000 units from Southernstar Exploration Company for $52 per unit. North Platt can manufacture the shaft at $22 per unit. Southernstar desires the diameter of the shaft to be 1.290 cm. The diameter of the shaft must not be less than 1.265 cm, in order to fit properly inside the sleeve. To be able to insert the shaft into a sleeve without the use of force, the diameter cannot be larger than 1.315 cm. A defective shaft is discarded and a replacement has to be shipped via express freight to locations around the world. North Platt estimates that the average cost of handling and shipping a replacement shaft will be approximately $42. Shown below are the diameters from a sample of 100 shafts manufactured during a trial run. Set up an Excel spreadsheet that uses a Taguchi loss function to determine:

1. The expected loss from this process. (Do not round intermediate calculations. Round your answer to 2 decimal places.)

2. The diameter tolerance that should be set for the manufacture of the shaft. (Do not round intermediate calculations. Round your answer to 3 decimal places.)

Diameter Number of Units Diameter Number of Units Diameter Number of Units 1.247      2 1.288      7     1.307     3 1.255      3 1.289      8     1.308     2 1.265      4 1.290      18     1.309     5 1.273      3 1.291      9     1.313     3 1.277      3 1.292      6     1.315     3 1.285      4 1.295      3     1.319     2 1.287      7 1.303      3     1.335     2

Explanation / Answer

he Taguchi’s loss function for one piece of product is:

Loss in Dollars = Constant*(quality characteristic – target value)^2

The Average Taguchi loss per item for a sample set is

Loss in Dollars= Constant*(standard deviation^2+ (process mean –target value) ^2)

Diameter

Number of Units

1.247     

2

1.255     

3

1.265     

4

1.273     

3

1.277     

3

1.285     

4

1.287     

7

1.288     

7    

1.289     

8    

1.290     

18    

1.291     

9    

1.292     

6    

1.295     

3    

1.303     

3    

1.307    

3

1.308    

2

1.309    

5

1.313    

3

1.315    

3

1.319    

2

1.335    

2

Diameter

Number of Units

1.247     

2

1.255     

3

1.265     

4

1.273     

3

1.277     

3

1.285     

4

1.287     

7

1.288     

7    

1.289     

8    

1.290     

18    

1.291     

9    

1.292     

6    

1.295     

3    

1.303     

3    

1.307    

3

1.308    

2

1.309    

5

1.313    

3

1.315    

3

1.319    

2

1.335    

2

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