Taguchi Loss Function Analysis (Appendix) North Platt Machinery Company manufactures a shaft that must fit inside a sleeve. The firm has just received an order of 50,000 units from South- ernstar Exploration Company for $80 per unit. North Platt can manufacture the shaft at $50 per unit. Southernstar desires the diameter of the shaft to be 1.275 cm. The diameter of the shaft must not be less than 1.25 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 1.30 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 $70. Shown below are the diameters from a sample of 80 shafts manufactured during a trial run.
|
Diameter
|
Number of Units
|
Diameter
|
Number of Units
|
Diameter
|
Number of Units
|
|
1.232
|
1
|
1.273
|
6
|
1.292
|
2
|
|
1.240
|
2
|
1.274
|
7
|
1.293
|
1
|
|
1.250
|
3
|
1.275
|
18
|
1.294
|
4
|
|
1.258
|
2
|
1.276
|
8
|
1.298
|
2
|
|
1.262
|
2
|
1.277
|
5
|
1.300
|
2
|
|
1.270
|
3
|
1.280
|
2
|
1.304
|
1
|
|
1.272
|
6
|
1.288
|
2
|
1.320
|
1
|
Required: Set up an Excel spreadsheet that uses a Taguchi loss function to determine:
1. The expected loss from this process.
2. The diameter tolerance that should be set for the manufacture of the shaft.