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 Southernstar 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
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 Southernstar 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 quality loss function to determine:
1. The expected loss (total quality cost) per unit, E[L(x)], 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 4 decimal places.)
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