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Suppose that we are making an auto part and that the mean length of the part is 5 inches with standard deviation of 0.25 inches, and the length is normally distributed. The upper pecification limit is 5.5 inches and the lower specification limit is 4.2 inches. The z-score table provided on the next page. a. What is the process capability index, Cpk? b. Under this process, what is the rate of defects per unit (DPU) and the defects per million units (DPMU)? c. If you have five auto parts made under this process, what is the probability that all five of them are not defective?

Suppose that we are making an auto part and that the mean length of the part is 5 inches with standard deviation of 0.25 inches, and the length is normally distributed. The upper pecification limit is 5.5 inches and the lower specification limit is 4.2 inches. The z-score table provided on the next page. a. What is the process capability index, Cpk? b. Under this process, what is the rate of defects per unit (DPU) and the defects per million units (DPMU)? c. If you have five auto parts made under this process, what is the probability that all five of them are not defective?

Practical Management Science
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
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2. Suppose that we are making an auto part and that the mean length of the part is 5 inches with a standard deviation of 0.25 inches, and the length is normally distributed. The upper specification limit is 5.5 inches and the lower specification limit is 4.2 inches. The z-score table is provided on the next page. a. What is the process capability index, Cpk? b. Under this process, what is the rate of defects per unit (DPU) and the defects per million units (DPMU)? c. If you have five auto parts made under this process, what is the probability that all five of them are not defective? d. Suppose you can modify the process to change the mean, while the standard deviation will remain the same. What should the mean be changed to, to minimize the DPU? What will be the DPU with this change?
Transcribed Image Text:2. Suppose that we are making an auto part and that the mean length of the part is 5 inches with a standard deviation of 0.25 inches, and the length is normally distributed. The upper specification limit is 5.5 inches and the lower specification limit is 4.2 inches. The z-score table is provided on the next page. a. What is the process capability index, Cpk? b. Under this process, what is the rate of defects per unit (DPU) and the defects per million units (DPMU)? c. If you have five auto parts made under this process, what is the probability that all five of them are not defective? d. Suppose you can modify the process to change the mean, while the standard deviation will remain the same. What should the mean be changed to, to minimize the DPU? What will be the DPU with this change?
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