Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-umit production run in the following situations. (a) The process standard deviation is 0.15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be dassified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number. Probability of a defect: 0.3173 Number of defects: 317 (b) Through process design improvements, the process standard deviation can be reduced to 0.05. Assume that the process control remains the same, with weights less than 9.85 or greater than 10,15 ounces being classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number Probability of a defect Number of defects: 31.74 () What is the advantage of reducing process varation, thereby causing process control lenits to be at a greater number of standarnd deviations from the mean? Reducing the process standard deviation couses a substantial decrease in the number of defects
Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-umit production run in the following situations. (a) The process standard deviation is 0.15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15 ounces will be dassified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number. Probability of a defect: 0.3173 Number of defects: 317 (b) Through process design improvements, the process standard deviation can be reduced to 0.05. Assume that the process control remains the same, with weights less than 9.85 or greater than 10,15 ounces being classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest whole number Probability of a defect Number of defects: 31.74 () What is the advantage of reducing process varation, thereby causing process control lenits to be at a greater number of standarnd deviations from the mean? Reducing the process standard deviation couses a substantial decrease in the number of defects
Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter16: Probabilistic Inventory Models
Section16.6: The Eoq With Uncertain Demand: The (r, Q) And (s, S) Models
Problem 1P
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Transcribed Image Text:Suppose that Motorola uses the normal distribution to determine the probability of defects and the number of defects in a particular production process. Assume that the
production process manufactures items with a mean weight of 10 ounces. Calculate the probability of a defect and the suspected number of defects for a 1,000-umit
production run in the following situations.
(a) The process standard deviation is 0.15, and the process control is set at plus or minus one standard deviation. Units with weights less than 9.85 or greater than 10.15
ounces will be classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the number of defects to the nearest
whole number.
Probability
of a defect:
0.3173
Number of defects:
317
(b) Through process design improvements, the process standard deviation can be reduced to 0.05. Assume that the process control remains the same, with weights less
than 9.85 or greater than 10,15 ounces being classified as defects. If required, round your answer for the probability of a defect to four decimal places and for the
number of defects to the nearest whole number
Probability of a defect
Number of defects
31.74
() What is the advantage of reducing process vanation, thereby causing process control lenits to be at a greater number of standarnd deviations from the mean?
Reducing the process standard deviation .couses a substantial decrease
in the number of defects
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