Answered: (a) Check that the system is still…

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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Transcribed Image Text:4. A soda drink bottling company is interested in winning a contract with a popular drink brand. To win the contract the company must show that it is capable of meeting 6o quality. The contract is for the production of 355mL cans, for which a tolerance of +0.5mL is specified. The company believes the facility is in statistical control and has calculated a global value of R 0.15mL and 355.025mL for its production system. The com- pany ran a capability test by obtaining 10 samples (each of 8 elements) on which capability calculations will be performed. The data obtained is in the following table: Sample R Sample F R 0.18319 354.98938 0.15714 355.02304 B 0.15361 355.01149 G 0.19205 355.06814 0.14892 355.00997 H 0.16240 355.05145 0.19912 355.01490 I 0.19179 355.00207 E 0.18389 355.04694 J 0.11900 355.02327 The parameters A2, D3 and D4 for various n are shown in the following table. A2 2 1.880 3.268 3 1.023 2.574 4 0.729 2.282 5 0.577 2.115 6 0.483 2.004 D3 D3 0.419 1.924 0.076 A2 D4 0. 7. 8 0.373 1.864 0.136 9 0.337 1.816 0.184 10 0.308 1.777 0.223

(a) Check that the system is still under statistical control by obtaining UCLR
and LCLR. Is the machine variability under control?
(b) Calculate UCL, and LCLp. Is the machine mean under control?
(c) Considering the required client specifications and that o = 0.05776mL,
calculate C, and Cpk. Is the system capable with 6ơ quality?
(d) The company is proud of its production facility and wants to promote
itself to other drink brands. To do this it believes that it can claim that it
is capable of producing a tolerance of +0.25mL with 60 quality. Given
0.05776mL, calculate the tightest tolerance that will still
provide 60 quality to check if the claim can be made by the company.
a tested o

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