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Operations Management Ch 9 and 10 Homework

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Question;Chapter 91. Pepsi uses six-sigma technique to evaluate whether its 12 oz Gatorade has consistent weight. Pepsi took a sampling of 1000 12 oz Gatorade and found out that the average weight was 11.58 oz with a standard deviation of 0.3 oz. Pepsi considers a tolerance of ? 5% from 12 oz acceptable.a). What is the percentage of 12 oz Gatorade that meets the specification?b). What are the percentages of 12 oz Gatorade that are considered ?overweight? and ?underweight??c). If Pepsi improves its production process, and samples another 1000 bottles and finds a average weight of 12 oz with a standard deviation of 0.2 oz. What is the % of 12 oz Gatorade that meets the specification? What quality standard does this new process achieve (in terms of number of ?sigma?)?d) Following c, what is the standard deviation that Pepsi needs to achieve in order to achieve the 6-sigma standard without having to change the specification?Chapter 10 2. a. Following problem 1(a) from chapter 9. What is the process capability index (Cpk)? b. Following problem 1(c) from chapter 9. What is the process capability ratio (Cp)? 3. A process that produces computer chips has a mean of .04 defective chip and a standard deviation of .004 chip. The allowable variation is from .03 to .06 defective. The manufacturer aims to achieve performance of 3-??sigma standard. a. Compute the process capability ratio (Cp). b. Compute the process capability index (Cpk). c. Is the process capable? (meaning, does it fulfill 3-??sgima standard?) 4. An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in El Paso. The company has set an acceptable range of repair time of 50 minutes to 90 minutes. Two firms have submitted bids for the work. In test trials, one firm had a mean repair time of 69 minutes with a standard deviation of 6 minutes and the other firm had a mean repair time of 72 minutes with a standard deviation of 4 minutes. Using the process capability index (Cpk) to evaluation the firms? performances. a. Compute Cpk for firm 1 b. Compute Cpk for firm 2 c. Which firm has a better performance? 5. The Good Chocolate Company a 12-??ounce chocolate bar (340 grams). Specifications for the 12-??ounce bar are 330 grams to 350 grams. Based on sampling result, the company knows that the average fill is exactly 340 grams. a. Identify the largest standard deviation (in grams) the machine that fills the bar molds can have so that the process can be considered capable of achieving 3-??sigma standard (Hint: you use either Cp or Cpk to identify the sigma since the center is exactly at 340 grams.) b. Identify the largest standard deviation (in grams) the machine that fills the bar molds can have so that the process can be considered capable of achieving 4-??sigma standard.

 

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