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Specifications for a part for a 3-D printer state that the part should weigh between 24 and 25 ounces. The process that produces the parts has a mean of 24.5 ounces and a standard deviation of .2 ounce. The distribution of output is normal. What percentage of parts will not meet the weight specs? Within what values will 95.44 percent of the sample means of this process fall if samples of n = 16 are taken and the process is in control (random)? Using the control limits from part b, would the following sample means be in control? 24.52, 24.53, 24.44, 24.51, 24.41, 24.39 An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approxi- mately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control. Given the following sample means—1.005, 1.001, .998, 1.002, .995, and .999—is the process in control? Is the process in control given the following sample means—1.003, .999, .997, 1.001, 1.002, .998, and 1.004?

Specifications for a part for a 3-D printer state that the part should weigh between 24 and 25 ounces. The process that produces the parts has a mean of 24.5 ounces and a standard deviation of .2 ounce. The distribution of output is normal. What percentage of parts will not meet the weight specs? Within what values will 95.44 percent of the sample means of this process fall if samples of n = 16 are taken and the process is in control (random)? Using the control limits from part b, would the following sample means be in control? 24.52, 24.53, 24.44, 24.51, 24.41, 24.39 An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approxi- mately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control. Given the following sample means—1.005, 1.001, .998, 1.002, .995, and .999—is the process in control? Is the process in control given the following sample means—1.003, .999, .997, 1.001, 1.002, .998, and 1.004?

Practical Management Science
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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  1. Specifications for a part for a 3-D printer state that the part should weigh between 24 and
    25 ounces. The process that produces the parts has a mean of 24.5 ounces and a standard deviation of .2 ounce. The distribution of output is normal.
    1. What percentage of parts will not meet the weight specs?
    2. Within what values will 95.44 percent of the sample means of this process fall if samples of

n = 16 are taken and the process is in control (random)?

  1. Using the control limits from part b, would the following sample means be in control? 24.52,

24.53, 24.44, 24.51, 24.41, 24.39

  1. An automatic filling machine is used to fill 1-liter bottles of cola. The machine’s output is approxi- mately normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations.
    1. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control.
    2. Given the following sample means—1.005, 1.001, .998, 1.002, .995, and .999—is the process in control?
    3. Is the process in control given the following sample means—1.003, .999, .997, 1.001, 1.002, .998, and 1.004?
AutoSave w- Operation hw 3 chegg - Saved to my Mac OFF Home Insert Draw Design Layout References Mailings Review View Acrobat Tell me Share Q Comments Calibri (Bo... A A Аa v E v E v E v 12 AaBbCcDdEe AaBbCcDdEe AaBbCcDc > Paste v ab x, x' A Αν Normal No Spacing Heading 1 Styles Dictate Sensitivity Editor Create and Share Adobe PDF Request Signatures В I Pane * Office Update To keep up-to-date with security updates, fixes, and improvements, choose Check for Updates. Check for Updates Specifications for a part for a 3-D printer state that the part should weigh between 24 and 25 ounces. The process that produces the parts has a mean of 24.5 ounces and a standard deviation of .2 ounce. The distribution of output is normal. 1. What percentage of parts will not meet the weight specs? Within what values will 95.44 percent of the sample 1. 2. of this process fall if samples of n = 16 are taken and the process is in control (random)? 3. Using the control limits from part b, would the following sample means be in control? 24.52, 24.53, 24.44, 24.51, 24.41, 24.39 2. An automatic filling machine is used to fill 1-liter bottles of cola. The machine's output is anproxi- mately.normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations. 1. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control. Given the following sample means-1.005, 1.001,.998, 1.002, .995, and .999–is the process in control? Is the process in control given the following sample means-1.003, .999, .997, 1.001, 1.002, .998, and 1.004? 2. 3. 24. Each of the processes listed is non-centered with respect to the specifications for that process. Compute the appropriate capability index for each, and decide if the process is capable. 7ITIT Process Mean Standard Deviation Lower Spec Upper Spec H 15.0 0.32 14.1 16.0 7. The postmaster of a small western town receives a certain number of complaints each day about mail delivery. Determine three-sigma control limits using the following data. Is the process in control? K 33.0 1.00 30.0 36.5 18.5 0.40 16.5 20.1 DAY 25. An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis. 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 1 2 4 5 6 7 8 10 11 12 13 14 repair time of 74 minutes with a standard deviation of 4.0 minutes and the other firm had a Number of complaints 4 10 14 8 9. 6. 12 13 7 6 4 10 mean repair time of 72 minutes with a standard deviation of 5.1 minutes. Which firm would you choose? Why? 20. A teller at a drive-up window at a bank had the following service times (in minutes) for 20 random selected customers. SAMPLE 1 2 4 4. Software upgrade times (in minutes) are being evaluated. Samples of five observations each have been taken, and the results are as listed. Using factors from Table 10.3, determine upper and lower control limits for mean and range charts, and decide if the process is in control. 4.5 4.6 4.5 4.7 4.2 4.5 4.6 4.6 4.2 4.4 4.4 4.8 4.3 4.7 4.4 4.5 4.3 4.3 4.6 4.9 SAMPLE a. Determine the mean of each sample. b. If the process parameters are unknown, estimate its mean and standard deviation. 1 2 3 4 6 c. Estimate the mean and standard deviation of the sampling distribution. d. What would three-sigma control limits for the process be? What alpha risk would they provide e. What alpha risk would control limits of 4.14 and 4.86 provide? f. Using limits of 4.14 and 4.86, are any sample means beyond the control limits? If so, which one(s 79.2 80.5 79.6 78.9 80.5 79.7 78.8 78.7 79.6 79.4 79.6 80.6 80.0 81.0 80.4 79.7 80.4 80.5 g. Construct control charts for means and ranges using Table 10.3. Are any samples beyond the control limits? If so, which one(s)? h. Explain why the control limits are different for means in parts d and g. 78.4 80.4 80.3 79.4 80.8 80.0 i. If the process has a known mean of 4.4 and a known standard deviation of .18, what would three-sigma control limits be for a mean chart? Are any sample means beyond the control limits? If so, which one(s)? 81.0 80.1 80.8 80.6 78.8 81.1 Zoom 211 words English (United States) Focus 100%
Transcribed Image Text:AutoSave w- Operation hw 3 chegg - Saved to my Mac OFF Home Insert Draw Design Layout References Mailings Review View Acrobat Tell me Share Q Comments Calibri (Bo... A A Аa v E v E v E v 12 AaBbCcDdEe AaBbCcDdEe AaBbCcDc > Paste v ab x, x' A Αν Normal No Spacing Heading 1 Styles Dictate Sensitivity Editor Create and Share Adobe PDF Request Signatures В I Pane * Office Update To keep up-to-date with security updates, fixes, and improvements, choose Check for Updates. Check for Updates Specifications for a part for a 3-D printer state that the part should weigh between 24 and 25 ounces. The process that produces the parts has a mean of 24.5 ounces and a standard deviation of .2 ounce. The distribution of output is normal. 1. What percentage of parts will not meet the weight specs? Within what values will 95.44 percent of the sample 1. 2. of this process fall if samples of n = 16 are taken and the process is in control (random)? 3. Using the control limits from part b, would the following sample means be in control? 24.52, 24.53, 24.44, 24.51, 24.41, 24.39 2. An automatic filling machine is used to fill 1-liter bottles of cola. The machine's output is anproxi- mately.normal with a mean of 1.0 liter and a standard deviation of .01 liter. Output is monitored using means of samples of 25 observations. 1. Determine upper and lower control limits that will include roughly 97 percent of the sample means when the process is in control. Given the following sample means-1.005, 1.001,.998, 1.002, .995, and .999–is the process in control? Is the process in control given the following sample means-1.003, .999, .997, 1.001, 1.002, .998, and 1.004? 2. 3. 24. Each of the processes listed is non-centered with respect to the specifications for that process. Compute the appropriate capability index for each, and decide if the process is capable. 7ITIT Process Mean Standard Deviation Lower Spec Upper Spec H 15.0 0.32 14.1 16.0 7. The postmaster of a small western town receives a certain number of complaints each day about mail delivery. Determine three-sigma control limits using the following data. Is the process in control? K 33.0 1.00 30.0 36.5 18.5 0.40 16.5 20.1 DAY 25. An appliance manufacturer wants to contract with a repair shop to handle authorized repairs in Indianapolis. 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 1 2 4 5 6 7 8 10 11 12 13 14 repair time of 74 minutes with a standard deviation of 4.0 minutes and the other firm had a Number of complaints 4 10 14 8 9. 6. 12 13 7 6 4 10 mean repair time of 72 minutes with a standard deviation of 5.1 minutes. Which firm would you choose? Why? 20. A teller at a drive-up window at a bank had the following service times (in minutes) for 20 random selected customers. SAMPLE 1 2 4 4. Software upgrade times (in minutes) are being evaluated. Samples of five observations each have been taken, and the results are as listed. Using factors from Table 10.3, determine upper and lower control limits for mean and range charts, and decide if the process is in control. 4.5 4.6 4.5 4.7 4.2 4.5 4.6 4.6 4.2 4.4 4.4 4.8 4.3 4.7 4.4 4.5 4.3 4.3 4.6 4.9 SAMPLE a. Determine the mean of each sample. b. If the process parameters are unknown, estimate its mean and standard deviation. 1 2 3 4 6 c. Estimate the mean and standard deviation of the sampling distribution. d. What would three-sigma control limits for the process be? What alpha risk would they provide e. What alpha risk would control limits of 4.14 and 4.86 provide? f. Using limits of 4.14 and 4.86, are any sample means beyond the control limits? If so, which one(s 79.2 80.5 79.6 78.9 80.5 79.7 78.8 78.7 79.6 79.4 79.6 80.6 80.0 81.0 80.4 79.7 80.4 80.5 g. Construct control charts for means and ranges using Table 10.3. Are any samples beyond the control limits? If so, which one(s)? h. Explain why the control limits are different for means in parts d and g. 78.4 80.4 80.3 79.4 80.8 80.0 i. If the process has a known mean of 4.4 and a known standard deviation of .18, what would three-sigma control limits be for a mean chart? Are any sample means beyond the control limits? If so, which one(s)? 81.0 80.1 80.8 80.6 78.8 81.1 Zoom 211 words English (United States) Focus 100%
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