cHAPTER 5 6 [PDF]

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Mary Beth Marrs, the manager of an apartment complex, feels overwhelmed by the num complaints she is receiving. Below is the check sheet she has kept for the past 12 weeks Develop a Pareto chart using this information. What recommendations would you make



WEEK 1 2 3 4 5 6 7 8 9 10 11 12 Total



PARKING/ DRIVES 2 3 3 4 3 4 3 4 2 4 3 3



GROUNDS 3 1 3 1 2 1 1 1 1 2 16



TENANT ISSUES 3 2 1 1 2



POOL 1 2 2 1 4 2 2 2 1 2 2 3 38



ELECTRICAL/ PLUMBING 1 2



2 3



1



2 1 1 24



18



4



This chart isn't available in your version of E



Number of Area of Complaints Complaints Percentage Grounds 16 16% Parking/Drives Pool Tenant Issues Electrical/ Plumbing Total



38 24 18 4 100



38% 24% 18% 4%



Editing this shape or saving this workbook i chart.



erwhelmed by the number of for the past 12 weeks. tions would you make?



WEEK 1 2 3 4 5 6 7



8 9 10 11 12



GROUNDS ✓✓✓ ✓ ✓✓✓ ✓ ✓✓ ✓



✓ ✓ ✓ ✓✓



available in your version of Excel.



pe or saving this workbook into a different file format will permanently break the



PARKING/ DRIVES ✓✓ ✓✓✓ ✓✓✓ ✓✓✓✓ ✓✓✓ ✓✓✓✓ ✓✓✓



✓✓✓✓ ✓✓ ✓✓✓✓ ✓✓✓ ✓✓✓



POOL ✓ ✓✓ ✓✓ ✓ ✓✓✓✓ ✓✓ ✓✓



✓✓ ✓ ✓✓ ✓✓ ✓✓✓



TENANT ISSUES ✓✓✓ ✓✓ ✓ ✓ ✓✓



ELECTRICAL/ PLUMBING ✓ ✓✓



✓✓



✓✓✓ ✓✓ ✓ ✓



✓



Twelve samples, each containing five parts, were taken from a process that produces ste rods at Emmanuel Kodzi’s factory. The length of each rod in the samples was determine The results were tabulated and sample means and ranges were computed. The results were: a) Determine the upper and lower control limits and the overall means for x -charts and -charts. b) Draw the charts and plot the values of the sample means and ranges. c) Do the data indicate a process that is in control? d) Why or why not?



A B



UCL=



10.0071



LCL=



9.9939



10.01 10.0071 10.005



10.006



10.006



10.005



10.002 10.002 10



10.001



10.001 10.001



9.999



Colum 10.007 9.9939



9.997



9.995



9.995



9.9939 9.99



9.991



9.985



9.98



1



2



3



4



5



6



7



8



9



10



11



12



m a process that produces steel in the samples was determined. ere computed. The results



erall means for x -charts and R



s and ranges.



C 10.006



10.001 10.001 Column L 10.0071 9.9939



995



9



SAMPLE 1 2 3 4 5 6 7 8 9 10 11 12 Total Average



10



11



12



D



SAMPLE MEAN(in.) RANGE (in.) 10.002 0.011 10.002 0.014 9.991 0.007 10.006 0.022 9.997 0.013 9.999 0.012 10.001 0.008 10.005 0.013 9.995 0.004 10.001 0.011 10.001 0.014 10.006 0.009 120.006 0.138 10.0005 0.0115



Jamison Kovach Supply Company manufactures paper clips and other office products. Although inexpen-sive, paper clips have provided the firm with a high margin of profita Sample size is 200. Results are given for the last 10 samples: a) Establish upper and lower control limits for the control chart and graph the data. b) Has the process been in control? c) If the sample size were 100 instead, how would your limits and conclusions change?



SAMPLE DEFECTIVES



A



SAMPLE 1 2 3 4 5 6 7 8 9 10 AVERAGE



1 5



2 7



3 4



DEFECTIVES SAMPLE SIZE 5 200 7 200 4 200 4 200 6 200 3 200 5 200 6 200 2 200 8 200



PROPORTION UCL 0.025 0.058 0.035 0.058 0.02 0.058 0.02 0.058 0.03 0.058 0.015 0.058 0.025 0.058 0.03 0.058 0.01 0.058 0.04 0.058 0.025



=0.025+3 √((0.025)(1−0.025))/200



UCL= 0.058 =0.025−3 √((0.025)(1−0.025))/200



LCL=



(-0.008)



Chart Title 0.07 0.06 0.05 0.04 0.03 0.02 0.01 0



4 4



0.07 0.06 0.05 0.04 0.03 0.02 0.01 0 -0.01



1



2



3



4



5



6



7



-0.02 PROPORTION



UCL



LCL



8



9



10



nd other office products. h a high margin of profitability.



t and graph the data.



and conclusions change?



5 6



LCL -0.008 -0.008 -0.008 -0.008 -0.008 -0.008 -0.008 -0.008 -0.008 -0.008



6 3



7 5



B C



8 6



9 2



10 8



This process has been under control.



SAMPLE 1 2 3 4 5 6 7 8 9 10 Average



DEFECTIVES SAMPLE SIZE PROPORTION 5 100 0.05 7 100 0.07 4 100 0.04 4 100 0.04 6 100 0.06 3 100 0.03 5 100 0.05 6 100 0.06 2 100 0.02 8 100 0.08 0.05 =0.05+3 √((0.05)(1−0.05))/100



UCL 0.115 LCL



=0.05−3 √((0.05)(1−0.05))/100



C



(-0.015) 0.14 0.12 0.1



C 0.14 0.12 0.1 8



9



10



0.08 0.06 0.04 0.02 0



1



2



3



4



-0.02 -0.04



PROPOR



UCL 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115 0.115



LCL -0.015 -0.015 -0.015 -0.015 -0.015 -0.015 -0.015 -0.015 -0.015 -0.015



Chart Title



1



Chart Title



2



3



4



5



PROPORTION



6



UCL



7



LCL



8



9



10



The school board is trying to evaluate a new math program introduced to second-grader in five elementary schools across the county this year. A sample of the student scores on standardized math tests in each elementary school yielded the fol-lowing data: Construct a c -chart for test errors, and set the control limits to contain 99.73% of the random variation in test scores. What does the chart tell you? Has the new math program been effective?



Chart Title 70 60 50 40 30 20 10 0 cbar=



LCL=



UCL=



introduced to second-graders mple of the student scores on the fol-lowing data: s to contain 99.73% of the u? Has the new math program



SCHOOL A B C D E



cbar= LCL= UCL=



UCL=



# OF TEST ERRORS 52 27 35 44 55 213 42.6 23.02 62.18



One of New England Air’s top competitive priorities is on-time arrivals. Quality VP Cla Bond decided to personally monitor New England Air’s performance. Each week for the past 30 weeks, Bond checked a random sample of 100 flight arrivals for on-time performance. The table that follows contains the number of flights that did not meet New England Air’s definition of “on time”: a) Using a 95% confidence level, plot the overall percentage of late flights ( p ) and the upper and lower control limits on a con-trol chart. b) Assume that the airline industry’s upper and lower control limits for flights that are not on time are .1000 and .0400, respectively. Draw them on your control chart. c) Plot the percentage of late flights in each sample. Do all sam-ples fall within New England Air’s control limits? When one falls outside the control limits, what should be done? d) What can Clair Bond report about the quality of service?



time arrivals. Quality VP Clair rformance. Each week for the ht arrivals for on-time f flights that did not meet New



ge of late flights ( p ) and the



rol limits for flights that are on your control chart. sam-ples fall within New ontrol limits, what should be



?



SAMPLE (WEEKS) 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15



LATE FLIGHTS 2 4 10 4 1 1 13 9 11 0 3 4 2 2 8



SAMPLE (WEEKS) 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30



LATE FLIGHTS 2 3 7 3 2 3 7 4 3 2 2 0 1 3 4



Meena Chavan Corp.’s computer chip production process yields DRAM chips with an average life of 1,800 hours and s=100 hours. The tolerance upper and lower specificatio limits are 2,400 hours and 1,600 hours, respectively. Is this pro-cess capable of producin DRAM chips to specification?



USL= LSL= x=



2,400 1,600 1,800 100 hrs Cp



800/(6*100) 1.33



yields DRAM chips with an upper and lower specification pro-cess capable of producing