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S6.11 Twelve samples, each containing five parts, were taken - from a process that produces steel rods. The length of each rod in the samples was determined. The results were tabulated and sample means and ranges were computed. The results were: SAMPLE SAMPLE MEAN (in.) RANGE (in.) 1 10.002 0.011 2 10.002 0.014 3 9.991 0.007 4 10.006 0.022 5 9.997 0.013 6 9.999 0.012 7 10.001 0.008 8 10.005 0.013 9 9.995 0.004 10 10.001 11 0.011 10.001 12 0.014 10.006 0.009 a) Determine means for the upper and lower control limits and the overall x-charts and R-charts. b) Draw ranges. the charts and plot the values of the sample means c) d) Do Why the data indicate a process that is in control? and or why not? S6.23 The school board is trying to evaluate a new math program introduced to second-graders 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: SCHOOL NO. OF TEST ERRORS A 52 B 27 C 35 D 44 E 55 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? Px S6.27 Meena Chavan Corp.'s computer chip production pro- cess yields DRAM chips with an average life of 1,800 hours and O = 100 hours. The tolerance upper and lower specification limits are 2,400 hours and 1,600 hours, of producing DRAM chips to specification? Px respectively. Is this process capable S6.35 One of New England Air's top competitive pli- orities is on-time arrivals. Quality VP Clair Bond decided to person- ally monitor New England Air's performance. Each week for the past 30 weeks, Bond checked a random sample of 100 flight arrivals for of on-time performance. The table that follows contains the number flights that did not meet New England Air's definition of "on time": LATE SAMPLE LATE SAMPLE (WEEK) (WEEK) FLIGHTS FLIGHTS 2 16 2 1 4 17 3 2 18 7 3 10 19 3 4 4 1 20 2 5 6 1 21 3 7 13 22 7 8 9 23 4 11 24 3 9 10 25 2 3 26 2 11 4 27 12 13 2 28 1 14 2 29 3 8 30 4 15 a) Using a 95% confidence level, plot the overall percentage of late flights (p) and the upper and lower control limits on a control 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 samples fall within New England Air's control limits? When one falls out- side the control limits, what should be done? d) What can Clair Bond report about the quality of service? Px

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