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Internet Exercises 1. Visit http://www.qualitymag.com, search for “statistical quality control,” find an application, and summarize it. 2. Visit http://jobs.isixsigma.com, choose a job announce- ment related to Six Sigma quality, and describe the job description. 3. Visit http://www.inspection.gc.ca/about-the-cfia/news room/food-safety-system/haccp/eng/1346306502207 Problems 1. Design specification for a motor housing states that it \/ should weigh between 24 kg and 25 kg. The process that produces the housing yields a mean of 24.5 kg and a standard deviation of 0.2 kg. The distribution of output is Normal. a. What percentage of housings will not meet the design specification? b. Within what values should 95.44 percent of sam- ple means of this process fall if samples of n = 16 are taken?
3. Process time at & workstaion i © * om0 roge conem o Sonitored using sample Y observations have been o 5. Six samples of o incd. 10 and ranges computed (in minuteg), Sample means. Sample Maan Renge m 2 3 gg 3 U 1 4 an o4s b 308 046 s 309 oss 2. Using the fctos in Table 10-3, dtermne Jower lits o sample mean a rage m,.u:n"mm,‘w b. Is the process in control? 4. i samples of five observtions each @ of 80 kg concrte sabs produced by mm:n.vb-:muum results are displayed below, o . Usng factos fom Tabe 103, deermin e 08 loweecontol i o sample meanan o in control, and decide f the process s . A new sample resuls in the followin ing slab weights: 810,808,806, 805, Use th cont 0+ mined in parta to decide if the process s il Sample W T2 85 796 785 w05 o7 78 787 794 74 e 800 810 84 797 804 sos 784 804 803 794 808 o0 810 801 808 806 788 s ,/@ 8. 1In a refinery, the octane rating of gasoline produced is measured by taking one observation from each baich, Tweaty observations follow. 2. Construct Three Sigma control charts for the individ- ‘val unit and moving range. I the process in control?* b. A new batch has an octane rating of 94.0. Using the Chapter 10 Statistical Quallty Control 381 @ 6 Usiogfour camples o 20 crit cand et cachan v auditor found the following number of erroneous state- ments in cach sample: Momberoferos 4 2 5 o Soerofenos 4 2 5 9 - Determine the proportion of defectves in each sample. - Ifthe true proportion of defectives for this process is unknown, what s your best estimate of it? - Whatis your estimate of the mean and standard devia- tion of the sampling disribution of the sample propor- tion of defectives for samples of 2007 . What control limits would give an alpha risk of 0.03 forthis process? - Whatalpha risk would controllimits of 0.047 and 0.003 provide? 1. Using control limits of 0047 and 0.003, s the process in control? 9- Suppose that the long-term proportion of defectives of the process is known (0 be 2 percent. What ae the val- ves of the mean and standard deviation of the sam- pling distibution? h. Construct a p-control chart for the process, assuming & proportion of defcctives of 2 percent, and Two Sigma ‘controllimits. I the process in control? P v @ 7 Amedicalfacility does MRS or sport njuries. Occasion- ally atestyieldsinconclusive results and must be repeated. Using the following 13 sample results for the number of retests in n = 200 observations cach, consiruet a control chartfor the proportion of retests using Two Sigma limits. s the process in control? Sample 123456789 0nuean Number Amiasts 12 202152502 7 dBkd al controlcharts in part a, i th process sl in conwrol? /@) 8. The operations manager of a lage manufacturer rceived Observation Octane Number Rating Number Rating 1 802 " 884, 2 865 2 bord 3 884 B &1 4 o8 " sl s %03 3 s 6 o5 . 903 7 026 ” 8, [ 870 ® ) 5 iy w 821 0 52 20 858 @ certain number of complaints during the last two weeks. a. Construct a control chart with Three Sigma limits for the number of complaints received each day using the following data. Is the process in control? b 1616 complaints are received today (day 15),using the ontrol chart of part a i there a change i the average ‘mumber of complaints per day? Day 12345678 s0nunmn Number of Complaints 410 48 9652 B 7 6420 e Bl -l atas of Quality Control and Impeovement, 20d ed., Englewood it Preatice Hall, 1998,
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1. Using the control limts of 4, means beyond these cono] g. Construct the control char ple range using Table 1.3, 14and 486, o sample: lmits? 1f g, wigh one(s)? s for sampig s R T e Diagram for Probien 17 Chapter 10 Statistical Quality Control 383 1. Ifthe process has a known mean of 4.4 and a known standard deviation of 0.18, what would Three Sigma ontrol imits be for a sample mean chart? Are any sam- ple means beyond the control limits? If so, which one(s)? v@ 7. For each of the following control charts, analyze the data using both median and upklown run tesis with z = 1.96 limits. Are nonrandom variations present? Assume the centre line i the long-term median. ueL A = e ucL 8 Ler
9"30. The management of a dried milk manufacturer wanted to evaluate the process capability of its packaging lines. A can line was studied for weight of filled cans. The specification is 974 grams plus or minus 14 grams (including the weight of the can itself). Thirty-five samples of six cans were weighed, and sample mean and range were calculated. The process was in control. The grand mean was 975.7 grams and process standard deviation was 47581 grams. a. Calculate the C, and Cy ratios. Is the filling line capable? b. After changing the wearable parts of the line, includ- ing the piston cylinders, workers weighed 46 samples of six cans. The grand mean was 976.19 grams and process standard deviation was 2.891 grams. Calculate the new values of C, and Cy ratios. Has the filling line become capable?
+35. Stat-Ease Inc., the producer of a design of experiments @ software, performed an experiment 3 fey years ago to identify the factors that were important in increasing the response rate of engineers to Stat-Ease workshop announcements. The factors and their levels were; 5 Factor A: Number of colours (two vs, four) Factor B: Postcard size (4” x 6 vs. 5.5"x8.5") Factor C: Paper stock (index vs, heavyweight) Stat-Ease made eight types of its announcement postcard @ and sent each type to 1/8 of this mailing list of engineers. The levels of each type and number of fax responses received were: Factor A Factor C Number of Factor B Postcard Version Colours Postcard Size Thickness Response 1 2-colour (—) 4" x6"(-) Index(-) 34 4-colour (+) 4"x6"(-) Index(-) 18 2-colour (—) 5.5”x 85"(+) Index(-) 44 4-colour (+) 5.5” x 85"(+) Index (-) 26 2-colour (=) 4" x 6"(-) Heavyweight (+) 26 4-colour (+) 4" x 6"(-) Heavyweight (+) 17 2-colour (-) 55" x85"(+) Heavyweight (+) 29 4-colour (+) 5.5" x 85" (+) Heavyweight (+) 21 0w N o g s W N Determine the influence of each level of each factor on the response and prescribe the best levels for each factor. What do you recommend Stat-Ease should do?
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