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Statistical Process Controls: Please solve and submit the following questions (50 points). 1. A major record-of-the-month club collected data on the reasons for returned shipments during a quarter. Results are: wrong selection, 50,000; refused, 195,000; wrong address, 68,000; order canceled, 5,000; and other, 15,000. Construct a Pareto diagram and recommend what are the major problems that demand investment. The diagram shows that most of the problems came from the refused and the wrong address. I would put forth most of the effort in fixing these two areas. 2. Calculate the average, median, mode, range, and standard deviation for each group of numbers. (a) 50, 45, 55, 55, 45, 50, 55, 45, 55 (b) 89,87,88,83,86,82,84 (c) 11,17,14,12,12,14,14,15,17,17 (d) 16,25,18,17,16,21,14 (e) 45,39,42,42,43 Descriptive Statistics: C1, C2, C3, C4, C5 Variable C1 C2 C3 C4 C5 N 9 7 10 7 5 N* 0 0 0 0 0 Mean 50.56 85.571 14.300 18.14 42.200 SE Mean 1.55 0.997 0.700 1.40 0.970 StDev 4.64 2.637 2.214 3.72 2.168 Minimum 45.00 82.000 11.000 14.00 39.000 Q1 45.00 83.000 12.000 16.00 40.500 Median 50.00 86.000 14.000 17.00 42.000 Q3 55.00 88.000 17.000 21.00 44.000 Variable C1 C2 C3 C4 C5 Maximum 55.00 89.000 17.000 25.00 45.000 3. Control charts for X and R are to be established on a certain dimension part, measured in millimeters. Data were collected in subgroup sizes of 6 and are given below. Calculate the trial central line and control limits. Assume assignable causes and revise the central line and limits. ----------------------------------------------------------------------------------------------------------Subgroup Subgroup Number X R Number X R -----------------------------------------------------------------------------------------------------------1 20.35 0.34 14 20.41 0.36 2 20.40 0.36 15 20.45 0.34 3 20.36 0.32 16 20.34 0.36 4 20.65 0.36 17 20.36 0.37 5 20.20 0.36 18 20.42 0.73 6 20.40 0.35 19 20.50 0.38 7 20.43 0.31 20 20.31 0.35 8 20.37 0.34 21 20.39 0.38 9 20.48 0.30 22 20.39 0.33 10 20.42 0.37 23 20.40 0.32 11 20.39 0.29 24 20.41 0.34 12 20.38 0.30 25 20.40 0.30 13 20.40 0.33 ----------------------------------------------------------------------------------------------------------- 4. The following table gives the average and range in kilograms for tensile tests on an improved plastic cord. The subgroup size is 4. Determine the trial central line and control limits. If any points are out of control, assume assignable causes, and determine the revised limits and central line. 5. The Get-Well Hospital has completed a quality improvement project on the time to admit a patient using: XC- and R charts. They now wish to monitor the activity using median and range charts. Determine the central line and control limits with the latest data in minutes, as given here. 6. The viscosity of a liquid is checked every half hour during one three-shift day. What does the run chart indicate? Data are 39, 42,38,37,41,40,36,35,37,36, 39,34,38,36,32,37,35,34,33,35,32,38,34,37,35,35, 34, 31, 33, 35, 32, 36,31,29,33,32,31,30,32, and 29. The viscosity of the liquid breaks down over time from shift to shift it keeps degrading 7. Determine the trial central line and control limits for a p chart using the following data, which are for the payment of dental insurance claims. Plot the values on graph paper and determine if the process is stable. If there are any out -of-control points, assume an assignable cause and determine the revised central line and control limits. P Chart of C1 0.07 1 0.06 Proportion 0.05 0.04 UCL=0.04016 0.03 _ P=0.01747 0.02 0.01 0.00 LCL=0 1 3 5 7 9 11 13 15 17 19 21 23 25 Sample As you can see the subgroup number 5 is out of the control limits. P Chart of C1 0.04 UCL=0.03676 Proportion 0.03 0.02 _ P=0.01542 0.01 0.00 LCL=0 1 3 5 7 9 11 13 15 17 19 Sample Here is the new chart with out of control point taken out. 21 23 8. Determine the trial limits and revised control limits for a u chart using the data in the table for the surface finish of rolls of white paper. Assume any out -of-control points have assignable causes. U Chart of C1 1 UCL=5.028 Sample Count Per Unit 5 4 _ U=3.304 3 2 LCL=1.579 1 1 1 0 1 4 7 10 13 16 19 Sample As you can see there are 3 points out of control 22 25 28 U Chart of C1 5.5 UCL=5.169 Sample Count Per Unit 5.0 4.5 4.0 _ U=3.416 3.5 3.0 2.5 2.0 LCL=1.663 1.5 1 3 5 7 9 11 13 15 17 19 21 23 25 Sample Here is the chart with the points taken out 9. A quality technician has collected data on the count of rivet nonconfonnities in four meters travel trailers. After 30 trailers, the total count of nonconfonnities is 316. Trial control limits have been determined and a comparison with the data shows no out-of-control points. What is the recommendation for the central line and the revised control limits for a count of nonconformities chart? Since there are no out of control points the process seems to be in control and the process should continue. 10. By means of a scatter diagram, determine if a relationship, exists between product temperatures and percent foam for a soft drink. From the look of the graph the data indicates that there is a correlation between the temperature and the percentage of foam in the product. For some reason I could not get the graph to upload to the doc.