Statistical Process Controls: Please solve and submit the following questions (50 points).
- 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.
It does appear that communication is the largest issue in the organization. The customers are refusing their orders as 60% of our total losses because we are apparently not getting them proper service. We also have the wrong addresses for 20% of our customers with issues and 50,000 we have the wrong address for. Communication with the customer is apparently the largest flaw in need of most investment.
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
N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
C1 9 0 50.56 1.55 4.64 45.00 45.00 50.00 55.00 55.00
Variable Range
C1 10.00 MODE = 45
(b) 89,87,88,83,86,82,84
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
C1 7 0 85.571 0.997 2.637 82.000 83.000 86.000 88.000
Variable Maximum Range Mode = 83
C1 89.000 7.000
(c) 11,17,14,12,12,14,14,15,17,17
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
C1 10 0 14.300 0.700 2.214 11.000 12.000 14.000 17.000
Variable Maximum Range Mode
C1 17.000 6.000 13
(d) 16,25,18,17,16,21,14
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3 Maximum
C1 7 0 18.14 1.40 3.72 14.00 16.00 17.00 21.00 25.00
Variable Range mode
C1 11.00 17
(e) 45,39,42,42,43
Variable N N* Mean SE Mean StDev Minimum Q1 Median Q3
C1 5 0 42.200 0.970 2.168 39.000 40.500 42.000 44.000
Variable Maximum Range Mode
C1 45.000 6.000 42
- 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 aregiven below. Calculate the trial central line and control limits. Assume assignable causes and revise the central line and limits.
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Subgroup Subgroup
Number X R Number X R
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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
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- The following table gives the average and range in kilograms for tensile tests onan improved plastic cord. The subgroup size is 4. Determine the trial central lineand control limits. If any points are out of control, assume assignable causes, anddetermine 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 appears to be dropping over time from the average. If this deterioration trend continues, then the liquid will have to be replaced to prevent damage to equipment.
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 controllimits.
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.
9. A quality technician has collected data on the count of rivet nonconformities in four meters travel trailers. After 30 trailers, the total count of nonconformities 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?
If the data has been compared to the original data done for testing and all of the data indicates there are no out of spec process controls, then the revised control limits will have to be moved to fit the newly gathered data for the next run. If the nonconformities occurred on the low side of the spectrum, then move the revised control limits lower. If the phenomenon occurred on the high side, then move the control limits up.
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 of Product Temperature VS Foam, the data indicates that there is a correlation between the temperature and the percentage of foam in the product. My suggestion if foam is a deterrent to a quality end product, is to add equipment that would eliminate air entrapment to the liquid in the beginning or add coolers to the process to control the temperature of the product.