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Developing Mean and Range Chart

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Twelve sample, 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 0.011
11 10.001 0.014
12 10.006 0.009

a) Determine the upper and lower control limits and the overall means for x-charts and R-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?

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https://brainmass.com/business/operations-research/602161

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Solution Summary

This solution develops and analyzes the mean and range charts for the given process in an Excel file. It determines the grand mean, average of sample ranges, central line, upper control limit, lower control limit and graphs the relationship.

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Part 1: (20 Points) Moore Travel Agency, a nationwide travel agency, offers special rates on certain Caribbean cruises to senior citizens. The president of Moore Travel wants additional information on the ages of those people taking cruises. A random sample of 70 customers taking a cruise last year revealed these ages.

57 77 85 72 80 58 55
74 70 60 85 59 66 61
91 59 57 83 79 52 91
70 81 66 86 66 80 81
53 55 68 77 80 86 74
66 55 82 55 69 63 77
82 87 64 90 56 70 89
78 72 60 85 67 76 69
62 54 90 53 91 75 77
53 74 89 67 67 56 67

Use the 2k > n rule to prepare a Frequency Distribution of the above data set and then construct a Histogram, Frequency Polygon and Ogive.

Part 2: (30 Points) The following list contains the number of customers assisted by three financial advisors in a local bank over a 10-day period.

Financial Day
Advisor 1 2 3 4 5 6 7 8 9 10
Alan 41 36 30 26 23 22 23 20 17 18
Beth 33 31 35 29 32 32 30 29 34 27
Clair 22 24 25 26 31 35 35 37 38 39

Prepare: a.) Stem-and-Leaf Chart for Alan
b.) Ordered Array for Beth
c.) Box-and-Whisker Plot for Clair
d.) Pie Chart showing percentages for Alan, Beth and Clair
e.) Time Line (on one chart) for Alan, Beth and Clair
f.) 100% Bar Chart (on one chart) for Alan, Beth and Clair based on the company standard that financial advisors must assist at least 30 customers a day to be considered successful. (i.e., less than 30 is considered unsuccessful)

Part 3: (50 Points) Systematic Inflammatory response syndrome (SIRS) is a major problem for patients with disfunctioning organs. Medical researchers at the University of Pittsburgh (Journal of the American Medical Association, July 5, 1995) conducted a study of the incidents of SIRS in 22 patients with cirrhosis of the liver. The clinical characteristics of the 22 patients—all waiting liver transplants in the intensive care unit (ICU)—are reported in the accompanying table.
Organ Bile
Dysfunction Blood Level Age Apache Goris Blood
Group (mg/dL) (years) Scale Scale SIRS Culture Infection
Mild 1.22 54 21 6 No Positive No
Mild 1.89 37 21 5 No Positive Yes
Mild 0.58 59 19 5 No Negative No
Mild 0.13 24 12 4 No Negative No
Mild 2.21 39 7 3 No Negative No
Mild 0.96 75 10 2 No Negative No
Mild 0.54 40 23 9 Yes Positive No
Mild 1.11 44 27 8 Yes Negative No
Mild 2.81 51 26 10 Yes Positive No
Mild 1.11 28 18 7 Yes Positive No
Moderate 0.58 65 16 4 Yes Positive No
Moderate 0.38 57 15 5 Yes Positive No
Moderate 0.88 61 20 7 No Negative No
Moderate 2.45 37 15 5 Yes Positive No
Moderate 2.12 40 21 8 Yes Negative No
Moderate 0.68 48 29 11 Yes Negative No
Moderate 0.33 47 29 9 Yes Positive Yes
Moderate 0.18 60 31 12 Yes Positive Yes
Severe 0.76 57 30 9 Yes Positive Yes
Severe 1.05 48 23 7 Yes Positive Yes
Severe 0.44 58 25 8 Yes Positive Yes
Severe 1.39 65 27 9 Yes Positive Yes

a.) Develop a Pareto Chart for the Organ Dysfunction Group.
b.) Draw a Box-and-Whisker Plot for the Bile Blood Level
c.) Construct a Stem-and-Leaf Chart for age.
d.) Develop a Scatter plot for the Goris Scale (x-axis) and the Apache Scale (y-axis).
e.) Develop a 100% Bar Chart for Blood Culture
f.) Develop a Pie Chart for Infection

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