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STATISTICS, Applied Statistics

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Ask 3. Precision Manufacturing has a government contract to produce stainless steel rods for use in military aircraft. Each rod is required to be 20 millimeters in diameter. Each hour, random samples of size n = 4 rods are measured to check process control. Five hours of observations yielded the following:

Diameter
Time Rod 1 Rod 2 Rod 3 Rod 4
9 A.M. 19.8 20.4 19.9 20.3
10 A.M. 20.1 20.2 19.9 19.8
11 A.M. 19.9 20.5 20.3 20.1
Noon 19.7 19.8 20.3 20.2
1 P.M. 19.7 20.1 19.9 19.9

Construct the xbar-chart and the R-chart.
Is the process in control?

4. Modern Electronics specializes in manufacturing modern electronic components. It also builds the equipment that produces the components. Modern Electronics is considering building a new facility but the estimated profits would be impacted by the type of market that develops. The probability for a strong market is 0.3; for a fair market is 0.5; and for a poor market is 0.2. You are responsible for advising the president of Modern Electronics on the type facility that should be built or to not build a facility at all. The table shows the estimated profits under each market and for each size facility.

Estimated Profits
Strong Market Fair Market Poor Market
Build a large facility 550,000 110,000 -310,000
Build a medium-size facility 300,000 129,000 -100,000
Build a small facility 200,000 100,000 -32,000
Do not build a facility 0 0 0

Provide a recommendation to the president that maximizes profits
Provide a second recommendation to the president that minimizes regret.

5. Consulting income at Kaplan Associates for the period February – July is shown in the table below. Assume that the initial forecast for February is $65,000. Use Exponential smoothing to forecast August’s income.

Month Income ($1,000)
February 70.0
March 68.5
April 64.8
May 71.7
June 71.3
July 72.8

Use a smoothing constant of a = 0.2.
Use a smoothing constant of a = 0.5.
Which forecasting constant is best in this situation?
question #Minimum 100 words accepted#

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