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# Six Sigma Analysis

1. A company makes a part with a diameter of 1 inch with a tolerance of plus or minus .005 of an inch. The process has a mean of 0.997 and a standard deviation of 0.001 inch. Is the process capable? Why or why not?

2. A company owns a lease granting it the right to explore for oil on a property. The company may sell the lease for \$50,000, or they may drill. Four possible outcomes are listed below, together with probabilities and payouts. Should the company sell the lease or drill?

Outcome Probability Payoff
Dry Well 16% -\$200,000
Gas Only 40% \$50,000
Oil and Gas 24% \$100,000
Oil Only 20% \$200,000

3. Use the following data to construct upper and lower control limits for X bar and R charts.

"The manager of an assembly line took 5 samples each with 6 observations under ideal conditions to develop control limits for an X bar chart The mean and range of each sample is shown in the table below:"

Sample Number Sample Mean Sample Range
1 2.18 .33
2 2.12 .38
3 1.86 .40
4 1.98 .38
5 2.02 .35

Construct upper and lower control limits for X bar and R charts.

4. At a movie theater customers arrive at the rate of 1 every minute. The ticket seller averages 30 seconds per customer.

a. What is the average customer time in the system?

b. What is the average customer time in line?

c. what is the average number of customers in line?

d. What is the probability that the ticket taker is idle?

5. The total output from production system A in one day is 500 units and the total labor necessary to produce the 500 units is 350 hours. Production system B requires 70 minutes of labor per unit. Using the appropriate productivity measure, which of the following numbers represents the resulting productivity ratios? Which is the best process?

#### Solution Summary

This solution is comprised of detailed step-by-step calculations and analysis of the given problems and provides students with a clear perspective of the underlying concepts.

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