QUESTION3
3a. A quality analyst wants to construct a sample mean chart for controlling a packaging process. He knows from experience that when the process is operating as intended, packaging weight is normally distributed with a mean of twenty grams, and a process standard deviation of two grams. Each day last week, he randomly selected four packages and weighed each. The data from that activity appears below.
|
Weight
|
Day
|
Package 1
|
Package 2
|
Package 3
|
Package 4
|
Monday
|
23
|
22
|
23
|
24
|
Tuesday
|
23
|
21
|
19
|
21
|
Wednesday
|
20
|
19
|
20
|
21
|
Thursday
|
18
|
19
|
20
|
19
|
Friday
|
18
|
20
|
22
|
20
|
i. If he sets an upper control limit of 21 and a lower control limit of 19 around the target value of twenty grams, what is the probability of concluding that this process is out of control when it is actually in control?
ii. With the UCL and LCL of part a, what do you conclude about this process? is it in control?
3b. Determine which of these three processes are capable:
Provide a detailed explanation of how you arrived at your answer.
Process
|
Mean
|
Standard
Deviation
|
Lower
Specification
|
Upper
Specification
|
1
|
6.0
|
0.14
|
5.5
|
6.7
|
2
|
7.5
|
0.10
|
7.0
|
8.0
|
3
|
4.6
|
0.12
|
4.3
|
4.9
|
QUESTION4
A decision maker faced with four decision alternatives and four sates of nature develops the following cost matrix.
States of nature
Decision alternative
|
S_1
|
S_2
|
S_3
|
S_4
|
d_1
|
14
|
9
|
10
|
5
|
d_2
|
11
|
10
|
8
|
7
|
d_3
|
9
|
10
|
10
|
11
|
d_4
|
8
|
10
|
11
|
13
|
For each question show calculations where applicable and provide an explanation of how the answer was reached:
a. State and use the
average payoff strategy
to choose the best decision.
- State and use the
aggressive strategy
to choose the best decision.
- State and use the
conservative strategy
to choose the best decision.
- State and use the
regret strategy
to make the best decision.
- Suppose the decision maker obtains information that enables the following
probabilities assessments:
P(s_1) = 0.5; P(s_2) = 0.2; P(s_3) = 0.2; and P(s_4) = 0.1.
Use the
expected value
approach to determine the optimal strategy.