Problem 1: Estimate the area of the colored region (in orange) by Monte-Carlo simulation with 5000 replications given the distances shown in the figure below.
Problem 2: Quality assurance procedure of a manufacturer consists of 2 consecutive tests. Probability that a part passes the first quality test is 0.8. This probability remains the same for the second test if the part passed the first test. If a part fails the first test, then probability that it passes the next test is lower and estimated to be around 0.6. If a part passes the other, then it is reworked. Finally, if a part fails both tests then it is considered a lost cause and is scrapped. Using the U[0, 1] numbers given below:
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Parts
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1
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2
|
3
|
4
|
5
|
6
|
7
|
8
|
9
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10
|
|
Test 1
|
0.32
|
0.68
|
0.23
|
0.45
|
0.39
|
0.10
|
0.40
|
0.95
|
0.99
|
0.67
|
|
Test 2
|
0.66
|
0.86
|
0.78
|
0.63
|
0.16
|
0.68
|
0.91
|
0.80
|
0.61
|
0.64
|
a. Simulate the quality assurance procedure for 10 parts. Use your simulation results to estimate the probability that a part is used in production, reworked or scrapped.
b. Estimate the probability that a part that is send to rework had failed the first test.
c. Compute the true probabilities that a part is used in production, reworked or scrapped.
d. Compute the true probability that a part had passed the first test given that it is sent for rework.