Solution Found!
Solved: The article "Second Moment Reliability Evaluation
Chapter 4, Problem 7E(choose chapter or problem)
Problem 7E
The article "Second Moment Reliability Evaluation vs. Monte Carlo Simulations for Weld Fatigue Strength" (Quality and Reliability Engr. Intl., 2012: 887496) considered the use of a uniform distribution with A = .20 and B = 4.2.5 for the diameter X of a certain type of weld (mm).
a. Determine the pdf of X and graph it.
b. What is the probability that diameter exceeds 3 mm?
c. What is the probability that diameter is within I mm of the mean diameter?
d. For any value a satisfying .20 < a < a + 1 < 4.25, what is P(a < X < a + 1)?
Questions & Answers
QUESTION:
Problem 7E
The article "Second Moment Reliability Evaluation vs. Monte Carlo Simulations for Weld Fatigue Strength" (Quality and Reliability Engr. Intl., 2012: 887496) considered the use of a uniform distribution with A = .20 and B = 4.2.5 for the diameter X of a certain type of weld (mm).
a. Determine the pdf of X and graph it.
b. What is the probability that diameter exceeds 3 mm?
c. What is the probability that diameter is within I mm of the mean diameter?
d. For any value a satisfying .20 < a < a + 1 < 4.25, what is P(a < X < a + 1)?
ANSWER:
Answer :
Step 1 of 4 :
Given, The article "Second Moment Reliability Evaluation vs. Monte Carlo Simulations for Weld Fatigue Strength" considered the use of a uniform distribution with A = .20 and B = 4.2.5 for the diameter X of a certain type of weld (mm).
a)
The claim is to find the probability density function of x.
Let X be uniform random variable with intervals (0.20, 4.25),
X~U(0.20, 4.25)
Probability density function of X is f(x; A, B) =
where , A = 0.20 and B = 4.25
Therefore, f(x; 0.20, 4.25) =
=
= 0.2469
