ISYE 6644 - Summer 2026 - Final Exam Questions and
Answers with complete solution
,ISYE 6644 - Simulation - Summer 2024 Final Exam: 30 Most Challenging
Questions with Complete Solutions
Question 1: Random Variate Generation
Problem: Suppose you want to generate random variates from a distribution with
CDF F(x) = 1 - e^(-λx³) for x ≥ 0, where λ > 0. Using the inverse transform method,
which of the following correctly represents the generated variate?
A) X = (-ln(U)/λ)^(1/3)
B) X = (-ln(1-U)/λ)^(1/3)
C) X = (-ln(U)/λ)^(3)
D) X = (1 - e^(-λU))^(1/3)
-answer-: B) X = (-ln(1-U)/λ)^(1/3)
Rationale:
• Given F(x) = 1 - e^(-λx³) for x ≥ 0
• Set U = F(X) where U ~ Uniform(0,1)
• U = 1 - e^(-λX³)
• Solve for X: e^(-λX³) = 1 - U
• -λX³ = ln(1 - U)
• X³ = -ln(1-U)/λ
• X = (-ln(1-U)/λ)^(1/3)
• Note: Since U and 1-U have the same distribution, we can also use X = (-
ln(U)/λ)^(1/3), but the exact inverse from the formula gives option B.
Question 2: ARENA Modeling
, Problem: In ARENA, which module would you use to simulate a machine that can
break down and require repair, where breakdowns occur randomly during
operation?
A) Process module with failure defined in the "Failure" tab
B) Separate Process modules for operation and repair
C) Hold module with condition-based release
D) Both A and B are correct approaches
-answer-: D) Both A and B are correct approaches
Rationale:
• The Process module in ARENA has a "Failure" tab where you can define
uptime and downtime distributions, making it straightforward to model
equipment failures (Option A).
• Alternatively, you could use separate Process modules with logic to route
entities when failures occur (Option B).
• The Hold module (Option C) is for conditional releases, not specifically for
failure modeling.
• Experienced modelers know multiple valid approaches exist in ARENA for
failure modeling.
Question 3: Output Analysis - Confidence Intervals
Problem: You simulate a manufacturing system for 50 independent replications.
For each replication, you record the average waiting time. The sample mean
across replications is 12.5 minutes with a sample standard deviation of 2.1
minutes. What is the approximate 95% confidence interval half-width for the true
mean waiting time?
A) 0.595
B) 0.840
C) 1.645
D) 1.960
-answer-: A) 0.595
Answers with complete solution
,ISYE 6644 - Simulation - Summer 2024 Final Exam: 30 Most Challenging
Questions with Complete Solutions
Question 1: Random Variate Generation
Problem: Suppose you want to generate random variates from a distribution with
CDF F(x) = 1 - e^(-λx³) for x ≥ 0, where λ > 0. Using the inverse transform method,
which of the following correctly represents the generated variate?
A) X = (-ln(U)/λ)^(1/3)
B) X = (-ln(1-U)/λ)^(1/3)
C) X = (-ln(U)/λ)^(3)
D) X = (1 - e^(-λU))^(1/3)
-answer-: B) X = (-ln(1-U)/λ)^(1/3)
Rationale:
• Given F(x) = 1 - e^(-λx³) for x ≥ 0
• Set U = F(X) where U ~ Uniform(0,1)
• U = 1 - e^(-λX³)
• Solve for X: e^(-λX³) = 1 - U
• -λX³ = ln(1 - U)
• X³ = -ln(1-U)/λ
• X = (-ln(1-U)/λ)^(1/3)
• Note: Since U and 1-U have the same distribution, we can also use X = (-
ln(U)/λ)^(1/3), but the exact inverse from the formula gives option B.
Question 2: ARENA Modeling
, Problem: In ARENA, which module would you use to simulate a machine that can
break down and require repair, where breakdowns occur randomly during
operation?
A) Process module with failure defined in the "Failure" tab
B) Separate Process modules for operation and repair
C) Hold module with condition-based release
D) Both A and B are correct approaches
-answer-: D) Both A and B are correct approaches
Rationale:
• The Process module in ARENA has a "Failure" tab where you can define
uptime and downtime distributions, making it straightforward to model
equipment failures (Option A).
• Alternatively, you could use separate Process modules with logic to route
entities when failures occur (Option B).
• The Hold module (Option C) is for conditional releases, not specifically for
failure modeling.
• Experienced modelers know multiple valid approaches exist in ARENA for
failure modeling.
Question 3: Output Analysis - Confidence Intervals
Problem: You simulate a manufacturing system for 50 independent replications.
For each replication, you record the average waiting time. The sample mean
across replications is 12.5 minutes with a sample standard deviation of 2.1
minutes. What is the approximate 95% confidence interval half-width for the true
mean waiting time?
A) 0.595
B) 0.840
C) 1.645
D) 1.960
-answer-: A) 0.595
