Homework9
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School
Florida State University *
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Course
6501
Subject
Industrial Engineering
Date
Jan 9, 2024
Type
docx
Pages
3
Uploaded by tkumar001
Question 12.1
Describe a situation or problem from your job, everyday life, current events, etc., for which a design of
experiments approach would be appropriate.
Answer:
I do not have any examples from my job or everyday life for DOE, but I think it can be effective in many
situations. One example that I can think of is a new company that is trying to launch a sports drink to the
market. They could design a simple experiment to get the intensity and taste of their drink correct. In
this experiment they would first launch a baseline product with proportions they think works best. Then
they could launch in either new market or within same with formula adjusted. If the sales of new
formula are better they could switch to new formula else they could abandon new formula and launch
new product with again adjusted formulation.
Question 12.2
To determine the value of 10 different yes/no features to the market value of a house (large yard, solar
roof, etc.), a real estate agent plans to survey 50 potential buyers, showing a fictitious house with
different combinations of features.
To reduce the survey size, the agent wants to show just 16 fictitious
houses. Use R’s
FrF2
function (in the
FrF2
package) to find a fractional factorial design for this
experiment: what set of features should each of the 16 fictitious houses have?
Note: the output of
FrF2
is “1” (include) or
“-1” (don’t include) for each feature.
Answer:
As the question suggests, I named 10 random variables for a house and used R function
FrF2.
Result is
in below screenshot.
Question 13.1
For each of the following distributions, give an example of data that you would expect to follow this
distribution (besides the examples already discussed in class).
a.
Binomial
b.
Geometric
c.
Poisson
d.
Exponential
e.
Weibull
Answer:
Binomial
The binomial distribution describes the probability of a certain number of successes or failures in a given
number of trials or events. This type of distribution is used when there are only two possible outcomes
for each trial, such as success or failure, heads or tails, yes or no etc., with equal probabilities for each
product. An example of this data could be a quiz game (like who wants to be a millionaire) where there
are questions where you are either correct or wrong.
Geometric
The geometric distribution describes the probability of a success occurring on any given trial in a series
of independent trials when the probability of success for each trial is known. A good example of this data
distribution can be lab trials of a drug. Where drug is reformulated with every trial and we slowly move
toward successfully creating the drug.
Poisson
The Poisson distribution describes the probability that an event will occur within a fixed time period
when its rate is known but its exact timing cannot be predicted accurately enough to measure it directly.
This can be a really great distribution to model any retail store where we know the average people that
come at certain times of the day or days of week. But they can show up at random time with mean rate
following poisson distribution.
Exponential
Exponential distributions measure data points with an exponential curve – a curve beginning at zero and
gradually increasing in value. This can be a great way to keep track of population of earth which
increases continuously.
Weibull
Weibull distribution is unimodal and describes probabilities associated with continuous data. However,
unlike the normal distribution, it can also model skewed data. Its extreme flexibility allows it to model
both left- and right-skewed data. This is a great model to model failure times and access product
reliability.
Question 13.2
In this problem you, can simulate a simplified airport security system at a busy airport. Passengers arrive
according to a Poisson distribution with λ
1
= 5 per minute (i.e., mean interarrival rate
1
= 0.2 minutes) to
the ID/boarding-pass check queue, where there are several servers who each have exponential service
time with mean rate
2
= 0.75 minutes. [Hint: model them as one block that has more than one
resource.]
After that, the passengers are assigned to the shortest of the several personal-check queues,
where they go through the personal scanner (time is uniformly distributed between 0.5 minutes and 1
minute).
Use the Arena software (PC users) or Python with SimPy (PC or Mac users)
to build a simulation of the
system, and then vary the number of ID/boarding-pass checkers and personal-check queues to
determine how many are needed to keep average wait times below 15 minutes.
[If you’re using SimPy,
or if you have access to a non-student version of Arena, you can use λ
1
= 50 to simulate a busier airport.]
Answer:
I created this simulation in Arena software. With my model, my first observation was that ID/boarding-
pass was a chokepoint in my model even after using 4 servers with λ
1
= 5 per minute. When I tried to
simulate λ
1
= 50, I had to increase ID/boarding-pass resources to 10 and even then I saw queuing
happening at that same point.
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