Chapter 13 Vocabulary - Monte Carlo Simulation

Monte Carlo Simulation

A simulation method that uses repeated random sampling to represent uncertainty in a model representing real system, and that computes the values of model outputs

Random Variables

Input to a simulation model whose value is uncertain and described by a probability distribution

Controllable Inputs

Input to a simulation model that is selected by the decision maker

Risk Analysis

The process of evaluating a decision in the face of uncertainty by quantifying the likelihood and magnitude of an undesirable outcome

Base-Case Scenario

Output resulting from the most likely values for the random variables of a model

What-If Analysis

A trial-and-error approach to learning about the range of possible outputs for a model; trial values are chosen for the model inputs (these are the what-ifs), and the value of the output(s) is computed

Worst-Case Scenario

Output resulting from the worst values that can be expected for the random variables of a model

Best-Case Scenario

Output resulting from the best values that can be expected for the random variables of a model

Discrete Probability Distribution

A probability distribution for which the possible values for a random variable can take on only specified discrete values

Continuous Probability Distribution

A probability distribution for which the possible values for a random variable can take any value in an interval or collection of intervals; an interval can include negative and positive infinity

Trial

A set of values for the random variables and the associated values of output measures for a single scenario in a simulation model

Verification

The process of determining that a computer program implements a simulation model as it is intended

Validation

The process of determining that a simulation model provides an accurate representation of a real system

Discrete-Event Simulation

A simulation method that describes how a system evolves over time by using events that occur at discrete points in time

Normal Distribution

A bell-shaped, symmetric distribution centered at its mean m; often a good way to characterize a quantity that is the sum of many independent random variables

Beta Distribution

Has a very flexible shape that can be manipulated by adjusting alpha and beta; useful in modeling an uncertain quantity that has a known minimum and maximum value

Gamma Distribution

Has a very flexible shape controlled by the values of alpha and beta; useful in modeling an uncertain quantity that can be as small as zero but can also realize large values

Exponential Distribution

Characterized by a mean value equal to its standard deviation and a long right tail stretching from a mode value of 0

Triangular Distribution

Often used to subjectively assess uncertainty when little is known about a random variable besides its range, but it is thought to have a single mode

Uniform Distribution

Appropriate when a random variable is equally likely to be any value between a and b; may be a conservative choice t model an uncertain quantity

Log-Normal Distribution

A unimodal distribution (like the normal distribution) that has a minimum value of 0 and a long right tail (unlike the normal distribution); often a good way to characterize a quantity that is the product of many independent, positive random variables

Integer Uniform Distribution

An integer uniform random variable assumes that the integer values between the lower parameter and the upper parameter are equally likely

Discrete Uniform Distribution

A discrete uniform random variable is equally likely to be any of the specified set of values

Custom Discrete Distribution

Can be used to create a tailored distribution to model a discrete, uncertain quantity

Binomial Distribution

A binomial random variable corresponds to the number of times an event successfully occurs in n trials, and the probability of a success at each trial is p and independent of whether a success occurs on other trials

Hypergeometric Distribution

A hypergeometric random variable corresponds to the number of times an element labeled a success is selected out of n trials in the situation where there are N total elements, s of which are labeled a success and, once selected, cannot be selected again

Negative Binomial Distribution

A negative binomial random variable corresponds to the number of times that an event fails to occur until an event successfully occurs s times, given that the probability of an event successfully occurring at each trial is p

Poisson Distribution

A Poisson random variable corresponds to the number of times that an event occurs within a specified period of time, given that m is the average number of events within the specified period of time