This document discusses statistical models used in simulation. It describes mathematical models that embody assumptions about generating sample data from a larger population. Common models discussed include queueing systems, inventory and supply chain models, and reliability and maintainability models. Specific distributions discussed for these models include the exponential, normal, truncated normal, Poisson, negative binomial, geometric, gamma, Weibull, uniform, triangular, beta, Bernoulli and binomial distributions. The document provides information on when each distribution would be applicable or its common usage.

1. Statistical models
in Simulation
Name: Meheraz Ahmed Sakil
ID: 183-15-11839
Section: Old-A

2. Insight of
statistical Model
It is a mathematical model that embodies assumptions concerning the generation of some
sample data and similar data from a larger population.
Mathematically defined as (S,P) where S stands for sample space and p stands for
probability.
Purposes are:
Predictions
Extraction of information
Description of stochastic structures

3. Common models
used in Simulation
Queueing system
Inventory and supply chain
Reliability and maintainability
Limited data

4. Queue System
Queueing theory is the mathematical of waiting lines, or queues. A
queueing model is constructed so that queue lengths and waiting time can
be predicted.
Distribution:
Exponential distribution
Normal distribution
Truncated normal distribution
Usages:
Service time is completely random
Fairly constant but with some random variability
Similar to normal distribution

5. Inventory models
and supply chain
There are at list three random variables :
The number of units demanded per order or per time period
The time between demands
The lead time
Demand Distribution:
Poisson
Negative binomial distribution
Geometric
Usage:
Simply and extensively tabulated
Longer tail than poisson
Special case of negative binomial given at list one demand has occurred

6. Reliability and
Maintainability
Reliability emphasizes dependability in the life cycle management of a
product. Dependability, or reliability, describe the ability of a system or
components of function under stated conditions for a specified period of
time.
Distribution (Time to Failure)
Exponential
Gamma
Weibull
Normal
Usage:
Failure are random
For standby redundancy where each component has an exponential TTF
Failure is due to the most serious of a large number of defects in a system
of components
Failures are due to wear

7. Other Models
For cases with limited data, some useful distribution are:
Uniform
Triangular
Beta
Other distribution:
Bernoulli
Binomial
Hyper-Exponential

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