# Monte Carlo Simulation

## 4.1 Introduction

Monte Carlo (MC) simulation is a useful tool for modelling phenomena with significant uncertainty in inputs and has a multitude of applications including reliability, availability and logistics forecasting, risk analysis, load-strength interference analysis (Chapter 5), random processes simulation including repairable systems (Chapter 13), probabilistic design, uncertainty propagation, geometric dimensioning and tolerancing, and a variety of business applications.

The concept of the Monte Carlo method comes from the gaming tables at the casinos of Monte Carlo. It is a class of probabilistic computational algorithms that rely on repeated sampling of random variables of interest to compute the results.

Simplistic simulation can be done with spreadsheet software, while more sophisticated modelling can be done with the use of software packages, like Palisade @Risk¯, Minitab¯, Crystal Ball¯ and many others.

## 4.2 Monte Carlo Simulation Basics

Monte Carlo simulation can be defined as a method for iteratively evaluating a deterministic model using sets of random numbers as inputs. It is a fairly simple mathematical procedure, with random inputs and random outputs: γ = f(x1, x2, . . ., xn), where the input values are sampled and the output values are recorded and analysed as illustrated in Figure 4.1.

In order to run Monte Carlo simulation we need to generate random variables that follow an arbitrary statistical distribution. The inputs are randomly ...

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