Monte Carlo Simulation Process in Reliability and Maintenance

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ABSTRACT
Simulation is based on the statistical concept that when the number of trials of an experiment approaches infinity, the average of the experiment's outcome is equivalent to the real value of variable under study. In the Reliability Block Diagrams, the application of the Monte Carlo Method is useful to observe the dynamic behavior of a system with variation in the set of inputs. Performing an infinite number of simulations is impossible; therefore, an appropriate number of iterations must be estimated to reach feasible results with an acceptable level of error. The numerical result for R(t) can be obtained by computing the probability distribution formula with the specified parameters values and t. In general, analytical methods are quick and accurate, but they are feasible only if there are no complex dependencies. The uncertainty is an inherent factor in every system and must be quantified to make decisions with a better understanding of the system.

Monte Carlo Simulation Method
Monte Carlo simulation is a powerful analysis tool that involves a random number generation and simulates the behavior of a variable when the data is insufficient to make decisions. The random number generation is based on a probability density function that defines the variable variation in the time. Randomness is used to describe events whose outcomes are uncertain; random variables count or measure that which is of interest to analyze.

The first step to the Monte Carlo process is to build a mathematical model with a set of relationships that simulates a real system. Then it is necessary to define the inputs and outputs variables. When the inputs and outputs are restricted to one value (each parameter takes only one value), we are dealing with a deterministic model. On the other hand, when the inputs and outputs are represented by random numbers or a probability density function, the model is known as stochastic or probabilistic. Monte Carlo simulation combines the principles of probability and statistics with the expert opinion and data sources to quantify the uncertainty associated with the real systems.

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