Monte-carlo For Reliability

Monte-Carlo Simulation for Reliability Engineering

Anil Kumar Ammina Prateeck Biswas Reliability Engineering HCL Technologies

What is Monte Carlo simulation? Monte Carlo simulation is a method for iteratively evaluating a deterministic model using sets of random numbers as inputs. This method is often used when the model is complex, nonlinear, or involves more than just a couple of uncertain parameters. A simulation can typically involve over 10,000 evaluations of the model, a task which in the past was only practical using super computers.

A Monte Carlo method is a technique that involves using random numbers and probability to solve problems It also furnishes the decision-maker with a range of possible outcomes and the probabilities they will occur for any choice of action

How Monte Carlo simulation works Step 1: Create a parametric model, y = f(x1, x2, ..., xq). Step 2: Generate a set of random inputs, xi1, xi2, ..., xiq. Step 3: Evaluate the model and store the results as yi. Step 4: Repeat steps 2 and 3 for i = 1 to n. Step 5: Analyze the results using histograms, summary statistics, confidence intervals, etc.

where 0 < R(T) < 1. If we assume that the values of R(T) are uniformly distributed over the interval between 0 and 1, then we can let U, a uniformly distributed random number in the same interval, represent R(T).

This equation is valid for any uniform random number U, 0 < U < 1.

Random numbers for other distributions

Simulations can be done using Excel, or software's like @Risk, Crystal Ball

Applications of Monte Carlo Simulation Product life cycle analysis R&D estimation Safety Analysis Case Studies Reliability Analysis & Prediction Drug effectiveness Resource allocation Military war games Cost estimation Supply chain distribution Product Pricing Six Sigma and quality analysis

Case Studies

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