Monte Carlo Simulation Method

The Monte Carlo simulation method serves as a reliability estimation technique when system components' reliability parameters are known, but the overall system reliability is too complex for exact mathematical modeling. This method approximates system reliability predictions by simulating numerous random events. Implementation typically involves generating random variables representing component states (using functions like rand() or random number generators), running multiple system trials, and calculating reliability as successful trials divided by total trials. As simulation iterations increase, prediction accuracy improves significantly—often following O(1/√n) convergence. The computationally intensive nature necessitates computer execution, typically achieved through loop structures and statistical analysis functions.

In hospital queueing theory applications, Monte Carlo simulation optimizes waiting times and operational efficiency. The implementation models patient flow by simulating stochastic variables: arrival times (often following Poisson distributions), service durations (modeled with exponential or log-normal distributions), and departure events. Key algorithmic steps include initializing queue states, processing events chronologically using priority queues, and collecting performance metrics. Through thousands of simulations with varying parameters (staff levels, appointment intervals), analysts can identify optimal queue configurations that minimize patient waiting times while maintaining service quality. This approach enables data-driven decisions for patient flow management, ultimately enhancing healthcare service efficiency and quality through computational experimentation.