利用MINITAB做蒙特卡洛模拟

⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯最新 料推荐⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯Doing Monte Carlo Simulation in Minitab Statistical

⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯最新 料推荐⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯⋯ Doing Monte Carlo Simulation in Minitab Statistical Software Doing Monte Carlo simulations inMinitab Statistical Software isvery easy. This article illustrates how to use Minitabfor Monte Carlo simulations using both aknown engineering formula and aDOE equation. by Paul Sheehy and Eston Martz Monte Carlo simulation uses repeated random sampling to simulate data for agiven mathematical model and evaluate the outcome. This method was initially applied back in the 1940s, when scientists working on the atomic bomb used it to calculate the probabilities of one fissioning uranium atom causing afission reaction in another. With uranium in short supply, there was little room for experimental trial and — error .The scientists discovered that as long as they created enough simulated data, they could compute reliable probabilitiesand reduce the amount of uranium needed for testing. Today,simulateddataisroutinelyusedinsituationswhereresourcesarelimitedorgatheringrealdatawouldbetooexpensiveor ’ impractical. By using Minitabs ability to easily create random data, you can use Monte Carlo simulation to: Simulate the range of possible outcomes to aid in decision-making Forecast financial results or estimate project timelines Understand the variability in aprocess or system Find problems within aprocess or system Manage risk by understanding cost/benefit relationships Steps in the Monte Carlo Approach Depending on the number of factors involved, simulations can be very complex. But at abasic level, all Monte Carlo simulations have four simple steps: 1. Identify the Transfer Equation To doa MonteCarlosimulation,youneeda quantitativemodelofthebusinessactivity,plan,orprocessyouwishtoexplore. The “” mathematical expression of your process is called thetransfer equation.This may be aknown engineering or business formula, or it may be based on amodel created from adesigned experiment (DOE) or regression analysis. 2. Define the Input Parameters For each factor in your transfer equation, determine how its data are distributed. Some inputs may follow the normal distribution, while others follow atriangular or uniform distribution. You then need to determine distribution parameters for each input. For instance, you would need to specify the mean and standard deviation for inputs that follow anormal distribution. 3. Create Random Data — To do valid simulation, you must create avery large, random data set for each inputsomething on the order 100,000 instances. These random data points simulate the values that would be seen over along period for each input. Minitab can easily create random data that follow almost any distribution you are likely to encounter. 4. Simulate and Analyze Process Output With the simulated data in place, you can use your transfer equation to calculate simulated outcomes. Running alarge enough quantity of simulated input data through your model will give you areliable indication of what the process will output over time, given the anticipated variation in the inputs. ’ Those are the steps any Monte Carlo simulation needs to follow. Heres how to apply them in Minitab. Monte Carlo Using aKnown Engineering Formula Amanufacturing company needs to evaluate the design of aproposed product: asmall piston pump that must pump 12 ml of fluid per minute. You want to estimate the probable performance over thousands of pumps, given natural variation in piston diameter (D), stroke length (L), and strokes per minute (RPM). Ideally, the pump flow across thousands of pumps will have astandard deviation no greater than 0.2 ml. 1