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1、Doing Mon te Carlo Simula tion in Min itab Statisti cal Soft wareDoing Monte Carlo simulations in Minitab Statistical Software is very easy. This article illustrates how to use Minitab for Monte Carlo simulations using both a known engineering formula and a DOE equation.by Paul Sheehy and Eston Mart
2、zMonte Carlo simulation uses repeated random sampling to simulate data for a given 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
3、 a fission 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 probabilitieand reduce the amount of uranium needed for testing Today, simula
4、ted data is routinely used in situations where resources are limited or gathering real data would be too expensive or impractical. By using Minitab s ability to easily create random data, you can use Monte Carlo simulation to: Simulate the range of possible outcomes to aid in decision-making Forecas
5、t financial results or estimate project timelines Understand the variability in a process or system Find problems within a process or system Manage risk by understanding cost/benefit relationshipsSteps in the Monte Carlo ApproachDepending on the number of factors involved, simulations can be very co
6、mplex But at a basic level, all Monte Carlo simulations have four simple steps:1 Identify the Transfer EquationTo do a Monte Carlo simulation, you need a quantitative model of the business activity, plan, or process you wish to explore The mathematical expression of your process is called the atrans
7、fer equation ” This may be a known engineering or business formula, or it may be based on a model created from a designed experiment (DOE) or regression analysis 2 Define the Input ParametersFor each factor in your transfer equation, determine how its data are distributed Some inputs may follow the
8、normal distribution, while others follow a triangular 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 a normal distribution 3 Create Random DataTo do valid simulat
9、ion, you must create a very large, random data set for each input something on the order 100,000 instances These random data points simulate the values that would be seen over a long period for each input Minitab can easily create random data that follow almost any distribution you are likely to enc
10、ounter 4 Simulate and Analyze Process OutputWith the simulated data in place, you can use your transfer equation to calculate simulated outcomes Running a large enough quantity of simulated input data through your model will give you a reliable indication of what the process will output over time, g
11、iven the anticipated variation in the inputs Those are the steps any Monte Carlo simulation needs to follow Here s how to apply them in MinitabMonte Carlo Using a Known Engineering FormulaA manufacturing company needs to evaluate the design of a proposed product: a small piston pump that must pump 1
12、2 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 a standard deviation no greater than 0.2 ml.Ste
13、p 1: Identify the Transfer EquationThe first step in doing a Monte Carlo simulation is to determine the transfer equation. In this case, you can simply use an established engineering formula that measures pump flow:Flow (in ml) = n (D/2) ? L ? RPMStep 2: Define the Input ParametersNow you must defin
14、e the distribution and parameters of each input used in the transfer equation. The pump s piston diameter and stroke length are known, but you must calculate the str okes-per-minute (RPM) needed to attain the des ired 12 ml/minute flow rate. Volume pumped per stroke is given by this equation:n (D/2)
15、2 * LGiven D = 0.8 and L = 2.5, each stroke displaces 1 256 ml. So to achieve a flow of 12 ml/minute the RPM is 9549Based on the performance of other pumps your facility has manufactured, you can say that piston diameter is normally distributed with a mean of 0.8 cm and a standard deviation of 0.003
16、 cm. Stroke length is normally distributed with a mean of 2.5 cm and a standard deviation of 0.15 cm. Finally, strokes per minute is normally distributed with a mean of 9 549 RPM and a standard deviation of 0.17 RPM Step 3: Create Random DataNow you re ready to set up the simulation in Minitab. With Minitab you can instantaneously create 100,000 rows of simulated data.Starting with the
