1  Num Columns:
You can specify the number of columns to display for the input area. The input area can be used to develop your Monte Carlo Simulation model. There are no limits on the number of rows you can use, but you are limited on the number of columns (50 max) so that there is sufficient space to display analysis results and store your simulation data. If you need to build a large simulation model, build it vertically rather than horizontally. Note that changing the number of columns will only hide or unhide the columns in the model area; it does not delete or add columns. You can change the number of columns to display at any time, even after partially building your model. For example, you can start by displaying ten columns. While building your model, you realize you need more columns. Just click on Analysis Setup and increase the number of columns here so more columns are displayed on the worksheet.  
2  Column Width: Specify the width of each cell in the input area. You can specify the width here or manually adjust the widths on the worksheet. This option provides sufficient space for your text for the simulation model. This option is currently disabled, and you are recommended to manually adjust the column widths on the worksheet as required directly on the worksheet.  
3  Runs Criteria:
Specify how many iterations you need to run your Monte Carlo simulation model. There are two options available:
 
4  Num Iterations: Specify the number of iterations for the simulation. There are no limits on the number of iterations you can run, but note that many may require increased memory and additional computing resources. There may not be a benefit to increasing the number of iterations beyond a certain level. It is recommended that you start with a smaller number of iterations and keep growing this number until you do not find much difference in the results with an increase in the number of iterations. Formulae available can estimate the number of iterations to run based on your standard deviation, the degree of confidence you need, and your margin of error.  
5  Tolerance: When you specify the Runs Criteria as Tolerance, you can select the tolerance level you want to achieve in your results. The software starts with 100 runs and continues to increase the number of runs until it meets your tolerance criteria. For example, suppose you specify a 1% tolerance band. In that case, the software will continue adding runs to your model until the difference in mean results between consecutive runs doesn't exceed the given tolerance level. It does this check for all inputs and outputs defined in your model.  
6  Num Simulations: Specify the number of simulations you would like to run for this model. For example, if you have selected 1000 iterations and two simulations, the entire Monte Carlo simulation of 1000 iterations will be performed two times. You will be able to change some parameters between these simulation runs and analyze each simulation separately. This is a valuable feature when you want to do some whatif analysis. For example, if you use the standard deviation for one of the inputs as 12.5 and wonder how your results will change if your standard deviation changes to 20, you could run two simulations with 1000 iterations each. You will need to use a Simulation Table for this study. More information regarding the Simulation Table is shared later in this help file.  
7  Help Button: Click on this button to open the help file for this topic.  
8  Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.  
9  OK Button: Click on this button to save all changes and exit this dialog box. 
1  Generator: Specify the algorithm to use for the random number generator. The only available option is Auto, which uses the default method to generate the random numbers. The software uses a Mersenne Twister algorithm and generates a very long period of random numbers. It is the industry standard for generating random numbers and is used by many packages available in the market. It is very reliable and passes most tests for statistical randomness.  
2  Sampling:
Specify the sampling method. There are two options available:
 
3  Random Seed: Specify the seed for the random number generator. The seed could be either random or fixed. If the seed is random, the system will generate different random numbers for you each time you run the simulation. However, if the seed is fixed, you will get the same set of random numbers when you run the simulation each time so that you can reproduce the model results.  
4  Seed Value: Specify the value of the seed. For random numbers, the seed value is 0. Use a positive integer value for the seed if you want it fixed.  
5  Initial Value:
Specify the initial value to display on the worksheet for input cells. The available options are:
 
6  Multiple Simulations:
Specify how you want to simulate multiple simulation runs. There are two options available:

1  Cells:
You can set the colors for the following cells you create for the Monte Carlo simulation.
 
2  Foreground Color: You can click on this button to specify the foreground color for the cells.  
3  Background Color: You can click on this button to specify the background color for the cells.  
4  Example Color: The example shows how the cells would appear on the worksheet. If you are unhappy with these colors, click on the foreground and background colors to change the settings.  
5  Default Colors: You can reset the colors for all the cells to the default values.  
6  No Colors: You can remove the colors for all the cells by clicking this button. 
1  Name: Specify a name for your input variable. Make sure that the names are unique and do not contain special characters such as comma (","), colon(":"), semicolon (";"), parenthesis ("(", ")"), or ampersand ("&"). Keep the name short to keep your text output manageable. 
2  Cell Location: By default, the cell location will show the selected active worksheet cell before clicking on the Inputs button. You can click the icon next to this textbox to choose a different location on the worksheet for the input location. You can also define a range of cells; the software will create inputs for each cell. Note that if you specify a range, the input variables' names are appended with name.1, name.2, etc. 
3  Distribution: Specify a distribution for your input from the dropdown box. This distribution generates the random numbers for this input variable. Make sure you pick a distribution that matches how you expect this variable to behave in the real world. For example, use a uniform distribution if the input is uniformly distributed between minimum and maximum values. If the input is normally distributed, use a normal distribution, etc. 
4  Parameters: Specify the parameters for the selected distribution. Each distribution has its own set of parameters, and you need to specify them accordingly. For example, a normal distribution requires that you specify the mean and standard deviation. 
5  Percent: The percent data at the top of the density function shows the 5% limits on the left and right sides of the distribution as reference values. For example, the graph shows 90% of the values lie between 16.2 and 23.8. 
6  PDF: The graphs section shows a probability density function for the input distribution based on the parameters you have specified. This graph is just shown as a guide to give you an idea of the data points the random number generator will generate for this input variable. 
7  Stats: The stats section shows summary statistics for the distribution, such as min, max, mean, median, mode, range, stdev, quartiles, and percentiles. 
8  Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box. 
9  Add Button: If this is the first time you specify the input distribution, you must click the Add button at the bottom righthand corner to add this distribution to the model. If you have selected a cell for which input has already been defined, you can update any previously defined distribution settings. 
Option  Description 

=smBeta("Name", Nu, Omega, Min, Max)  General Beta distribution. Nu and Omega are shape parameters that need to be greater than zero. If the min and max values are 0 and 1. This can be reduced to a twoparameter beta distribution. If not, it is a general beta distribution. 
=smChiSquared("Name", Nu)  ChiSquared distribution. The specified DOF parameter Nu should be integer and greater than zero. 
=smCauchy("Name", Location, Scale)  Cauchy distribution. The scale parameter should be greater than zero. 
=smErlang("Name", Scale, Shape)  Erlang distribution. The scale and shape parameters should be greater than zero. 
=smExtremeValue("Name", Location, Scale)  Extreme Value distribution. The scale parameter should be greater than zero. 
=smExponential("Name", Scale)  Exponential distribution. The scale parameter should be greater than zero. 
=smF("Name", Nu, Omega)  F distribution. The degrees of freedom parameters Nu (Numerator) and Omega (Denominator) should be greater than zero. 
=smGamma("Name", Shape, Scale)  Gamma distribution. The shape and scale parameters should be greater than zero. 
=smLaplace("Name", Location, Scale)  Laplace distribution. The scale parameter should be greater than zero. 
=smLogNormal("Name", Mu, Sigma)  Log Normal distribution. The Mu and Sigma parameters should be greater than zero. 
=smLogistic("Name", Location, Scale)  Logistic distribution. The scale parameter should be greater than zero. 
=smLogLogistic("Name", Alpha, Beta)  Log Logistic distribution. The alpha and beta parameters should be greater than zero. 
=smNormal("Name", Mu, Sigma)  Normal distribution. The sigma parameter should be greater than zero. 
=smPareto("Name", Location, Scale)  Pareto distribution. The location and scale parameters should be greater than zero. 
=smPert("Name", Min, Max, Most Likely)  Pert distribution. The most likely value should be between the minimum and maximum values. 
=smPower("Name", Max, Shape)  Power distribution. The max and shape parameters should be greater than zero. 
=smRayleigh("Name", Scale)  Rayleigh distribution. The scale parameter should be greater than zero. 
=smT("Name", Nu)  Student's t distribution. The specified DOF parameter Nu should be greater than zero. 
=smTriangular("Name", Min, Max, Mode)  Triangular distribution. The mode parameter should be between min and max. 
=smUniform("Name", Min, Max)  Uniform distribution. The max value should be greater than the min value. 
=smWeibull("Name", Eta, Beta)  Weibull distribution. The scale (eta) and shape (beta) parameters should be greater than zero. 
=smBernoulli("Name", Prob)  Bernoulli distribution. The probability value should be between 0 and 1. 
=smBinomial("Name", Num Trials, Prob)  Binomial distribution. The probability value should be between 0 and 1. 
=smDiscreteUniform("Name", Min, Max)  Discrete Uniform distribution. The maximum value should be greater than the minimum value. 
=smGeometric("Name", Prob)  Geometric distribution. The probability value should be between 0 and 1. 
=smHyperGeometric("Name", PopSize, NumSuccess, SampleSize)  Hypergeometric distribution. Num Success should be less than population size. 
=smNegativeBinomial("Name", XthSuccess, Prob)  Negative Binomial distribution. The probability value should be between 0 and 1. 
=smPoisson("Name", Lambda)  Poisson distribution. The lambda value should be between 0 and 1. 
=smUserDefined("Name", XValues, Prob)  User Defined distribution. The size of the X values and Prob should be the same. Prob values don't have to be normalized 
Option  Description 

=smBetaAlt(Type1, Value1, Type2, Value2)  Beta distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Nu" or "Omega" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values specified correspond to the type as specified. For example, =smBetaAlt("Nu", 1, "0.95", "0.4") implies that the Nu value is 1.0 and the 95th percentile lies at 0.4. This function will return the values for the bestfit beta distribution parameters. 
=smCauchyAlt(Type1, Value1, Type2, Value2)  Cauchy distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Location" or "Scale" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smCauchAlt("0.05", "1", "0.95", "2") implies we need the parameters for the Cauchy distribution such that the 5th percentile is at 1 and the 95th percentile is at 2. 
=smErlangAlt(Type1, Value1, Type2, Value2)  Erlang distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Scale" or "Shape" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smErlangAlt("0.05", "1", "0.95", "2") implies we need the parameters for the Erlang distribution such that the 5th percentile is at 1 and the 95th percentile is at 2. 
=smExtremeValueAlt(Type1, Value1, Type2, Value2)  Extreme Value distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Location" or "Scale" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smExtremeValueAlt("0.05", "1", "0.95", "2") implies we need the parameters for the Extreme Value distribution such that the 5th percentile is at 1 and the 95th percentile is at 2. 
=smExponentialAlt(Type1, Value1)  Exponential distribution. Type 1 can be the keyword for the distribution parameter "Scale" or a value. If Type 1 is a value, it is assumed to be in the percentile and must be between 0 and 1. The values correspond to the type as specified. For example =smExponentialAlt("0.95", "2") implies we need the parameters for the Exponential distribution such that the 95th percentile is at 2. 
=smGammaAlt(Type1, Value1, Type2, Value2)  Gamma distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Shape" or "Scale" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smGammaAlt("0.05", "1", "0.95", "2") implies we need the parameters for the Gamma distribution such that the 5th percentile is at 1 and the 95th percentile is at 2. 
=smLaplaceAlt(Type1, Value1, Type2, Value2)  Laplace distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Location" or "Scale" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smLaplaceAlt("0.05", "1", "0.95", "2") implies we need the parameters for the Laplace distribution such that the 5th percentile is at 1 and the 95th percentile is at 2. 
=smLogNormalAlt(Type1, Value1, Type2, Value2)  Log Normal distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Mu" or "Sigma" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smLogNormalAlt("0.05", "1", "0.95", "2") implies we need the parameters for the Log Normal distribution such that the 5th percentile is at 1 and the 95th percentile is at 2. 
=smLogisticAlt(Type1, Value1, Type2, Value2)  Logistic distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Location" or "Scale" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smLogisticAlt("0.05", "1", "0.95", "2") implies we need the parameters for the Logistic distribution such that the 5th percentile is at 1 and the 95th percentile is at 2. 
=smLogLogisticAlt(Type1, Value1, Type2, Value2)  Log Logistic distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Alpha" or "Beta" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smLogLogisticAlt("0.05", "1", "0.95", "2") implies we need the parameters for the Log Logistic distribution such that the 5th percentile is at 1 and the 95th percentile is at 2. 
=smNormalAlt(Type1, Value1, Type2, Value2)  Normal distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Mu" or "Sigma" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smNormalAlt("0.05", "10", "0.95", "20") implies we need the parameters for the Normal distribution such that the 5th percentile is at 10 and the 95th percentile is at 20. 
=smParetoAlt(Type1, Value1, Type2, Value2)  Pareto distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Location" or "Scale" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smParetoAlt("0.05", "10", "0.95", "20") implies we need the parameters for the Pareto distribution such that the 5th percentile is at 10 and the 95th percentile is at 20. 
=smPertAlt(Type1, Value1, Type2, Value2, Type3, Value3)  Pert distribution. Type 1, Type 2, and Type 3 can be the keywords for the distribution parameters "Min", "Max", "Most Likely" or a value. If Type 1, Type 2, or Type 3 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smPertAlt("0.05", "10", "0.95", "20", "0.50", "18") implies we need the parameters for the Pert distribution such that the 5th percentile is at 10 and the 95th percentile is at 20, and the 50th percentile is at 18. 
=smPowerAlt(Type1, Value1, Type2, Value2)  Power distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Max" or "Shape" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smPowerAlt("0.05", "1", "0.95", "2") implies we need the parameters for the Power distribution such that the 5th percentile is at 1 and the 95th percentile is at 2. 
=smRayleighAlt(Type1, Value1)  Rayleigh distribution. Type 1 can be the keyword for the distribution parameter "Scale" or a value. If Type 1 is a value, it is assumed to be in the percentile and must be between 0 and 1. The values correspond to the type as specified. For example =smRayleighAlt("0.95", "2") implies we need the parameters for the Rayleigh distribution such that the 95th percentile is at 2. 
=smTriangularAlt(Type1, Value1, Type2, Value2, Type3, Value3)  Triangular distribution. Type 1, Type 2, and Type 3 can be the keywords for the distribution parameters "Min", "Max", "Mode" or a value. If Type 1, Type 2, or Type 3 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smTriangularAlt("0.05", "10", "0.95", "20", "0.50", "18") implies we need the parameters for the Triangular distribution such that the 5th percentile is at 10 and the 95th percentile is at 20, and the 50th percentile is at 18. 
=smUniformAlt(Type1, Value1, Type2, Value2)  Uniform distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Min" or "Max" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smUniformAlt("0.05", "1", "0.95", "2") implies we need the parameters for the Uniform distribution such that the 5th percentile is at 1 and the 95th percentile is at 2. 
=smWeibullAlt(Type1, Value1, Type2, Value2)  Weibull distribution. Type 1 and Type 2 can be the keywords for the distribution parameters "Eta" or "Beta" or a value. If Type 1 or Type 2 are values, they are assumed to be percentiles and must be between 0 and 1. The values correspond to the type as specified. For example =smWeibullAlt("0.05", "1", "0.95", "2") implies we need the parameters for the Weibull distribution such that the 5th percentile is at 1 and the 95th percentile is at 2. 
1  Name: Specify a name for your output variable. Make sure that the names are unique and do not contain special characters such as comma (","), colon(":"), semicolon (";"), parenthesis ("(", ")"), or ampersand ("&"). Keep the name short to keep your text output manageable.  
2  Cell Location: By default, the cell location will show the selected active worksheet cell before clicking on the Outputs button. You can click the icon next to this textbox to choose a different location on the worksheet for the output location. You can also define a range of cells; the software will create outputs for each cell. Note that if you specify a range, the output variables' names are appended with name.1, name.2, etc.  
3  Formula: Each output cell must contain a formula. The formula is used to calculate the values for the output variables. If a formula is already defined on the worksheet, it will be displayed in this textbox. If not, you can also define a formula in this textbox, which will be updated on the worksheet.  
4  Capability Analysis:
Specify the method to use for performing the capability analysis for this output. The available options are:
 
5  LSL: Specify the Lower Specification Limit (LSL) for the output variable. These specification limits come from the customer. All values of the output below this LSL value are considered defective. If an output does not have a lower limit, leave this field blank.  
6  USL: Specify the Upper Specification Limit (USL) for the output variable. These specification limits come from the customer. All values of the output above this value of USL are considered defective. If an output has no upper limit, leave this field blank.  
7  Sensitivity Analysis: Specify the number of input variables to use for the sensitivity analysis. If you specify all variables, the software will use all the input variables to compute the sensitivity analysis. However, some of the inputs may not be of interest to you. If there are a large number of input variables, you may want to limit the sensitivity analysis to only those of interest to you. Specify the number of input variables and specify which ones you want to consider in the dropdown boxes below.  
8  Select Inputs: Specify the input variables you want the software to use for sensitivity analysis in these dropdown boxes.  
9  Cancel Button: Click on this button to cancel all changes to the settings and exit this dialog box.  
10  Add Button: If this is the first time you specify the output distribution, you must click the Add button at the bottom righthand corner to add this output definition to the model. If you have selected a cell for which output has already been defined, you can update any previously defined settings. Click the Delete button to delete previously defined outputs. 
1  Cell Location:
The location textbox defines the location on your worksheet that stores the correlation matrix. To define the correlations, click the select button next to the range input textbox. Select a range on the worksheet where you want the correlation matrix stored. Make sure the range is blank and does not include any other data since this range will be overwritten when the dialog box defines the correlations. 
2  Input Variables: Once the range has been selected, the dropdown boxes on the right will appear for each input variable. Select the variables of interest here. If you have ten inputs, defining a correlation between them is unnecessary. You only need to determine the correlation between those variables that are correlated. Anything that is not defined will be assumed to be uncorrelated. Once you specify the variables, the correlation matrix is shown below. Note that the correlation matrix is symmetric with a value 1 in the diagonals. Enter the correlation coefficients in the white text boxes. Make sure that the correlation coefficients are between 1 and +1. 
3  Correlation Table: The correlation table shows the currently defined correlation coefficients. Review this matrix to check for any errors in the correlation coefficients, and update this matrix if required. 
4  Update Coefficients: The correlation table shows the currently defined correlation coefficients. Note that the matrix is symmetric, and the correlation coefficients can be updated in the white cells. If the values in the white cells are 0, then there is no correlation between the two selected variables. Make sure that all correlation coefficients are between 1 and +1. 
5  Cancel Button: Exit this dialog box without making any changes. 
6  Delete Button: Click on this button to delete the entire correlation matrix table from your simulation. Note that all the correlation coefficients will be removed, and your inputs will no longer be correlated if you click this button. 
7  OK Button: Click the OK button to save the correlation coefficients. The values defined in the dialog box will be saved to the worksheet. Note that once you define the correlation matrix, you can click on the Correlations button to review what has been defined earlier. 
1  Cell Location:
The location textbox defines the location on your worksheet that stores the simulation table. To define the simulation table, click the select button next to the range input textbox. Select a range on the worksheet where you want the simulation table stored. Pick three if you have two simulation runs (one for the header). If you only change one variable, you must pick two columns (one for row number). If you are modifying two variables, you need to pick three columns, and so on. The appropriate number of cells is displayed in the dialog box depending on the size of the range you pick. Make sure the range is blank and does not include any other data since this range will be overwritten when the dialog box defines the simulation table. 
2  Target Cell: Once the range has been selected, a textbox will appear on the top of each column. You will need to specify the location of the worksheet cell that the simulation table will modify. For example, suppose you enter K5 in this cell for each simulation run. In that case, the values from the simulation table will be used to update the location K5 on the worksheet before that particular simulation is run. The first simulation is run by placing the value 12 in cell K5. The second simulation is run by placing the value 13.5 in cell K5. If you have two variables defined, then you will need to specify two worksheet locations that will be modified. It is up to the simulation model you have developed and how you incorporate K5 in your model equations. 
3  Table Values: Define the values to be used for each simulation run. These values can be directly edited in the dialog box or entered on the worksheet. In the example shown above, the simulation table values are 12 for the first simulation, 13.5 for the second simulation, and 15 for the third simulation. You can define any number of simulations (rows) and simultaneously modify any number of variables (columns) for each simulation. 
4  Delete Button: Click on this button to delete the entire simulation table from your simulation. Note that all the simulation values will be removed, and your inputs will no longer be correlated if you click this button. 
5  OK Button: Click the OK button to save the simulation table to the worksheet. The values defined in the dialog box will be saved to the worksheet. Note that once you define the simulation table, you can click on the Sim Table button to review what has been defined earlier. 
1  Function Name: Defines a name for the function. Currently, this feature is not enabled for the user to select the function name.  
2  Cell Location: The location textbox defines the location on your worksheet that stores the function value. To define the function, click the select button next to the range input textbox. Select a range on the worksheet where you want the simulation table stored.  
3  Variable: Select the input or output variable for which you want to compute the function value. You can only pick one variable at a time. If you need to summarize other variables, you must define more than one function for your simulation.  
4  Simulation Number: Specify the simulation number for which this function needs to summarize the values. If you have three simulations and you want a summary for each simulation, you will need to define three functions and store them in different cells on the worksheet.  
5  Measure:
Specify what sort of measure you want to report. The available options are:

1  Inputs: This tab shows you all the inputs you have defined in the model. The number within the parenthesis shows the number of inputs. The list box contains the input number, the name of the input, the cell number that stores the input variable, and the distribution name & parameters for that input. 
2  Outputs: This tab shows you all the outputs you have defined in the model. The number within the parenthesis shows the number of outputs. The list box contains the output number, the name of the output, the cell number that stores the output variable, the method used to calculate process capability, and the lower and upper specification limits. 
3  Functions: This tab shows you all the functions you have defined in the model. The number within the parenthesis shows the number of functions. The list box contains the function number, the variable name, the cell number that stores the function variable, the simulation number for which the data is calculated, and the metric (such as mean) and any required parameters. For example, if you have an output variable ABC, when you generate 100 random numbers, you will be generating 100 values of the variable ABC. You can define a function to calculate the mean value of ABC and store it in a cell, say E4. Functions can be useful to save summary statistics of your input and output variables on your worksheet. 
4  Correlations: This tab shows you all the correlations you have defined in the model. The number within the parenthesis shows the number of correlations defined. The list box contains the correlation number, the two input variables between which the correlation is defined, and the correlation value. Note that if the correlation value is 0 (which means no correlation), then those pairs of inputs are not listed in this dialog box. 
5  Sim Table: This tab shows you all the simulation table values defined in the model. The number within the parenthesis shows the number of simulations defined. The list box contains the simulation number, the cell location that needs to be modified, and the values that must be put into that cell for each simulation run. For example, if three simulations are defined for cell D4 with values 1, 2, and 3. Then the first simulation is run with D4 = 1, the second simulation is run with D4 = 2, and the third simulation is run with D4 = 3. 
6  Errors: This tab shows you all the errors that were detected in the model. The number within the parenthesis shows the number of errors detected. The list box contains the error number, the source of the error (input, output, function, etc.), and a brief description of the error. Note that you cannot simulate until you fix all the reported errors. 
1  Seed: The seed value determines how the random numbers are generated. If the value of the seed is 0, then new random numbers are generated for each run. Otherwise, the same set of random numbers will be generated. This can be especially useful if you want repeatable results or want to compare your analysis with someone else. 
2  Iterations: The number of iterations indicates the number of times random numbers will be generated. It would be best to have sufficient iterations to simulate the full range of variation of the input variables. If the number of iterations is small, you will get different results each time you run the simulation. If the number of iterations is too large, it will consume significant computer bandwidth to generate and store many data points. The simulation results may not significantly get better after a certain point. Hence, it is recommended that you keep the number of iterations small initially and then slowly increase the number of iterations until you don't find much change in the analysis results. If you use the tolerance feature to achieve a certain tolerance level, this value will be set at Auto. However, if your Analysis Setup option for Runs Criteria is "Iterations," then the value in this textbox should be numeric. 
3  Simulations: The number of simulations determines how many rows of the simulation table are executed. The appropriate parameters of the simulation table are set for each simulation. For example, for the simulation table described earlier, for the first simulation, the J10 cell is set to 10; for the second simulation, the J10 cell is set to 20, etc., before the simulation is run. If the number of simulations is less than the number of rows in the simulation table, then only the corresponding rows are run. It will report an error if you specify the software to run more simulations than what is available in the simulation table. In most cases, we recommend that the number of simulations equals the number of rows defined in the simulation table. Hence, there is no confusion about the parameters set for each simulation. Try to avoid using the simulation table when running model optimization. 
1  Variable: Select the variable for which you would like to compare simulation runs. The dropdown box lists all the input and output variables. You can plot a single variable or select All to compare all variables on the same plot.  
2  Group: Select the simulation number you want to use to create the box plot. You can select All, where all the groups are used, or use a single simulation data to compare the groups.  
3  Outliers: Specify whether you want to show or hide outliers. If you choose to show outliers, any data points too far away from the median value are shown as a dot outside the whiskers.  
4  Box Plot: At the bottom, you can specify if you want to display the data as a box plot or a confidence interval of the means.  
5  Statistics:
A brief set of statistics for the given data set is shown on the righthand side. Currently, the following stats are shown for each group.
 
6  Overlay Lines: If you want to superimpose additional horizontal or vertical lines on your boxplot, you can specify the values in these textboxes, and those additional lines are displayed on your plot. Note that only lines within the current graph boundaries are displayed. 
1  Variable: Select the variable for which you would like to analyze the capability. The dropdown box lists all the input and output variables.  
2  Group: Select the group variable. The group variable is the simulation number. So, if you would like to create a histogram for the first simulation, select the group number as 1.  
3  Distribution: Specify the distribution you want to fit to estimate the process capability. If you specify "Normal," for example, the software will fit the best possible Normal distribution and use this distribution to estimate process capability.  
4  Specs: Specify which tails you want to include in your capability analysis. If you specify LSL, only the lower specification limit is included in the calculations. If you specify USL, only the upper specification limit is included in the calculations. If you select Both, lower and upper specification limits are included in the process capability calculations.  
5  Textbox Options: At the bottom, you can specify the specification limits for LSL and USL. The software will try to get these from the model, but you can change them and try out different values to see how they will impact your analysis results.  
6  Capability Stats: The statistics section shows the following metrics:
 
6  Spec Limits: Specify the values for the LSL and USL. These values are used to calculate the capability indices and update the chart. Note that these values are used for analysis only on "blur"  moving your cursor away from that textbox after entering the data. Changing the Spec Limits will automatically update the probability values on the right.  
7  Prob Limits: Specify the values for the probability to the left of LSL and to the right of USL. These values are used to calculate the capability indices and update the chart. Note that these values are used for analysis only on "blur"  moving your cursor away from that textbox after entering the data. Changing the Prob Limits will automatically update the spec limits on the left. 
1  Variable: Select the variable for which you would like to generate the histogram. The dropdown box lists all the input and output variables.  
2  Group: Select the group variable. The group variable is the simulation number. So, if you would like to create a histogram for the first simulation, select the group number as 1.  
3  Distribution: Specify the distribution you want to fit and superimpose on the histogram. If you specify "Normal," for example, the software will fit the best possible Normal distribution to the data and superimpose it on the histogram in green.  
4  Prob: Specify if you want to highlight the tails of the distribution fit. If you specify P10, the software will draw the vertical lines, which show 5% of the data points to the left, 90% in the middle, and 5% on the right. These tails are based on the actual data points  the software will calculate the percentile values to determine these limits. The data shown at the top is for the bestfit distribution. So, these numbers may not match the raw data if there is a poor fit for the distribution of the data points. You can click on the percentages or the limit values to change these numbers to see how the shaded areas change.  
5  Checkbox Options: At the bottom, there are three checkbox options. You can plot the probability density function (PDF), the cumulative probability density function (Ascending), or the cumulative probability density function (descending) for the best histogram.  
6  Histogram: Your data histogram is listed in this area. It includes the histogram, the distribution fit for the given data, and areas shown in red if the fit falls outside the specification limits.  
7  Statistics:
A brief set of statistics for the given data set is shown on the righthand side. Currently, the following stats are shown.
 
8  Spec Limits: Specify the values for the LSL and USL. These values are used to calculate the capability indices and update the chart. Note that these values are used for analysis only on "blur"  moving your cursor away from that textbox after entering the data. Changing the Spec Limits will automatically update the probability values on the right.  
9  Prob Limits: Specify the values for the probability to the left of LSL and to the right of USL. These values are used to calculate the capability indices and update the chart. Note that these values are used for analysis only on "blur"  moving your cursor away from that textbox after entering the data. Changing the Prob Limits will automatically update the spec limits on the left. 
1  X Variable: Select the variable that you would like to use for your Xaxis for your scatter plot. The dropdown box lists all the input and output variables.  
2  Y Variable: Select the variable that you would like to use for your Y axis for your scatter plot. The dropdown box lists all the input and output variables.  
3  Group: Select the group variable. The group variable is the simulation number. So, if you would like to create a histogram for the first simulation, select the group number as 1. If you select All, all the simulation groups will be used to create the scatter plot. Note that each subgroup (or simulation) is plotted using a different color.  
4  Distribution: Specify the distribution you want to fit and superimpose on the histogram. If you specify "Normal," for example, the software will fit the best possible Normal distribution to the data and superimpose it on the histogram in green.  
5  Filter: Sometimes, you may not want to plot all the data points on the scatter plot, especially if you have too many points in your data set. The scatter plot can become very crowded and consume significant computing resources to generate the scatter plot. In this case, we can use the filter to randomly select a subset of the data to create the scatter plot. Note that sequential sampling is used to select the random numbers. For example, if you choose a filter of 10%, then only 10% of the data points are used to generate the scatter plot. The default value is None or no filter, where all the data points are used to create the scatter plot.  
6  Checkbox Options: At the bottom are three checkbox options, and you can superimpose a fit on the data points, which are either linear, quadratic, or cubic.  
7  Statistics:
A brief set of statistics for the given data set is shown on the righthand side for the X and Y data sets. Currently, the following stats are shown.
 
8  Overlay Lines: Suppose you want to superimpose additional horizontal or vertical lines on your scatter plot. In that case, you can specify the values in these textboxes, and those additional lines are displayed on your plot. Note that only lines within the current graph boundaries are displayed. 
1  Variable: Select the variable for which you would like to generate sensitivity analysis. The dropdown box lists all the output variables. A sensitivity analysis of the input variables is performed.  
2  Group: Select the simulation number you want to use to create the box plot. The sensitivity analysis results may change between different simulation runs.  
3  Method: Specify the method used to determine sensitivity analysis numbers. You can choose between correlation or regression. If you pick correlation, then the Spearman rank correlation coefficients are used. If you pick regression, then the Pearson correlation coefficients are used.  
4  Filter: Sometimes, instead of looking at all the data, you may want only to consider the top 10% of the data points. You want to determine if the top 10% of the data points have a different sensitivity compared to using all the data. In this case, you can choose the filter as Top 10%. Similarly, you can compute sensitivity analysis for the top 20%, top 30%, bottom 10%, bottom 20%, and bottom 30% of the data.  
5  Statistics:
A brief set of statistics for the given data set is shown on the righthand side. Currently, the following stats are shown for each group.

1  Range: First, select a range to create the trend plot. The range you pick may contain input or output variables. The data from these variables is used to create the trend plot. Ensure that the range you select is in the proper time sequence: the first data point is plotted first, the second data point is plotted second, etc.  
2  Simulation: Select the simulation number you want to use to create the trend plot.  
3  Interval: If you would like confidence intervals on the plot, specify the period. For example, if you select P80, the 80% confidence interval bounds are plotted. The bottom red line will be 10%, and the top red line will be 90%.  
4  Statistics:
A brief set of statistics for the given data set is shown on the righthand side. Currently, the following stats are shown for each group.

Option  Description 

Input Summary  Specify what information you want to display in the notes section for the model, inputs, outputs, random numbers, and assumptions. 
Basic Stats (Inputs)  Specify for which of the input variables you want to display the basic statistical summary. A histogram is plotted for this selection. 
Basic Stats (Outputs)  Specify for which of the output variables you want to display the basic statistical summary. A histogram is plotted for this selection. 
Correlation Matrix  Specify for which combination of inputs and outputs you want to display the correlation matrix. A scatter plot will be plotted for this selection. 
Capability Analysis  Specify for which outputs you want to display the capability analysis. A capability plot will be plotted for this selection. 
Sensitivity Analysis  Specify for which outputs you want to display the sensitivity analysis results. A sensitivity chart of relative contribution will be plotted for this selection. 
Simulations Box Plot  Specify for which output variables you want to compare the simulations box plot. A box plot will be plotted for this selection. 
1  Num Variables: Specify the number of decision variables. You can have up to 100 decision variables for your optimization model. Decision variables are under the designer's control, and we are interested in finding those settings that will result in an optimal output from our model. For example, if we are designing a heating coil, the random variables could be voltage and current, which could change randomly within a range. The output of interest could be the time to heat the coil, and possible decision variables could be the coil's length or the coil's resistivity, which the designer can adjust. 
7  Data Type: Specify if your decision variable is continuous or discrete. A continuous decision variable can take any values between the min/max while a discrete decision variable can take only a limited set of values such as 0, 1 or 0, 0.5, 1.0, etc. 
8  Cell Location: Specify the location of the decision variable that needs to be optimized. The value on the worksheet will be varied to search for an optimum. Note that decision variables are not input variables defined in the model but vary depending on the specified probability distribution. 
9  Minimum: Specify the minimum value of the input variable. No values below this will be searched. Ensure the minimum value is based on what you can practically achieve for this model in the real world. For example, if the length of the coil is a decision variable, we can probably use coils that are 0.1 mm to 1 mm. Then, the minimum value is 0.1 mm. 
10  Maximum: Specify the maximum value of the input variable. No values above this will be searched. Make sure the maximum value is based on what you can practically achieve for this model in the real world. For example, if the length of the coil is a decision variable, we can probably use coils that are 0.1 mm to 1 mm. Then, the maximum value is 1 mm. 
11  Increment: Specify the increment value. This value is only used for discrete decision variables. In the previous example, if the increment value is 0.1, the software will only test decision values such as 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, and 1.0. This value will be ignored for continuous decision variables, and any continuous value between the minimum and maximum is selected. 
12  Cancel Button: Cancel all changes and exit this dialog box. 
13  OK Button: Save the changes and start the optimization. 
1  Num Objectives: Specify the number of objective functions you have for your optimization. For example, to maximize productivity while minimizing costs, you would have two objective functions: productivity and cost.  
2  Type:
Specify the type of objective. There are three options available
 
3  Cell Location: Specify the location of the cell that contains the objective function. The value located in this cell is optimized. Specify a valid Excel cell location such as E14 or $E$14.  
4  Lower Limit: Specify the lowest possible value for the objective function that can be achieved. This value is used to compute the desirability function for our optimization. For example, the room's temperature needs a target value of 21 but can range from 18 to 24. Then, the lower limit is set at 18. Any temperature value less than the lower limit is given a desirability value of 0 (for target optimization). If we try to minimize an objective, any value of the objective function less than the lower limit is given a desirability value of 1. Similarly, if we try to maximize an objective function, any value of the objective function less than the lower limit is given a desirability value of 0.  
5  Target Value: Specify the target value you would like to achieve. This value must only be specified if your objective type achieves a target value. The desirability is 1.0 when the objective function reaches the target value. This value is not required for the minimization or maximization of objective functions.  
6  Upper Limit: Specify the most significant possible value for the objective function that can be achieved. This value is used to compute the desirability function for our optimization. For example, the room's temperature needs a target value of 21 but can range from 18 to 24. Then, the upper limit is set at 24. Any temperature more significant than the upper limit is given a desirability value of 0 (for target optimization). If we try to maximize an objective, any objective function value more significant than the upper limit is given a desirability value of 1. Similarly, if we try to minimize an objective function, any value of the objective function more significant than the upper limit is given a desirability value of 0.  
5  Weight: Specify the weights. This is especially useful if there are multiple objective cells. The weights determine the relative importance of each objective. The desirability functions of each objective are calculated and combined into a single desirability function using the weights. The greater the weight specified, the more important is the objective function relative to other objective functions. 
1  Num Constraints: Specify how many constraints you would like to define for your optimization model. Note that there is no need to specify the minimum and maximum values for the decision variables since these are already specified in the variables dialog box. 
2  LHS Value: Specify the cells that contain the constraints. Select a cell or enter a value in the dialog box settings. 
3  Relation: Specify if the left side is less than, equal to, or greater than the right side. 
4  RHS Value: Specify the cells that contain the constraints. Select a cell or enter a value in the dialog box settings. 
1  Method:
Specify the method to use for optimization. There are three methods available for this optimization:
 
2  Screen Display: Specify if you want to update the display in between runs. If you specify Yes, then the screen updating is turned on. For each iteration, the values on the worksheet are updated. This can considerably slow down your optimization. It is recommended that you keep the Screen Display to No.  
3  Max Iterations: Specify the maximum number of iterations to run the optimization algorithm. Note that you can always continue to run from the last case to increase the number of runs. For example, if you set max iterations as 100 and complete your analysis, you can click the Continue button to run another 100 iterations.  
4  Max Time: Specify how long you want the optimization algorithm to run. If you specify an unlimited time, the stopping criteria are either the solution converges to an optimal solution or the number of iterations is exceeded. If you specify a time value, the optimization stops after reaching the time limit. It is recommended that you leave this setting at Unlimited time.  
5  Population Size:
The population size in a genetic algorithm refers to the number of individuals in the population at any given generation. It is a critical parameter that can affect the performance of the algorithm. A larger population typically leads to more diverse solutions and a higher probability of finding a better solution. This is because a larger population provides more genetic material for the recombination and mutation operations, which can lead to a broader exploration of the search space. However, a larger population also requires more computational resources and can result in slower convergence rates. Conversely, smaller population sizes can lead to faster convergence rates but at the cost of reduced diversity in the population, which can lead to premature convergence and suboptimal solutions. The population size choice depends on the problem's complexity, the available computational resources, and the desired convergence rate. In practice, the population size is often determined through experimentation and tuning to find a balance between exploration and exploitation.  
6  Tolerance:
The tolerance or stopping criterion in a genetic algorithm refers to a condition that signals the termination of the algorithm. This condition can be based on various factors, such as the fitness of the individuals in the population, the number of generations, or the time taken to reach a solution. Once the stopping criterion is met, the algorithm terminates, and the best individual in the final population is returned as the solution. The tolerance or stopping criterion choice depends on the problem and the application's requirements. Balancing the tradeoff between finding an optimal solution and the computational resources required is essential. For instance, if the goal is to find the best possible solution, a stringent stopping criterion may be used, even if it involves a lot of computational resources. On the other hand, if the goal is to find a suitable solution within a limited time or resources, a looser stopping criterion may be used to terminate the algorithm sooner.  
7  Crossover Rate:
The crossover rate in a genetic algorithm refers to the probability that two individuals will exchange genetic information during reproduction. It is a parameter that controls the frequency of the algorithm's crossover (recombination) operations. During the crossover operation, pairs of individuals are randomly selected from the population, and some of their genetic material is exchanged to create new offspring. The crossover rate determines the probability that a crossover operation will be applied to a pair of individuals. A high crossover rate can lead to a faster convergence rate, as it promotes the exchange of genetic material and the creation of diverse offspring. However, a very high crossover rate can lead to premature convergence and reduce the diversity of the population. Conversely, a low crossover rate can reduce the diversity of the population and increase the time required for convergence. It can also result in the algorithm getting stuck in local optima. The choice of the crossover rate depends on the complexity of the problem, the population size, and the desired balance between exploration and exploitation. The crossover rate is often determined through experimentation and tuning to find the optimal rate that balances exploration and exploitation for a particular problem.  
8  Mutation Rate:
The mutation rate in a genetic algorithm refers to the probability that an individual's gene will be subject to a random change during reproduction. In other words, it is the rate at which mutations occur in the genes of the offspring during the recombination process. The mutation rate is a critical parameter in genetic algorithms, as it controls the balance between exploration and exploitation. A higher mutation rate can increase the diversity of the population, which can help the algorithm to escape from local optima and explore the search space more extensively. However, a high mutation rate can lead to excessive randomness and decrease the convergence rate. Conversely, a lower mutation rate can lead to faster convergence rates, but at the cost of reduced exploration and the possibility of getting stuck in a local optimum. The choice of mutation rate depends on the complexity of the problem, the population size, and the desired balance between exploration and exploitation. In practice, the mutation rate is often determined through experimentation and tuning to find the optimal rate that balances exploration and exploitation for a particular problem. 
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