Simulator Report Options

Toggles histogram update, which sends changes to all histograms shown in the Profiler, so that histograms update with new simulated values when you drag distribution handles.

Defect Profiler

Shows the defect rate as an isolated function of each factor. This command is enabled when spec limits are available, as described below.

Defect Parametric Profile

Shows the defect rate as an isolated function of the parameters of each factor’s distribution. It is enabled when the Defect Profiler is launched.

Simulation Experiment

Used to run a designed simulation experiment on the locations of the factor distributions. A window appears, allowing you to specify the number of design points, the portion of the factor space to be used in the experiment, and which factors to include in the experiment. For factors not included in the experiment, the current value shown in the Profiler is the one used in the experiment.

The experimental design is a Latin Hypercube. The output has one row for each design point. The responses include the defect rate for each response with spec limits, and an overall defect rate. After the experiment, it would be appropriate to fit a Gaussian Process model on the overall defect rate, or a root or a logarithm of it.

A simulation experiment does not sample the factor levels from the specified distributions. As noted above, the design is a Latin Hypercube. At each design point, N Runs random draws are generated with the design point serving as the center of the random draws, and the shape and variability coming from the specified distributions.

Spec Limits

Shows or edits specification limits.

N Strata

Is a hidden option accessible by holding down the SHIFT key before clicking the Simulator red triangle menu. This option enables you to specify the number of strata in Normal Weighted. For more information also see Statistical Details.

Set Random Seed

Is a hidden option accessible by holding down the SHIFT key before clicking the Simulator red triangle menu. This option enables you to specify a seed for the simulation starting point. This enables the simulation results to be reproducible, unless the seed is set to zero. The seed is set to zero by default. If the seed is nonzero, then the latest simulation results are output if the Make Table button is clicked.

Using Specification Limits

The profilers support specification limits on the responses, providing a number of features

•	In the Profiler, if you do not have the Response Limits property set up in the input data table to provide desirability coordinates, JMP looks for a Spec Limits property and constructs desirability functions appropriate to those Spec Limits.

•	If you use the Simulator to output simulation tables, JMP copies Spec Limits to the output data tables, making accounting for defect rates and capability indices easy.

•	Adding Spec Limits enables a feature called the Defect Profiler.

In the following example, we assume that the following Spec Limits have been specified.

Spec Limits for Tiretread.jmp Data Table
Response	LSL	USL
Abrasion	110
Modulus		2000
Elong	350	550
Hardness	66	74

To set these limits in the data table, highlight a column and select Cols > Column Info. Then, click the Column Properties button and select the Spec Limits property.

If you are already in the Simulator in a profiler, another way to enter them is to use the Spec Limits command in the Simulator red triangle menu.

Spec Limits

After entering the spec limits, they are incorporated into the profilers. Click the Save button if you want the spec limits saved back to the data table as a column property.

With these specification limits, and the distributions shown in Profiler with Simulator, click the Simulate button. Notice the colored spec limit lines in the output histograms. The black dashed lines indicate the mean of the simulations.

Spec Limits in the Prediction Profiler

Look at the histogram for Abrasion. The lower spec limit is far below the distribution, yet the Simulator is able to estimate a defect rate for it. This despite only having 5000 runs in the simulation. It can do this rare-event estimation when you use a Normal weighted distribution.

Note that the Overall defect rate (0.05229) is close to the defect rate for ELONG (0.04756), indicating that most of the defects are in the ELONG variable.

To see this weighted simulation in action, click the Make Table button and examine the Weight column.

JMP generates extreme values for the later observations, using very small weights to compensate. Because the Distribution platform handles frequencies better than weights, there is also a column of frequencies, which is simply the weights multiplied by 1012.

The output data set contains a Distribution script appropriate to analyze the simulation data completely with a capability analysis.

Simulating General Formulas

Though the profiler and simulator are designed to work from formulas stored from a model fit, they work for any formula that can be stored in a column. A typical application of simulation is to exercise financial models under certain probability scenarios to obtain the distribution of the objectives. This can be done in JMP—the key is to store the formulas into columns, set up ranges, and then conduct the simulation.

Factors and Responses for a Financial Simulation
Inputs (Factors)	Unit Sales	random uniform between 1000 and 2000
	Unit Price	fixed
	Unit Cost	random normal with mean 2.25 and std dev 0.1
Outputs (Responses)	Revenue	formula: Unit Sales*Unit Price
	Total Cost	formula: Unit Sales*Unit Cost + 1200
	Profit	formula: Revenue – Total Cost

The following JSL script creates the data table below with some initial scaling data and stores formulas into the output variables. It also launches the Profiler.

dt = newTable("Sales Model");

dt<<newColumn("Unit Sales",Values({1000,2000}));

dt<<newColumn("Unit Price",Values({2,4}));

dt<<newColumn("Unit Cost",Values({2,2.5}));

dt<<newColumn("Revenue",Formula(:Unit Sales*:Unit Price));

dt<<newColumn("Total Cost",Formula(:Unit Sales*:Unit Cost + 1200));

dt<<newColumn("Profit",Formula(:Revenue-:Total Cost), Set Property(“Spec Limits”,{LSL(0)}));

Profiler(Y(:Revenue,:Total Cost,:Profit), Objective Formula(Profit));

Data Table Created from Script

Once they are created, select the Simulator from the Prediction Profiler. Use the specifications from Specifications for Profiler to fill in the Simulator.

Specifications for Profiler

Now, run the simulation, which produces the following histograms in the Profiler.

Simulator

Note: Your numbers might differ from those shown in Simulator.

It looks like we are not very likely to be profitable. By putting a lower specification limit of zero on Profit, the defect report would say that the probability of being unprofitable is 62%.

So we raise the Unit Price to $3.25 and rerun the simulation. Now the probability of being unprofitable is down to about 20%.

Results

If unit price cannot be raised anymore, you should now investigate lowering your cost, or increasing sales, if you want to further decrease the probability of being unprofitable.