What is the difference between random uniform and fixed setting of monte carlo simulation?

[#1]

I am making monte carlo simulation with DoE experiment result.

As I understood, monte carlo simulation (simulation experiment of prediction profiler) works with below sequence.

(1) Generate experiments with random X factors with ratin hypercube.

(2) Each experiment has X factors which is generated randomly. Each experiment makes N runs of draws which have X factors as center point and they follow distribution set in prediction profiler.

(3) Calulate failure rate at each experiment.

(Please correct if above things are worng)

My question is, what is the difference between random uniform and fixed setting of prediction profiler.

I thought, random normal means the X factors of (2) are following normal distribution durin N runs of draws,

thus, random uniform means the X factors of (2) have uniform distribution for N runs of draws and fixed means the X factors of (2) are fixed during the draw.

Please kindly provide your comment what am I understanding correctly.

[#2]

Hi @jmpneeeewbie,

Welcome in the Community !

What you're describing is the generation of points through the Simulator to create a datatable (a subset of the points generated by the Monte Carlo simulations) where you may find informations here : Simulation Experiment (jmp.com)

The Monte Carlo simulations is more general than the process you describe.

1. First, you define a domain of possible inputs : you specify the distributions of your input parameters (random normal, uniform, lognormal, Weibull, multivariate, ...). An input parameter set as "fixed" won't have any distribution of values, and only the single point value will be used in the calculations (so you don't take into account any random variability for this input variable for example). See : Simulation Settings for Factors (jmp.com)
2. Then, you can also add noise (random, weighted, multivariate, or no noise) for your responses as well, to take into account variability in the output measurement for example. See : Simulation Settings for Responses (jmp.com)
3. Then, a generation of inputs is done randomly from the inputs probability distributions over the domain you specified in step 1 and 2, when you click on "Simulate" and performs a  deterministic computation on the inputs, thanks to the model you have created before (linking the inputs to output(s)). If you added noise in the outputs, the noises are also taken into consideration in the calculated values.
4. Finally, results are aggregated to create responses distributions, that you can see in the profiler in above "Simulate" button.

You can see an example I did with the JMP datatable 2x3x4 Factorial (available in the Sample Data Folder, in "Design of Experiments"). I also join the datatable with the script "Monte Carlo Simulations" if you want to see it in more details.

If you want to find more informations about Monte Carlo simulations, you can find some here : Robust Optimisation of Processes and Products by Using Monte Carlo Simulation Experiments - JMP User...

I hope this answer will help you,

[#3]

Thank you Victor_G.

I thought "Monte Calro Simulation" is same with the simulation experiment in below pic.

[#4]

Hi @jmpneeeewbie,

Yes, "Simulation Experiment" is based on the Monte-Carlo simulations, and it give you only a subset of all possible values of your experimental space, based on the portion of experimental space you specify (and the number of points).
More infos here : Simulation Experiment (jmp.com)

But you also have the possibility to check graphically the impact of variability of your inputs (and possible noise in the response(s)) directly in the Profiler, by clicking on "Simulate" button, next (on the right) to the Desirability case on your screenshot.

I hope this answer will help you,

[#5]

Thank you for response @Victor_G.

Get back to my original question.

Than, at the "simulation experiment" what the fixed is meaning?

If it is fixed at the point I choose, the simulation experiment can not work at all experiment space.

Thus, I think it will fixed at X factor where each experiment point.

And, what is the difference with random uniform at the "simulation experiment"?

[#6]

Hi @jmpneeeewbie,

Fixed : Fixes the factor at the current value in the profiler for all simulation runs. (from : Simulation Settings for Factors (jmp.com))

So it means that in the computations, a portion of single values will be used in all simulations, depending on the portion of factor space you're specifying. There will be no random variations added for the "fixed" factors, so computations will be done directly using the model from the Profiler. 

For example in the example JMP datatable "2x3x4 Factorial", if I fix all factors and use "Simulation Experiment" and specify 128 runs and portions of factor space 0,5 then JMP will create 128 runs with continuous factor X1 in the range of -0,5 to 0,5 (instead of full factor range -1 to 1) and will test all levels for the categorical factors. But no random variations is added, so all computations are done with the model found before (completely deterministic outcome).

Between Simulation Experiment with fixed factor and Random Uniform factor, the difference will be in the output of the table and levels of the factor used. The "Simulation Experiment" platform uses a Latin Hypercube, so different levels will be chosen and approximately same number of experiments will be done for each levels. This is not necessarily the case with the "Random Uniform" factor option, since this process will be ... random. You can compare the two tables on the JMP dataset to see the differences (same number of runs, one table created with Simulation Experiment, the other with Random Uniform factor X1) or look at the images provided showing you the different distributions for X1 depending on which option you choose (Random Uniform on X1 or Simulation Experiment).

I hope I understood your questions correctly,

[#7]

Hi @Victor_G 

Thank you for reply.

For summary,

"simulation experiment" makes runs using Latin Hypercuber.

Each run has specific X factor level and calculate failure rate using setting in profiler.

Just for example, we have model with two X factors and simulation experiment 1000 runs made by Latin Hypercube (N runs for simulatior : 20,000)

There is a run which has two X factor (a,b)

At this run, 

Random normal: Calculate failure rate with 20,000 N draws which have normal distribution with center point (a,b).

Random uniform: Calculate failure rate with 20,000 N draws which have ramdom X factors not cosidering (a,b). It means (0,0), (a,b), (a,a), (b,b)...... have same probability.

Fixed : Calculate failure rate with 20,000 N draws with fixed X factor. During all N draws X factors are fixed at (a,b)

I hope I understand correctly.

Thank you @Victor_G !

[#8]

Hi @jmpneeeewbie,

Yes for Simulation Experiment, Random Normal and Random Uniform (for this last point, you're right about the same probability, the range of possible values will depend on the range you specify for this Uniform distribution).

For your Simulation experiment, you also have to take into account the portion of space you would like to explore. For Fixed factor value, you're right that values are fixed for Profiler, but if you use "Simulation Experiment" and specify a portion of the experimental space you would like to explore, then you'll get simulated X1 and X2 values centered at (a,b) but with broader ranges. You come back to the situation with Latin Hypercube.
For example, if X1 is set at -0,5 and X2 at 1 with a portion of experimental space set at 0,5 then the Simulation Experiment platform will create runs with Latin Hypercube with X1 in the range [-1;0] and X2 in the range [0;1]. If one of the factor is set at 0 with the same other setting, the range will be [-0,5; 0,5].

You can try these options with JMP datatables just for practice by using JMP Sample Index/Data Folder.

I hope I didn't confuse you more,