## Monte Carlo Simulation

Occasional Contributor

Joined:

May 10, 2017

Hi Community, I created a table of months (x) per failure frequency (y). After I analyse the distribuition and created an another colunn with randon for the best fit distribuition (smallest AICs). But I need the calculate the final probabilty of union the five events (TOP EVENT)  and the simulation (10000 iterations) give me in failure frequency. How did I get the probability failure X months the TOP EVENT with 10000 iterations?

2 ACCEPTED SOLUTIONS

Accepted Solutions

Community Trekker

Joined:

Jun 5, 2014

Solution
Hi, Mayre! Some people get hung up on the phrase "Monte Carlo" since it means something very specific to them, but let's just talk about simulation for a moment. For simulations to be successful, a few things are required: 1) the number generator produces values that pass tests for randomness, 2) enough samples are generated to yield accurate results, 3) proper sampling techniques are used, 4) the algorithm used is valid for what is being modeled, and 5) it simulates the phenomenon in question. JMP can deal well with numbers 1 and 2, but 3, 4, and 5 are up to the modeler (you) to specify correctly. It has been my experience that 4 and 5 are the most difficult and error-prone. I advise you to spend enough time studying those requirements as they relate to your situation. For instance, it might be better to use distributions chosen by theory than by best fit. By the way, one definition of Probability is a relative frequency of occurrence. Since you know the frequency of faults, and the total number of samples generated, why wouldn't that be an estimate of fault probability?

Occasional Contributor

Joined:

May 10, 2017

Solution

Hi Kevin,

I did the simulation considering the probability as the frequency the faults and the total number of samples generated , then I got the probability of faults. The algorithm used was the probability formula for independents events. I considered the exponencial  distribution the better because the faults values can not be negative.

Thank you a lot!!

7 REPLIES

Community Trekker

Joined:

Jun 5, 2014

Hi, Mayre!

JMP and JSL have great simulation capabilities.

If you could reformulate your problem, your data, and your intended approach with considerably more detail, perhaps we could help?

Occasional Contributor

Joined:

May 10, 2017

Hi Kevin,

I need to simulate  the failure probability of specific event (Top Event of FTA - FAILURE TREE ANALYSIS).

I performed the following steps:

I created the table with the data:

1) X (rows) - months and Y (column) the frequency that are historical dates of 23 months of observations.

example: 1     1

2     1

3      0  ......

2) Fit distributions to historical subassembly (total 5 subassembly)

3) Created  new data (with new column) set of with random draws from the distributions for the five subassemblies

4) Created the new colunm (TOP EVENT), but the colunm should be the failure probabilty of TOP EVENT ( TOPO EVENT = TOTAL PROBABILITY)

Question: I can not add the frequencies of failures. I need the calculate the probability. The final formula is:

P(T) = P(F1)+P(F3)+P(F4)+P(F5)+P(F6) - (P(F1).P(F2) - P(F3).P(F4) - P(F4).P(F5) - P(F5).P(F6)) - P(F1).P(F3).P(F4).P(F5).P(F6)

How do I transform frequency in probability in this case?

Community Trekker

Joined:

Jun 5, 2014

Hi, Mayre!

I'm assuming if a subsystem fails, the entire system fails.  Is that correct?

Are the subsystems completely independent?

Did you make a mistake in your formula, leaving out p(F2)?  Or was that your intention?

Occasional Contributor

Joined:

May 10, 2017

Hi, Kevin
First, I thank you for your attencion.

I´m assuming all the subsystens completely independents. There is no F2 subsystem, only F1, F3, F4, F5 and F6, all independent.

I´m following the steps the link above: "Using JMP to Assess Risk in Financial Predictions by Using Monte Carlo Simulations

But my work I´m using the FTA (Failure Tree Analysis) for calculate the probability the TOP EVENT. I´m using the cuts sets and the final formula was

E = F1 +F3+F4+F5+F6

As the event are independents, the probability  should be calculate. But my result is in frequency of faults is not probability.

Community Trekker

Joined:

Jun 5, 2014

Solution
Hi, Mayre! Some people get hung up on the phrase "Monte Carlo" since it means something very specific to them, but let's just talk about simulation for a moment. For simulations to be successful, a few things are required: 1) the number generator produces values that pass tests for randomness, 2) enough samples are generated to yield accurate results, 3) proper sampling techniques are used, 4) the algorithm used is valid for what is being modeled, and 5) it simulates the phenomenon in question. JMP can deal well with numbers 1 and 2, but 3, 4, and 5 are up to the modeler (you) to specify correctly. It has been my experience that 4 and 5 are the most difficult and error-prone. I advise you to spend enough time studying those requirements as they relate to your situation. For instance, it might be better to use distributions chosen by theory than by best fit. By the way, one definition of Probability is a relative frequency of occurrence. Since you know the frequency of faults, and the total number of samples generated, why wouldn't that be an estimate of fault probability?

Occasional Contributor

Joined:

May 10, 2017

Solution

Hi Kevin,

I did the simulation considering the probability as the frequency the faults and the total number of samples generated , then I got the probability of faults. The algorithm used was the probability formula for independents events. I considered the exponencial  distribution the better because the faults values can not be negative.

Thank you a lot!!

Occasional Contributor

Joined:

May 10, 2017

Hello Community,

I did the Monte Carlo simulation with 10.000 iterations, now I need to know what the statistical parameters of simulation evaluation. What is the best statistical parameter to evaluate the simulation.

Best regards

Mayre