I know, what Weibull approach does, but I do not know, what your neural network does.

If you perform a Weibull statistic, you obtain an estimate for the probability, that life time (from some "now" on) will be less than some value t. This function of t is the distribution function.

If your neural network provides this information, you can use it instead of the Weibull function to determine test or maintenance intervals.

Dear Günter,

Thanks your response. I mean, when we conclude that the ANN is better than Weibull for failure rate prediction or reliability prediction.

To my knowledge, ANN will not yield something in closed form. You train it based on a given set of life times, but what kind of question can you ask, and what result will you get?

Now, let us assume, that after proper training, you can give it a value of time, and the ANN will present you the probability, that life time is below that value. This would mean, the ANN calculates a reliability prediction.

Now, if you want to check the quality of the ANN, I suggest a MonteCarlo Experiment. Just take some life time distribution of your choice. Generate a number of realizations, and then use them to train your ANN and also perform a Weibul statistic.

Then, select some arbitrary times. As you know the life time distribution you selected, you can calculate the probability of life time below that value exactly. Given your Weibull model, you can use its parameter estimates to find the values of the distribution function. And - as we assumed your ANN also yields these probabilities, you would just have to look at the triples of true result, Weibull result, ANN result to find, how good your models are.

Of course, if you select a Weibull distribution to test this, a Weibull modell can be expected to perform better. If you take something different (Pearson, Johnson), this might provide more even chances.

Looking forward to here what came out.

Thank you so much for your valuable comments and suggestions.

I have already seen an article about the failure rate estimation with Monte Carlo and its comparison with Weibull and ANN methods as well as ANOVA.

I wanted to apply the Cumulative Distribution Function (CDF) and then prediction of CDF with ANN and finally, application of failure rate or reliability function in maintenance interval function. But, I have no information about accuracy of CDF and Monte carlo methods and their ability to failure rate or reliability prediction. I would be grateful if you could give me some feedback.

Thank you for taking the time again.

I am not sure, whether I completely understand this. CDF and (time dependent) failure rate are - provided the latter exists - are the same information. If you have CDF, you can calculate failure rate and vice versa.

My problem is, that I do not know, what your ANN does. Now, CDF (as well as failure rate) is time dependent. So, my guess was that after training with a sample of real life data, you can provide your ANN with a value of t, and it will tell your the CDF or failure rate at this time.

Second thing is: you could do the very same with Weibull estimation. You take the same sample a used for training to estimate Weibull parameters. Then, you could also take a value of t and ask your Weibull model for the value of CDF or failure rate at that time.

Now, you want to know, which one the two estimates is the better one. My problem is: If I do not know, from what distribution with what parameters the sample you used for training is taken, I cannot answer that question.

If, however, I knew the distribution (in terms of CDF or failure rate), than it is trivial to find the better estimate. It will be the one closer to the original distribution you used to find the sample.

This is why I suggested to use a random number generator to create your sample. And this is why there is no sense in asking for the accuracy of the Monte Carlo part. You will notice, that both the Weibull modell and the ANN will deviate from the true distribution used to generate the sample. And if your sample is small deviations will tend to be larger than for a large sample. The deviation will also depend on the actual value of t you used obviously.

So, there is a lot of analysis possible, if you vary:

• Type of distribution you sample from
• Size of sample
• Value(s) of t you use for testing.

Agreed with Günter Becker

Dear Günter Becker,

Sorry for my late reply.

Thanks for your taking time and effort to be responsive my question. I found them quite useful.

Warm regards,

Hamzeh

I think it depends on your focus. If you focus on discuss the methodoloy, you can choose a formula in literaure to illustrate your developed methodology. If you focus on analyzing a specific component, it may be very difficult unless you can do some experiments and get enough data which is very imporant to obtain the weibull parameter or train ANN.

First of all, there is no set rule which is applicable to all systems for preventive maintenance. It depends upon the type of system one is dealing with. You can apply ANN to improve the reliability .

I agree with Mohammad Asjad

Due to the Weibull distribution, you will be able to comment and create schedules about the behavior of the equipment and even the system.

Cost factor is the most important criterion in these scheduling. Thanks to the Weibull distribution, I suggest you take advantage of the relevant study below in order to determine maintenance periods about costs and failure.

Article A new approach to determine maintenance periods of the most ...

Dear all

Since this question goes back to two years ago, but thank you anyway and I found your comments very helpful :)

Cheers,

Hamzeh