Conditional Probability

[Robbie]

In Reno, how do I model conditional probability. If I want to model a (say a pump), which has already has survived to say 4 years, and want to find out the probability of survival for another year. (given I know eta and beta). I do this pretty easily using Weibull++, but am trying to work out how do it in Reno - I know its probably simple, but I'm just starting out with this tool.

Thanks,

Alex

[Robbie]

I guess I may be answering my own question, but I see one way to do it is by actually using the conditional relibaility formula of

R(t/T) = R(T+t)/R(T)

Is there a simpler way?

[Robbie]

I worked out how to do the conditional probability problem I asked earlier but here's the actual problem I'm trying to model. I have three pumps (current life = 1.5, 2.5 and 3.5 yrs respectively). I have carried out the life data analysis in Weibull++ and calculated 2P Weibull with Eta = 2 and Beta = 8. Repair time = normal dist. with mean = 0.1yrs and std dev = 0.01yrs. If these pumps are started runnning from their current run life, how many failures will I experience over three years, taking into account the repair times and that the pumps are non-repairable (and would be replaced on failure with a new one). Can anyone describe how I model this in Reno - My problem is actually more complicted than described above, but if I can see how this simplified model is done, I should be ok. (I actually have 23 pumps in my system with a wider range of current rune lifes)

[Arai.M]

As a first thought I would suggest using ReliaSoft’s BlockSim instead, just because it is already built to solve your problem.
Now to solve this in RENO, there are many approaches. It is a good idea to first come up with an algorithm that will solve what you are trying to do. Something along the lines of:
1. Draw 23 failures at random that follow Weibull(8, 2), given the current life of each pump
2. Find the pump that will fail first/next
3. Obtain a new failure for that pump, i.e. New Failure Time = Previous Failure Time + Repair Time + Random failure time
4. Update the expected number of failures
5. Return to step 2.
Because you want to be able to do this with a somewhat large number of components, I would suggest the use of tables. You can read and write to them and also get the value and row corresponding to the minimum values in the table. I suggest using the function wizard to identify the predefined functions available as well as their inputs. The functions that I just mentioned are: MIN_TABLE and MININDEX_TABLE.
Now in order to get the first failure considering that you have some usage on the unit you will have to use the conditional reliability equation you mention above:
R(t|T)=R(T+t)/R(T)
Assuming R(t|T) can be modeled with a uniform random number, you can use a predefined function in RENO as follows:
First failure = WEIBULLINV(failureprobability, beta, eta, gamma) - T
Where
Failureprobability = 1-R(t|T)*R(T) = 1 – URN*R(T)
and T = current life
I hope this helps.
Regards,
Arai

[Robbie]

It does help. I did, and will continue, to use a combination of BlockSim and Weibull++ to carry out the analysis with multiple pumps. In truth, I was trying to get up to speed on Reno using a something which is a known problem/challnge to me i.e. I know what the results should look like, so simulating it in Reno is helping me learn the 'art'. After a somewhat sceptical start, I'm now beginning to appeciate the flexibaility and ease of use and potential applications of Reno. I hope to attend a class in 2011 - any plans to run a course on Reno in Europe during 2011?

Thanks
Robbie

[Arai.M]

Yes it is quite a flexible platform. Unfortunately, we don't have immediate plans for a RENO course in Europe but we'll definitely keep it in mind.
Thanks,
Arai