evolvd
09-24-2009, 02:58 AM
Hi,
This is something that has been bother a colleague of mine and myself for a little while now. We are engineers, and we are trying to relate the probability distribution of a material strength, to the probability distribution of the capacity of the element.
For instance, first we applied the same percentage COV of the material to the design capacity of the component, and if the component got stronger, the probability density curve flattened out. This is somewhat illogical to me because if it's the same material, only more of it, my thoughts were that it should have the same PDF shape no matter how strong.
I then created a spreadsheet which calculated the PDF for each material strength across a set range (so material strength only, not the item capacity, i.e. irrespective of how much material there is), and then for each strength value in the range I calculated the capacity for a particular dimension of the unit. I then graphed the probability density values vs. the capacity (rather than the material strength), and the graphs were all the same height, but they became wider as the unit capacity increased. This means that the area under the graph changes, which means it isn't a true probability density curve.
I think the problem might be due to the fact that the capacity is a finction of the diameter cubed (section modulus of a circular section if interested), but this doesn't make total sense either.
I guess my question is - if you are trying to look at the probability desity function, or even the Cumulative probability of a system that contains a number of knowns and one variable, should the resulting PDF be that of the combined system, or that of the signle variable (i.e. apply the single variable COV to the mean capacity, calculated using the mean strength.
:confused: I'm going to stop talking now, because it is confusing enough. Maybe if you could have a look at the attached it might show you what I mean.
Any help is appreciated.
Cheers!
This is something that has been bother a colleague of mine and myself for a little while now. We are engineers, and we are trying to relate the probability distribution of a material strength, to the probability distribution of the capacity of the element.
For instance, first we applied the same percentage COV of the material to the design capacity of the component, and if the component got stronger, the probability density curve flattened out. This is somewhat illogical to me because if it's the same material, only more of it, my thoughts were that it should have the same PDF shape no matter how strong.
I then created a spreadsheet which calculated the PDF for each material strength across a set range (so material strength only, not the item capacity, i.e. irrespective of how much material there is), and then for each strength value in the range I calculated the capacity for a particular dimension of the unit. I then graphed the probability density values vs. the capacity (rather than the material strength), and the graphs were all the same height, but they became wider as the unit capacity increased. This means that the area under the graph changes, which means it isn't a true probability density curve.
I think the problem might be due to the fact that the capacity is a finction of the diameter cubed (section modulus of a circular section if interested), but this doesn't make total sense either.
I guess my question is - if you are trying to look at the probability desity function, or even the Cumulative probability of a system that contains a number of knowns and one variable, should the resulting PDF be that of the combined system, or that of the signle variable (i.e. apply the single variable COV to the mean capacity, calculated using the mean strength.
:confused: I'm going to stop talking now, because it is confusing enough. Maybe if you could have a look at the attached it might show you what I mean.
Any help is appreciated.
Cheers!