Percent of units experiencing conditions

[mecheng74]

Hello, I could use some help estimating the percentile of units experiencing mulitiple conditions.

A product can be installed in a wide range of environments. These effect the temperature of the product. There are three variables that have the biggest impact:
T = Room temperature
D = Distance to a local obstruction
H = Heat from a nearby product

For any given set of conditoins (T, B or H) we can calculate the resulting product temperature. Also for any condition (T, B or H) we can estimate percentile of products above/below that value. For example, a 21C room is at the 50th percentile, 30C room is at the 84th percentile, etc.

I would like to combine this info in a meaningful way. For example, we have several scenarios for T, D and H. How can I calculate the percentage of units that will experience each scenario? Or better, the number of units that will experience a certain temperature level?

 

[Hoaokapohaku]

What is the formula you are using to calculate the resulting product temperature? Are you looking for a spreadsheet solution?

 

[mecheng74]

I plotted test data on temperature vs T, D and H and correlated each set to a best-fit curve formula.

 

[btrueblood]

Well, take the simplest case. Suppose you have 2 subsets of each condition, i.e. T1, T2, D1, D2, H1 and H2. You have 2^3 distinct combinations to look at. For each condition, you have a weighting function that tells you probabilities for that condition, call them t1, t2, d1, d2, h1, h2. Doesn't matter what they look like, just that they are self-consistent numerical values, but ideally they should sum to 1.0

For condition T1-D1-H1, you would find the probability of that combination (lets call it P111) by mulitplying: t1 x d1 x h1

Etc. for remainining combinations.

It should work out that the sum of all combinations = 1.0

But it might not due to rounding errors, or if you didn't get the original weighting functions to sum to 1.0 for whatever reason...so I would just renormalize that sum to 1.0, i.e. figure out a factor to multiply it that gets the sum back to 1.0; then each individual combination value P111 could be multiplied by the normalization factor to get you to the final answer.

 

[btrueblood]

Sorry, forgot to add: the above can be generalized to any number/variety of combinations i.e. 3 T's, 4 D's and 2 H conditions.

 

[Hoaokapohaku]

Well...this sounds like a fun spreadsheet problem and the solution could have applicability to some of my own work. I'll take a stab at it if you will post the actual data in a spreadsheet.

 

[GregLocock]

As I posted in your annoyingly similar post elsewhere on eng-tips, you can either do it with statistics and maths, or a monte carlo sim of the population. The latter is easier and more fun, if less elegant.

Cheers

Greg Locock


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[btrueblood]

I like Monte Carlo sims too. Especially when you can bet on the outcomes...