SUMIFS with AND and OR

I've tried, I think most of the answers here, but I can not get them to work in my situation.

Translated to text, my problem would looked like this :

Sum Y:Y column with

condition 1 : Column B:B if string starts with "15*"
condition 2 : Column T:T must be greater then 0
condition 3 : OR (value from column U:U = 0 OR U:U > V:V )

Put in SUMIFS function, in theory, it would looked like this SUMIFS(Y:Y,B:B,"15*",T:T,">0",or(U:U,"=0", U:U>V:V)), but of course it doesn't work like that.

Also I've tried SUMPRODUCT and SUM(SUMIF...but I don't know how to translate what I like to accomplish into these two.

So please, if someone knows how to make this work. And some explanation please.

Thanks.

Solution

Here's SUMPRODUCT based solution which shall work for you.

=SUMPRODUCT(--(LEFT(B:B,2)="15"),--(T:T>0),((U:U=0)+(U:U>V:V)),Y:Y)

Caution: Apply complete column references only if necessary as it will slow down your sheet considerably. It is advisable to have a sufficiently large range (but not whole column references) as each column will have million cells to check.

Also note Barry's query about column V being negative has significance on the formula I have posted as it will calculate 2 TRUE conditions as 2 and therefore lead to erroneous result.