Since you are dealing with Booleans, I would name the array 'Booleans' (I'm creative like that!)
If you use logic operations, the formula would be
= OR(Booleans)
= OR(X, Y, Z)
There are a number of ways of converting the TRUE to 1, including
= SIGN(OR(Booleans))
= SIGN( OR(X, Y, Z) )
If you prefer to stick with arithmetic operators, you could turn to de'Morgan's laws to reformulate the formula
= 1 - PRODUCT(1 - Booleans)
= 1 - (1-X)*(1-Y)*(1-Z)
[equivalent to
= NOT(AND(NOT(Booleans)))
= NOT( AND(NOT(X), NOT(Y), NOT(Z)) ) ]