Application of a Boolean Identity for Fault Trees

In this paper various conditions that should exist in the fault trees for the application of Boolean identity x
_I
x
_j
+ x
_I
x
_j
= x
_I
have been discussed. It has also been algebraically proved that this identity is not required if preceded by x
_I
+ x
_I
x
_j
= x
_I
and x
_I
x
_j
+ x
_I
x
_{j = xIxj, in the simplification of logical expressions of fault trees, or else when the fault tree has a redundant arc.}