(4) For an event expression ee1 ∨ ee2, where ee1 and ee2 are two event expressions,

  P( e e 1  ∨ e e 2 )=P( e e 1 )+P( e e 2 )*P( e e 2 ), ∂P( e e 1 ∨e e 2 ) ∂P( e i ) ={ ∂P( e e 1 ) ∂P( e i ) *( 1−P( e e 2 ) ), if  e i  occurs in e e 1 ∂P( e e 1 ) ∂P( e i ) *( 1−P( e e 2 ) ), if  e i  occurs in e e 2 .           ( 12.8 )

Implementation Details. An event expression ee can be represented by a binary tree T where each leaf node denotes a basic event identifier and each non-leaf node denotes an operator ∧, ∨ or ∼. Figure 12.4 gives an example of a binary tree which represents the event expression (e1∧ ∼e2) ∨ (e3∧ ∼e4) ∨ (e5∧ ∼e6).

For each node

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