PENGGUNAAN ALJABAR BOOLEAN DALAM MENGANALISIS KEGAGALAN PADA FAULT TREE ANALYSIS

Abstract

System is the dimension which it limited by rule and have certain
characteristic. Execution of system do not always success, it is caused by some
component that causing fault at the system. Minimizing fault can be done by
searching the cause of the fault and then its construct to fault tree. Fault tree is a 

logic diagram that displays the connection between the fault event and the reason.
The connection between the fault event and the reason can be described by AND
gate and OR gate. AND gate is used if all of the input occurs and OR gate is used
if at least one of the inputs occurs. To analyze fault tree, for the first it is changed
to Boolean equation where AND gate and OR gate equivalent with product and
sum operation in algebra.
The methodology of this research is study of literature with search and collect
all of the materials that are related with fault tree analysis and Boolean algebra
and construct minimal cut set and minimal path set by using the construction of
fault tree which it is had and search the problem which it is solved by fault tree
analysis.
Minimal cut set from a fault tree can be obtained by using Boolean algebra.
But, not of all the rules of Boolean algebra are used. It is caused the fault at the
different of top event, so that different construction of fault tree for each different
fault. Minimal path set is obtained after getting the complement of minimal cut set
which it get before and using some rules of Boolean algebra. From minimal cut
set can be seen any kind of cause that can make the fault is happened and from
minimal path set can be seen any kind of cause that can make the fault is not
happened. Sum of minimal cut set and minimal path set are not always same for
each fault tree.