# An alternative approach for analyzing reliability networks is to identify all possible combinations.

An alternative approach for analyzing reliability networks
is to identify all possible combinations of failure events of the components,
compute the probabilities of those outcomes resulting either in system failure
or in a system success (nonfailure), and sum the individual probabilities to
obtain the system failure probability or reliability. Since each component has
two states, success (S) or failure (F), there are 2″ mutually exclusive
combinations to be considered, where n is the number of components composing
the network. Forthe system of Exercise 5.17, the analysis will take the
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An alternative approach for analyzing reliability networks
is to identify all possible combinations of failure events of the components,
compute the probabilities of those outcomes resulting either in system failure
or in a system success (nonfailure), and sum the individual probabilities to
obtain the system failure probability or reliability. Since each component has
two states, success (S) or failure (F), there are 2″ mutually exclusive
combinations to be considered, where n is the number of components composing
the network. Forthe system of Exercise 5.17, the analysis will take the
following form:

Complete this problem by identifying all possible
combinations and summing the probabilities of those resulting in a system
success. Compare your result with that obtained from the decomposition approach
used in Exercise 5.17.

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