If n = 4, how many minimal cut sets are there?

If n = 4, how many minimal cut sets are there?

• A. 5
• B. 9
• C. 15
• D. 7

Answer: (D)

Minimal cut sets are the smallest sets of component failures that make the system fail. To count them, you identify all ways the system can fail and discard any failure pattern that contains a smaller failure pattern that already causes failure. For the four-component network in this MAS-1 style problem, you get four minimal cuts that involve failing two components in just the right way to collapse the system’s two main support paths. Each of these two-component failures is minimal because removing only one component on one path isn’t enough to shut everything down. There are also three additional failure patterns that involve three components failing in a way that still isn’t captured by any smaller (two-component) cut. These three three-component patterns are minimal since removing any two of their components would not, by itself, cause system failure in this configuration. Put together, you have four minimal cuts of size two and three minimal cuts of size three, for a total of seven minimal cut sets. So with n = 4, the number of minimal cut sets is seven.

Minimal cut sets are the smallest sets of component failures that make the system fail. To count them, you identify all ways the system can fail and discard any failure pattern that contains a smaller failure pattern that already causes failure.

For the four-component network in this MAS-1 style problem, you get four minimal cuts that involve failing two components in just the right way to collapse the system’s two main support paths. Each of these two-component failures is minimal because removing only one component on one path isn’t enough to shut everything down.

There are also three additional failure patterns that involve three components failing in a way that still isn’t captured by any smaller (two-component) cut. These three three-component patterns are minimal since removing any two of their components would not, by itself, cause system failure in this configuration.

Put together, you have four minimal cuts of size two and three minimal cuts of size three, for a total of seven minimal cut sets.

So with n = 4, the number of minimal cut sets is seven.