Reliability Block Diagrams

Composing component reliabilities into a plant-level figure through series and parallel structure - the skeleton of the availability model.

Structure sets reliability

A reliability block diagram (RBD) expresses how component reliabilities combine into system reliability by their logical structure. Components in series all must work; components in parallel provide redundancy. The RBD is the skeleton the Monte-Carlo simulation walks and the fastest way to see where a single point of failure hides.

Series and parallel

from functools import reduce
def series(rs):    return reduce(lambda a, b: a * b, rs, 1.0)
def parallel(rs):  return 1.0 - reduce(lambda a, b: a * (1 - b), rs, 1.0)

# breeder magnet supply, no redundancy (series) vs redundant sensors (parallel)
print(series([0.99, 0.995, 0.98]))          # all must hold
print(parallel([0.9, 0.9, 0.9]))            # any one suffices

Series structure multiplies reliabilities, so a long series chain is fragile - each added component drags the product down. Parallel structure multiplies unreliabilities, so redundancy sharply reduces the chance all paths fail together, as long as failures are independent.

Single points of failure

Where it points the work

Any component in a series path with no parallel alternative is a single point of failure; the RBD makes these visible so they get either redundancy or intensified predictive maintenance. For the burner the plug coil is an inherent series SPOF - there is no spare - which is one reason the honest availability envelope cannot reach Tier III at single-unit scale. Independence assumptions are stress-tested in the Markov models and Monte-Carlo.