Risk Reduction Worth (RRW)
Risk Reduction Worth (RRW) measures how much risk reduction is on the table if a basic event is eliminated entirely. It's the ratio of baseline P(top) to P(top) with the event made perfectly reliable. RRW answers an offensive question: "what's the maximum I could improve the system by fixing this one component?" — the headline number for ranking improvement projects by leverage.
Formula
RRW(i) = P(top) / P(top | event i = FALSE)
Always ≥ 1. RRW = 1 means the event is irrelevant; RRW = 10 means perfecting that event would cut top-event probability by a factor of 10. RRW is sometimes also written as the inverse 1/RRW — check which form a given tool uses.
Worked example
Tree: TOP = OR(a, b, c) with P(a) = 0.1, P(b) = 0.001, P(c) = 0.0001.
P(top) ≈ 0.1 + 0.001 + 0.0001 ≈ 0.1011 (rare-event approx) P(top | a = 0) ≈ 0.001 + 0.0001 ≈ 0.0011 RRW(a) = 0.1011 / 0.0011 ≈ 91.9 P(top | b = 0) ≈ 0.1 + 0.0001 ≈ 0.1001 RRW(b) = 0.1011 / 0.1001 ≈ 1.01
RRW(a) ≈ 92 means perfecting a would reduce risk by a factor of 92. RRW(b) ≈ 1.01 means perfecting b barely moves the needle — a is so much more probable that b's contribution is dwarfed.
RRW vs Birnbaum vs FV
The three importance measures answer related but distinct questions:
- Birnbaum — marginal sensitivity (∂P(top)/∂P(i)).
- Fussell-Vesely — fraction of present risk attributable to the event.
- RRW — ratio improvement if the event is eliminated.
- RAW — ratio degradation if the event is forced to fail.
For improvement-prioritisation conversations with budget owners, RRW is usually the most intuitive number — "fixing X delivers a 90× risk reduction" lands harder than a partial-derivative explanation.