Reliability Block Diagram

About reliability block diagrams

A reliability block diagram (RBD) shows the success logic of a system: each component is a block on a path from an input node to an output node, and the system works as long as an unbroken path of working blocks connects the two. Components in series all have to work; components in parallel give redundancy (any one suffices); a k-of-n group works when at least k of its n members do. It is the standard tool of RAMS (reliability, availability, maintainability, safety) engineering, defined by IEC 61078:2016 and MIL-HDBK-338B.

Schematex's edge is that the engine computes the answer, not just the picture: from the per-block reliabilities it reduces the structure to the system reliability (∏ for series, 1−∏(1−Rᵢ) for parallel, exact enumeration for k-of-n), derives the Birnbaum reliability importance of every block (which one moves the needle most), and flags single points of failure — blocks whose failure alone fails the system — in red. That is the same stance faulttree takes toward cut sets and pert toward scheduling. RBD is the success-space dual of the fault tree's failure-space.

1. Your first diagram

Every document starts with the rbd keyword (alias reliability), an optional title, then nested success-logic groups around block leaves:

rbd "Two redundant pumps"
  parallel {
    block A "Pump A" R=0.9
    block B "Pump B" R=0.9
  }

The engine draws the two pumps on parallel rails between a split node and a join node, computes the system reliability 1 − (1−0.9)(1−0.9) = 0.99, and prints it as the headline. A bare top-level list of blocks (no outer group) is treated as a series chain.

2. Blocks

A block is one component on a success path:

block ID "Label" R=0.99

• ID — a short identifier (shown when no label is given).
• "Label" — an optional display name (CJK quotes welcome).
• Reliability is given as R=0.99 (reliability/availability), p=0.01 (probability of failure, → R = 1−p), or a percentage R=99%. A block with no reliability leaves the system figure symbolic (n/a).

3. Success-logic groups

Groups nest freely, so you can model redundant chains, voting banks, and standby pairs:

series {
  block CTRL "Controller" R=0.995
  parallel {
    series { block P1 "Path 1 sensor" R=0.97
             block A1 "Path 1 actuator" R=0.98 }
    series { block P2 "Path 2 sensor" R=0.97
             block A2 "Path 2 actuator" R=0.98 }
  }
}

4. Computed reliability, importance & SPOF

After parsing, the engine computes:

• System reliability — the headline figure, by recursive series/parallel/k-of-n reduction.
• Birnbaum importance Iᴮ(i) = R_sys(Rᵢ=1) − R_sys(Rᵢ=0) for every block; the highest-importance block (the improvement target) is accented.
• Criticality importance I_C(i) = Iᴮ(i)·(1−Rᵢ)/(1−R_sys) — the probability block i is failed and critical, given the system is failed.
• Single points of failure — any block where R_sys(Rᵢ=0) = 0 (its failure alone fails the system) is drawn with a red border. A non-redundant block in series is always a SPOF.

5. Time-dependent reliability — R(t)

A static R= is the entry point; in practice reliability is a function of mission time. Set a mission: <t> and give blocks a failure distribution instead of a constant — the engine evaluates R(t) and rolls it up exactly as before. Use consistent time units across mission and the rates.

rbd "Pump station — 1-year mission"
  mission: 8760            # hours
  parallel {
    block A "Pump A" mtbf=10000
    block B "Pump B" weibull=1.5,12000
  }

The headline becomes R(t=8760) = …. A block with a distribution but no mission: warns and falls back to its constant R= (if any).

6. Validation

The parser reports non-fatal warnings rather than failing:

• a kofn k/n threshold with k > n is clamped to n (and k < 1 to 1);
• a reliability outside 0..1 is clamped;
• a duplicate block id is flagged.

7. Theming

theme: default uses the shared risk-reliability palette (neutral blocks, blue reliability numerals, red single-point-of-failure borders). theme: monochrome renders a black-and-white print version (SPOF by border weight); theme: dark is the Catppuccin dark variant.