Reliability Block Diagram vs Line Simulation
Availability Is Not Throughput
A reliability block diagram answers one precise question, which is what fraction of the time a system is able to run. On a production line, people often ask it a different question, which is how much the line will make. The diagram answers that one poorly as soon as there’s storage between the machines.
What a reliability block diagram calculates
A reliability block diagram (RBD) draws a system as blocks, each with its own reliability or availability. The blocks are connected in series (the system needs every block) or in parallel (the system needs at least one, or some k of n). For repairable equipment, each block’s steady-state availability is its share of time up, and the diagram combines the blocks:
The RBD arithmetic
| Arrangement | Formula |
|---|---|
| One block | A = MTBF / (MTBF + MTTR) |
| Series (all blocks needed) | A = A1 × A2 × … × An |
| Parallel (any one block suffices) | A = 1 − (1 − A1)(1 − A2)…(1 − An) |
That arithmetic is exact under its assumptions, and everything depends on those assumptions. Every block fails and is repaired on its own clock, independently of the others. In a series diagram, the system is down whenever any block is down, starting at once and lasting exactly as long.
A production line isn’t a series diagram
Draw a bottling line as an RBD and it looks like a textbook series system. The line needs all five machines (Filler, Capper, Labeler, Case Packer, Palletizer), so you multiply their availabilities. On the five-machine bottling line in our case study, the per-machine availabilities are 84.3%, 75.9%, 88.5%, 97.9% and 84.3%. They multiply to 46.7%. The line’s tracked OEE was 54.3%. OEE also carries speed and quality losses, so any such loss on that line would make the availability gap even wider.
A gap of seven and a half points is too big to be rounding error. Gaps like it come from two things the multiplication can’t see.
Storage decouples failures
When there’s storage between two machines, such as a buffer, a surge table or an accumulating conveyor, a stop on one doesn’t immediately stop the other. The downstream machine keeps drawing on stock; the upstream machine keeps filling space. The series diagram charges every stop to the whole line the instant it happens. The physical line charges it only once the storage runs out, so for any stop shorter than that, the series product overstates the loss.
Idle machines don’t wear on the running clock
A machine that’s starved or blocked isn’t running. If its failures build up with operating time (jams, misfeeds, wear), it isn’t moving toward the next one while it waits. The product formula assumes every block keeps failing on its own clock regardless of the others. So even a close-coupled line with no storage at all tends to do better than the product predicts.
Illustrative example, not a result
Five identical machines, close-coupled with no storage, each 90% available (MTTR/MTBF = 1/9). Two textbook answers for line availability:
| Assumption | Line availability |
|---|---|
| Failures on wall-clock time, independent (series RBD) | 0.95 ≈ 59.0% |
| Failures only while running (a stopped line pauses every clock) | 1 / (1 + 5 × 1/9) ≈ 64.3% |
Whether a failure mode runs on operating time or on the calendar depends on the failure mode, not the line, so it has to be decided mode by mode. ReliaSim®’s interrupts support competing, cumulative and wall-clock criteria for that reason.
Decoupling has limits too. A buffer covers a stop only while it has stock to give, so long stops still propagate. Sorting out which stops get through takes a simulation, not a better formula. How much storage that takes is in How big should a buffer be?, and the range between no buffering and unlimited buffering is in Is 85% OEE achievable on your line?
Availability isn’t throughput, even when the RBD is right
Suppose the availability figure were exact. It still wouldn’t be line output, because a block diagram leaves out most of what sets output:
- Rates. An RBD has no rates. Output is set by the flow the line can sustain. Machines with different speeds don’t appear in a block diagram at all, and neither do converters that change the unit from bottles to cases to pallets.
- Starved and blocked. A block is up or down. A stopped machine on the floor may be down, starved or blocked, and only the first is its own fault. See Starved vs Blocked.
- Which fix pays. Because the diagram treats every block’s downtime as line downtime, it ranks improvements by availability. On a real line the same minutes cost different amounts, depending on where and how they happen. See micro stops vs breakdowns.
- Speed against failure rate. Running faster raises output only until failures that rise with rate eat the gain. The Winter Simulation Conference study below finds that throughput has an optimum rather than rising steadily. A static availability number has no rate to trade against.
Where the reliability block diagram is the right tool
None of this makes RBDs wrong. They’re the tool for a different level of the system, and the published study behind our validation work used them at exactly that level.
Fischel and Lange’s Winter Simulation Conference paper models a multi-line food plant with a reliability block diagram inside each rate-affecting unit operation. Each diagram carries that unit’s failure modes, up to twenty on each of more than twenty unit operations, and lets its failure rate scale with production rate. The line itself doesn’t come from a block diagram. It comes from discrete rate coupling through the valves, tanks and conveyors between the units. That model agrees with measured OEE to within 1% over a one-year run (salad dressing plant case study).
RBDs fit well in these places:
- Inside a unit operation. A machine with several failure modes behaves like a series of modes, since any one of them stops it. Its availability is the block’s natural output.
- Where nothing decouples. A shared utility or a control system with no storage behind it stops everything it serves, and series/parallel arithmetic describes that honestly.
- Early redundancy questions. Does a second unit in parallel pay for itself in availability? An RBD answers quickly, before there’s enough detail for a line model.
- Per failure mode, never averaged. The paper is blunt about why: “Had an averaged, single-failure-mode-per-unit-operation approach been followed, the gains and losses would be less accurate and essentially identical to each other.”
Where line simulation takes over
The handoff is storage and rate. Once the question is output from a line with buffers, accumulating conveyors, differing speeds or a product mix, the answer depends on the sequence of events. It matters which machine stopped, for how long, and how full the storage was at the time. A simulation plays that sequence forward. It takes the same per-failure-mode inputs an RBD uses and adds what the diagram leaves out.
Which tool answers which question
| Question | RBD | Line simulation |
|---|---|---|
| Availability of a machine or redundant subsystem | Yes, its natural output | Yes, carried as an input |
| Line throughput with storage between machines | Not from block-diagram arithmetic. Some RAM packages add a throughput simulation on top of the diagram | Yes |
| Starved and blocked time per machine | No | Yes |
| Which failure mode to fix first | By availability only | By output recovered |
| How big a buffer should be | No | Swept against efficiency |
| Speed against failure rate | No | Yes, where failure rate is tied to rate |
The inputs are the same for both: time to failure and time to repair for each failure mode. When a plant has event history, fitting them is downtime data analysis. When it doesn’t, ReliaSim’s Interrupt Designer lets you enter them directly. If you’re weighing tools for the line model itself, see manufacturing simulation software.
Frequently asked questions
What is a reliability block diagram?
A diagram of a system as blocks, each with its own reliability or availability, arranged in series (every block needed) or parallel (at least one needed). It calculates system reliability or availability from the blocks’ values, assuming they fail independently.
Can a reliability block diagram calculate production line throughput?
Not directly. An RBD produces availability. Throughput also depends on machine rates, unit conversions and the storage between machines, and a block diagram represents none of those.
Why does a series RBD understate a line’s output?
It charges every stop to the whole line immediately and keeps every machine failing on its own clock, while storage and idle time let a real line do better.
How do you calculate series and parallel availability?
Series: multiply the block availabilities, A = A1 × A2 × … × An. Parallel, where any one block suffices: A = 1 − (1 − A1)(1 − A2)…(1 − An). Each repairable block’s steady-state availability is MTBF / (MTBF + MTTR).
When should I use an RBD instead of line simulation?
Inside a unit operation, where nothing decouples, and for early redundancy decisions. Use line simulation once output depends on buffers, differing rates or a product mix.
Try it on a real bottling line: the Sandbox question What should we fix first?, or one move in Beat the Bottleneck.
See decoupling on a real line model
The bottling-line models in the ReliaSim Sandbox’s Lines tier need no signup. The Buffer-Options models carry a saved sweep for each inline buffer, and the Buffer/Reliability comparison sets a buffer against a more reliable machine.
Open the sandbox → The published validationWant to see it on a real line first? Read the case study or schedule a call.