Monte Carlo vs Analytical

Both methods answer the same questions about a reliability block diagram — availability, reliability, production — but they get there differently.

The analytical solver solves the system in closed form: exact RBD algebra for independent components, and a small Markov chain (CTMC)for coupled behaviour like standby, common-cause and multi-state components. It returns an exact result instantly — but it can’t represent shared resources such as repair crews, spare pools, buffers or preventive maintenance.

Monte Carlo simulation plays the system forward thousands of times with random failure and repair times, then reports the statistics. It handles every feature Ramly models — including those resource constraints — but each result carries a confidence interval that only narrows with more runs and more runtime.

For a system of independentcomponents combined through series, parallel and k-of-n structures, steady-state availability has a closed-form solution: each component’s availability is its mean up-time over its mean cycle, and the structure function combines them exactly. No sampling, no error.

When components are coupled — cold/warm standby redundancy, common-cause failures, or multi-state (partial-capacity) components — Ramly builds a small continuous-time Markov chainover the relevant states and solves it exactly (steady state for availability, and the transient solution for time-dependent results). This is the “Markov analysis” that desktop suites offer as a separate module; in Ramly it is folded into the same RBD.

The analytical solver returns:

• Steady-state availability — exact, to any number of nines.
• Production availability — capacity-weighted, accounting for partial-capacity (multi-state) components.
• Time-dependent A(t), R(t) and MTTF — point availability and the no-repair reliability (survivor) curve over a mission, plus mean time to first failure.

What it cannot represent: repair crew limits, shared spare pools, finite buffers/storage, and preventive-maintenance schedules. These couple components through shared resources or planned downtime in ways that have no compact closed form — they need simulation.

Monte Carlo simulation samples random failure and repair times from each component’s distributions, advances the system event by event over the mission, and records when the system is up or down. Repeating this thousands of times and averaging gives the answer; the spread across runs becomes a confidence interval. Fix the random seed and the run is exactly reproducible.

Because it just plays out what actually happens, simulation handles everything: limited repair crews that queue work, spare pools that can run out, buffers that ride through short outages, preventive maintenance that takes equipment offline on a schedule — plus importance and sensitivity measures computed across the runs. The price is runtime, and that the result is statistical: resolving a five-nines availability to a tight interval can take a very large number of runs.

Reach for the analytical solver when:

• Your model is series / parallel / k-of-n, standby, common-cause or multi-state — and nothing else.
• You want an exact answer instantly — especially for high-availability systems where Monte Carlo would need an enormous run count to resolve the last few nines.
• You need reliability R(t), MTTF, or partial-capacity production results.

Reach for Monte Carlo when:

• Your model has repair crews, shared spare pools, finite buffers, or preventive maintenance — anything where resources are shared or constrained.
• You want importance or sensitivity measures, or the full distribution of outcomes across runs.

Open the Analysis tab and pick the solver — Monte Carlo or Analytical. Settings that the chosen method doesn’t use (number of runs and seed for analytical; crews, spares, buffers and PM that analytical can’t model) are greyed out, and the callout lists anything in your model that would be ignored or would block the run. Everything else — the diagram, component data, tracked blocks, reports — is shared between both methods, so switching is a one-click comparison.