Multi-Step Agent Reliability Calculator (Independent Steps)

The model treats a workflow as steps running in series: the end-to-end result lands only when every step holds. Give each step an independent success probability p, and a chain of N steps succeeds end to end with probability p raised to the N. That is the sequential-chain worst case, and it is the assumption baked into every number here.

The name for the rule. Reliability engineering calls this the series-system model: the NIST series-system entry cited below gives system reliability as the product of the component reliabilities, which is the form used here. A chain is therefore at most as reliable as its weakest step, since multiplying by every other rate can only pull the product down. Older reliability literature also carries the rule under the name Lusser's Law. In an agent chain that product is error propagation in its simplest shape, where one step's failure ends the run and no later step recovers it. A system whose later steps repair a bad intermediate output has broken the series assumption, and the figure here is a floor for it rather than an estimate.

Worked example. At 0.95 per step over 20 steps, 0.95^20 = 0.358, so a chain of twenty 95%-reliable steps succeeds end to end about 35.8% of the time. Push each step to 0.99 and 0.99^20 = 0.818; let it slip to 0.90 and 0.90^20 = 0.122.

Solving for the budget. Invert the curve and it becomes a budget. To hold a twenty-step chain to a 90% end-to-end target, every step must clear 0.90^(1/20) = 0.9947; a 99% target demands 0.99^(1/20) = 0.9995 per step. That is the per-step reliability budget the target forces.

A heterogeneous list. The per-step list multiplies a mixed chain: end-to-end is the product of the entered rates, and the lowest rate is flagged as the weakest link, where one lever buys the most.

What a lever buys. Uniform mode also shows what one lever, applied to every step, buys. One retry raises a step to 1-(1-p)^2 = 0.9975; two retries to 1-(1-p)^3 = 0.999875; a fallback that recovers half of a step's failures to 1-(1-p)(1-0.5) = 0.975. Each effective per-step rate is raised to the N for its end-to-end payoff (0.9975^20 = 0.951, 0.975^20 = 0.603 at N = 20).

Counts and the interval. Enter a step as eval counts (c of n) and the point estimate is c/n, with a Wilson score interval at your chosen confidence. Raising the per-step interval bounds to the N (uniform) or multiplying the per-step bounds across steps (list) carries the interval through to the end-to-end estimate. That band is an interval on the reliability estimate under the same independent-and-uniform assumption, not an exact joint confidence region. The Wilson interval is used because the Wald normal approximation is unreliable near 0 and 1 and at small n.

Honest limits. Every figure is deterministic arithmetic on the inputs you enter. The independence-and-uniformity assumption is a modeling choice; a real system with shared state fails in correlated clusters, which changes what a failure costs more than it changes the all-steps-clean rate. The topology-aware playbook works through that in reliable AI agents in production. To put a number on that shared cause rather than assume it away, run the same chain through the shared-failure version of this calculator, which reports both figures side by side.

Formula: end-to-end = p^N; required per-step = target^(1/N); list = product of per-step rates

See Sources below