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CALCULATORS / RELIABILITY AND ENGINEERING STATISTICS

Supplied trial pass-rate calculator

Fixed supplied Monte Carlo sample outcomes summarized on-page; use full Study analyses to generate random trials.

reliability-monte-carlo.napkin / editable
× check failed

SCENARIO COMPARISON

Compare the numbers.

This source describes an analytical model. Its quantities and checks are the view.

Scenariomeanpassedfraction
0.93333320.666667
0.8820.666667

All calculated quantities are listed with the inputs. Switch to Source to inspect the equations.

SCENARIOS / CALCULATED VALUESSAME SOURCE

Change an input to see the consequences.

sample pass fraction target0.67 × fails

BASELINE INPUTS

CALCULATED

mean0.93333
passed2
fraction0.66667

Edits change the baseline source.

Calculated from your source · not saved
Baseline · Baseline
sample pass fraction target0.67 × fails
alternative · alternative
sample pass fraction target0.67 × fails

Illustrative first-order example. Checks are editable requirements, not design standards. The broader topic may require additional equations, data, and validation.

Formula and units

This example uses the following equations. Input names and units match the editable source above.

mean
mean = (trialA+trialB+trialC)/3
passed
passed = (trialA<=limit ? 1 : 0)+(trialB<=limit ? 1 : 0)+(trialC<=limit ? 1 : 0)
fraction
fraction = passed/3

Original worked example

These are the baseline values in the downloadable source. Edits above let you test your own values.

Given

trial a
0.8
trial b
1.1
trial c
0.9
limit
1

Calculated

mean
0.933333
passed
2
fraction
0.666667

Assumptions and limits

Fixed supplied Monte Carlo sample outcomes summarized on-page; use full Study analyses to generate random trials.

The requirement checks use the limits written in this example. Passing a check does not establish that the model covers every load, material behavior, or operating condition in a real design.

Download this .napkin example ↓

Take it further with your agent

Napkin keeps the inputs, equations, checks and assumptions together in one study. Your agent sets it up; you change the numbers.

Try with Claude ↗

codex 'Use Napkin (https://napkin.engineering/mcp, or the local Napkin plugin) to build a study: Uncertainty Monte Carlo explorer. Inputs: input distributions; correlations; model; random seed. Outputs: output samples; quantiles; convergence diagnostics. Model scope: Explicit distribution, independence and sample assumptions. Read napkin_capabilities and the current snapshot. Ask me for the values that matter, label assumptions with units, author .napkin source, validate it and apply it with napkin_source using the current revision, then open the study. Add checks for the limits I supply. Keep unsupported analyses explicit.'

Claude needs the Napkin connector; Codex needs the Napkin plugin. Set up your agent ↗

The broader study

The topic brief below describes the broader scope. The worked example above states the particular calculation it implements.

  • Inputs: input distributions, correlations, model, random seed
  • Outputs: output samples, quantiles, convergence diagnostics
  • Modes: calculate, compare, sweep
  • Drawing: Distribution and reliability plot

EXECUTABLE WORKED EXAMPLE · FIRST-ORDER MODEL · CHECK THE SCOPE & ASSUMPTIONS

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