CALCULATORS / RELIABILITY AND ENGINEERING STATISTICS

Zero-failure demonstration planning calculator

Confidence after zero failures in independent identical trials.

reliability-reliability-demonstration.napkin / editable

SCENARIO COMPARISON

Compare the numbers.

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

Scenario	confidence
	0.957609
	0.999948

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.

demonstration confidence target0.96 ✓ passes

BASELINE INPUTS

targetReliability0.9 trials30

CALCULATED

confidence0.95761

Edits change the baseline source.

THE SOURCE

Edits below update the same model.

# Zero-failure demonstration planning
# Scope: Confidence after zero failures in independent identical trials.
# Status: illustrative worked example; engineering review pending.
# Inputs are example values. Checks are editable example requirements, not standards.

targetReliability = 0.9
trials = 30

confidence := 1-targetReliability^trials

check demonstration confidence target: confidence >= 0.95

scenario alternative: targetReliability = 0.72

Calculated from your source · not saved

Baseline · Baseline

demonstration confidence target0.96 ✓ passes

alternative · alternative

demonstration confidence target1.00 ✓ passes

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.

confidence: confidence = 1-targetReliability^trials

Original worked example

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

Given

target reliability: 0.9
trials: 30

Calculated

confidence: 0.957609

Assumptions and limits

Confidence after zero failures in independent identical 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: Zero-failure demonstration planning. Inputs: target reliability; confidence; mission profile; sample model. Outputs: test sample size; exposure assumptions. 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: target reliability, confidence, mission profile, sample model
Outputs: test sample size, exposure assumptions
Modes: calculate, compare, sweep
Drawing: Distribution and reliability plot

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