Success run theorem is the statistical rule that links a run of zero failures to demonstrated reliability at a chosen confidence level - it provides quick planning equations for acceptance testing and is widely used in reliability demonstration programs.

What Is Success run theorem?

• Definition: Relationship between sample count, confidence level, and minimum reliability implied by all-pass results.
• Common Form: For N successful trials with no failures, lower-bound reliability can be computed at selected confidence.
• Assumptions: Independent identical trials and clear definition of pass-fail event for each unit.
• Application Scope: Component qualification, burn-in screening validation, and field-lot acceptance.

Why Success run theorem Matters

• Fast Planning: Enables rapid estimation of how many samples are needed for target assurance.
• Decision Transparency: Makes confidence-reliability tradeoff explicit to technical and business teams.
• Program Consistency: Provides repeatable acceptance logic across product families.
• Risk Framing: Clarifies that zero observed failures still implies residual uncertainty.
• Review Efficiency: Simple theorem-based evidence streamlines qualification signoff discussions.

How It Is Used in Practice

• Target Setting: Choose confidence and required demonstrated reliability before test execution.
• Run Planning: Calculate minimum successful sample count needed to support claim.
• Context Validation: Confirm assumptions hold, especially independence and representative stress conditions.

Success run theorem is a compact reliability demonstration tool for zero-failure evidence - it turns all-pass test outcomes into quantified confidence statements.