success run theorem

**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.