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Quantifying Uncertainty in FMEDA Safety Metrics: An Error Propagation Approach for Enhanced ASIC Verification

Antonino Armato, Christian Kehl, Sebastian Fischer

Abstract

Accurate and reliable safety metrics are paramount for functional safety verification of ASICs in automotive systems. Traditional FMEDA (Failure Modes, Effects, and Diagnostic Analysis) metrics, such as SPFM (Single Point Fault Metric) and LFM (Latent Fault Metric), depend on the precision of failure mode distribution (FMD) and diagnostic coverage (DC) estimations. This reliance can often leads to significant, unquantified uncertainties and a dependency on expert judgment, compromising the quality of the safety analysis. This paper proposes a novel approach that introduces error propagation theory into the calculation of FMEDA safety metrics. By quantifying the maximum deviation and providing confidence intervals for SPFM and LFM, our method offers a direct measure of analysis quality. Furthermore, we introduce an Error Importance Identifier (EII) to pinpoint the primary sources of uncertainty, guiding targeted improvements. This approach significantly enhances the transparency and trustworthiness of FMEDA, enabling more robust ASIC safety verification for ISO 26262 compliance, addressing a longstanding open question in the functional safety community.

Quantifying Uncertainty in FMEDA Safety Metrics: An Error Propagation Approach for Enhanced ASIC Verification

Abstract

Accurate and reliable safety metrics are paramount for functional safety verification of ASICs in automotive systems. Traditional FMEDA (Failure Modes, Effects, and Diagnostic Analysis) metrics, such as SPFM (Single Point Fault Metric) and LFM (Latent Fault Metric), depend on the precision of failure mode distribution (FMD) and diagnostic coverage (DC) estimations. This reliance can often leads to significant, unquantified uncertainties and a dependency on expert judgment, compromising the quality of the safety analysis. This paper proposes a novel approach that introduces error propagation theory into the calculation of FMEDA safety metrics. By quantifying the maximum deviation and providing confidence intervals for SPFM and LFM, our method offers a direct measure of analysis quality. Furthermore, we introduce an Error Importance Identifier (EII) to pinpoint the primary sources of uncertainty, guiding targeted improvements. This approach significantly enhances the transparency and trustworthiness of FMEDA, enabling more robust ASIC safety verification for ISO 26262 compliance, addressing a longstanding open question in the functional safety community.
Paper Structure (14 sections, 16 equations, 6 figures)

This paper contains 14 sections, 16 equations, 6 figures.

Table of Contents

  1. Introduction
  2. Context and Problem Statement
  3. Main Contributions
  4. Paper Structure
  5. Identified Source of Uncertainties and Gaps
  6. FMEDA Background and Uncertainty
  7. Fault Simulation and Accuracy
  8. Proposed approach
  9. Quantifying Uncertainty in FMEDA Metrics
  10. Error Importance Identifier (EII)
  11. Case Study: Application on Processor CORE Execution Stage
  12. Discussion of Results
  13. Impact and Workflow Integration
  14. Conclusion

Figures (6)

  • Figure 1: An Example of FMEDA focused on the execution unit of a generic CPU
  • Figure 3: Abstraction level (digital environment) where is possible to perform the fault injection correlated with the effort and accuracy.
  • Figure 4: An Example of sampling factor in the FMEDA table, where the number of faults (Samplig Faults column) to inject is significatly reduced. The confidence level is 95%.
  • Figure 5: FMEDA Analysis with Uncertainty and Error Importance Distribution for Core Execution Stage. The table includes the two uncertainties columns $\sigma_{DC}$ and $\sigma_{\lambda fm}$ and their contribution to "Error Importance Distribution" (in %). The Tot Error Important Distribution (in %) column sums the individual contributions (from both $\sigma_{DC}$ and $\sigma_{\lambda fm}$ for a given failure mode) to represent the total percentage on the overall SPFM attributed to that specific failure mode.
  • Figure 6: The final SPFM and the corresponding $\sigma_{\text{SPFM}}$ (in %) calculated using respectively the Equations (\ref{['eq:final_spfm_std_dev']}) (\ref{['eq:spfm_simplified_no_fm_error']}) and (\ref{['eq:spfm_simplified_no_dc_error']}).
  • ...and 1 more figures