A Framework for Performing Quantitative Fault Tree Analyses for Subsystems with Periodic Repairs

Summary & ConclusionsThe second edition of ISO 26262 came into effect in 2018, seven years after the publication of the first edition in 2011. Various improvements have been made, one of which is the revision of the equations for the probabilistic metric for random hardware failures (PMHF). The PMHF is so important, as it is one of the design specifications for the hardware of electronic control units (ECUs) in automobiles. However, the mathematical definitions and assumptions underlying the PMHF in the standard are still ambiguous. As the standard provides only the resulting formula for the PMHF, engineers have difficulty calculating the PMHF using quantitative fault tree analysis (FTA).Many papers have addressed safety analysis according to ISO 26262; however, very few papers have examined the PMHF calculation. Although a few papers have presented methods of calculating the PMHF using quantitative FTA, none of these papers is based on the PMHF equation, which has periodic inspections and repairs. Thus, inadequate methods have been widely adopted in the industry for calculating the PMHF from the perspective of ISO 26262.Our research aims to provide a framework for quantitative FTAs, while considering periodic inspections and repairs that are the key assumption of the standard. Our framework is based on models of the Markov stochastic process and the PMHF equations derived from those models. The use of unreliability in the PMHF calculation is a conservative evaluation, and thus compliant with the standard; however, it has proven to be a severe design constraint on the design of fault-tolerant systems. Therefore, it is reasonable to use the unavailability in the PMHF calculation.We applied a framework to correctly calculate the PMHF for a particular vehicle subsystem, using an existing paper as an example. Specifically, we found that the existing methodology underestimates the PMHF 2.7-fold in an autonomous emergency braking (AEB) subsystem. As an underestimation of the failure probability is a dangerous systematic failure, such underestimation should be avoided. Therefore, our framework can greatly benefit the automotive industry, as it allows quantitative FTA to be efficiently performed to accurately evaluate the PMHF.