Dependability metrics to assess safety-critical systems

Metrics are commonly used in engineering as measures of the performance of a system for a given attribute. For instance, in the assessment of fault tolerant systems, metrics such as the reliability, R(t) and the Mean Time To Failure (MTTF) are well-accepted as a means to quantify the fault tolerant attributes of a system with an associated failure rate, λ. Unfortunately, there does not seem to be a consensus on comparable metrics to use in the assessment of safety-critical systems. The objective of this paper is to develop two metrics that can be used in the assessment of safety-critical systems, the steady-state safety, S_ss, and the Mean Time To Unsafe Failure (MTTUF). S_ss represents the evaluation of the safety as a function of time, in the limiting case as time approaches infinity. The MTTUF represents the average or mean time that a system will operate safely before a failure that produces an unsafe system state. A 3-state Markov model is used to model a safety-critical system with the transition rates computed as a function of the system coverage C_sys, and the hazard rate λ(t). Also, λ(t) is defined by the Weibull distribution, primarily because it allows one to easily represent the scenarios where the failure rate is increasing, decreasing, and constant. The results of the paper demonstrate that conservative estimates for lower bounds for both S_ss & the MTTUF result when C_sys is assumed to be a constant regardless of the behavior of λ(t). The derived results are then used to evaluate three example systems.