Dependability

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1 Dependability Dependability is the collective term used to describe the availability performance of a system, which is the readiness for correct service, and its influencing factors: - Reliability, the continuity of correct service; - Maintainability, the reparation to restore correct service; - Maintenance support. It can be described only with probabilistic laws. The probability of failure f(t) is the probability that a component fails at a given time instant, it is the probability density function of the failure. The cumulative distribution F(t) is the unreliability, which is the probability of having a failure before the time t, knowing that at t=0 the system was working. Its opposite is the reliability R(t), which is computed as R(t) = 1-F(t) and represents the probability that a component fails after the time t. Some properties are: - 𝑅(0) = 1, the system is working when it is bought; - 𝑙𝑖𝑚𝑡 →∞𝑅(𝑡) = 0, the system will fail at a certain time, - 𝑓(𝑥) = − 𝑑𝑅(𝑡) 𝑑𝑡 Reliability is computed empirically: n independent and statistically identical elements are deployed at time t=0 in identical conditions, then the failure times 𝑡0, 𝑡1, … 𝑡𝑛 are observed, knowing that they are not related to each other. The function n(t) is computed by interpolating its shape from the failure times, then the reliability R(t) is calculated as 𝑅(𝑡) = 𝑙𝑖𝑚𝑛→∞ 𝑛(𝑡) 𝑛 . The mean of the reliability is the mean time to failure (MTTF), which is ∫ 𝑡 ⋅ 𝑓(𝑡)𝑑𝑡 0 ∞ = ∫ 𝑅(𝑡)𝑑𝑡 0 ∞ The quantities can be rewritten considering the failure rate 𝜆(𝑡), the probability of failure at instant t assuming that the component is working at time t, which differs from the probability of failure as it refers to a system which was working at time t=0. The sources of failures can be many: • Design failures: errors in…