Exercises for Course 4.10 Dependability and Security Evaluation of Computer-based Systems

Exercise 1 Let us consider a system composed of n different components denoted 1, 2 ……n, with m identical replicas of each component. Two redundancy strategies are studied:-GR, in which redundancy is applied globally at the system level: the architecture is composed of m identical copies of the system that are organized according to a parallel structure.-LR, in which redundancy is applied locally at the level of each component. Let us denote by r i (t) the reliability function of component i. The components are assumed to fail according to independent stochastic processes. 1) Derive the system reliability functions R GR (t) and R LR (t) corresponding to the two considered redundancy strategies, as a function of r i (t). 2) Consider the case m = n = 2 and r i (t) = r(t) Compare R GR (t) and R LR (t). Exercise 2 Let us study the two following architectures I and II. 1) Build a Fault Tree describing the failure scenarios associated to each architecture. 2) The reliability functions r(t) associated to the components are assumed to be identical and exponentially distributed with a constant failure rate λ. For each architecture, derive the system failure rate and mean time to failure (MTTF).