Modular Methods For The Reliability Assessment Of Large-scale Phased-mission Systems

In real-world engineering applications,there exists the systems whose structure,function,and component parameters may change from time to time.This kind of systems is normally termed as the phased-mission systems(PMS).As engineering applications become large and complex,PMS models show the tendency of containing more and more components and phases.As the result,most existing non-simulation methods may encounter the computational “explosion problem” for large PMS.For the development and security of China’s spaceflight project,it is not only academically valuable but also imperative to build the complete methodology for the reliability assessment of large PMS.This paper presents three analytical methods for the reliability evaluation of large-scale PMS:(1)Behavior-vector method for generalized PMS with repairable componentsSome PMS may contain a large number of repairable components,which tends to result in the well-known state-explosion problem in the conventional Markovian methods.This paper presents the “behavior-vector method” to analyze the PMS with many repairable components.The behavior-vector method decomposes mission success into the corresponding system behavior and component behavior,and use Markov models to compute the probability of component behavior.Compared to traditional Markovian methods,the behavior-vector method can analyze the PMS with more components,and can be directly applied to generalized PMS,which broaden the applicability of the behavior-vector method.(2)Truncation strategy based on the behavior-vector methodAlthough the behavior-vector method can be used to PMS with many components,this method may also become computationally expensive when the PMS contains a lot of phases.Therefore,this paper presents the truncation strategy based on the behavior-vector method.This truncation strategy reduces the computational burden of the behavior-vector method by deleting some “unimportant” computational steps.Because of the shrinking truncation limit,the presented truncation method is able to control the truncation error by the algorithm parameter,which suggests that the complicated discussion of truncation error is avoided.Experimental results show that the truncation strategy can reduce the time and the memory(space)cost of the behavior-vector method,making the truncation strategy an effective solution to broaden the applicability of the behavior-vector method.(3)Sampling method for large-scale PMS with repairable componentsIn fact,most of the existing analytical methods may encounter the dramatic increase in computational burden when the number of phases in the PMS increases.Experiments shows that the behavior-vector method cannot analyze the repairable PMS with thousands of phases even if the truncation strategy is added.For this problem,this paper designs the sampling method which is similar to the discretization solutions.By building the simplified success states,the sampling method combines the merits of the BDD methods and Markovian models,and avoids the exponential growth in computational complexity when the number of components and phases increases.The real-world spaceflight experiment shows that the sampling method is effective to analyze the PMS with thousands of phases and repairable components which is highly challenging to other analytical methods.Compared to other modular methods,another merit of the sampling method is that the sampling method can analyze the repair activity happened within phases,and do not need to make the impractical assumption in other modular methods.Additionally,the sampling method provide the new concept “discrete-time availability” on which a new assessment solution of system reliability is based.This new solution uses the discrete-time availability to describe the difference between system reliability and system availability,and approaches the system reliability by adding discrete nodes.Compared to the classic BDD,FT,and Markov models,the presented “discrete-time availability” idea is particularly effective to large-scale repairable PMS,and is a new solution for the assessment of system reliability.