A hierarchical combinatorial reliability model for smart home systems

Abstract

As an application of the Internet of Things, smart home systems have received significant attentions in recent years due to their precedent advantages, eg, in ensuring efficient electricity transmission and integration with renewable energy. This paper proposes a hierarchical and combinatorial methodology for modeling and evaluating reliability of a smart home system. Particularly, the proposed methodology encompasses a multi-valued decision diagram-based method for addressing phased-mission, standby sparing, and functional dependence behaviors in the physical layer; and a combinatorial procedure based on the total probability theorem for addressing probabilistic competing failure behavior with random propagation time in the communication layer. The methods are applicable to arbitrary types of time-to-failure and time-to-propagation distributions for system components. A detailed case study of an example smart home system is performed to demonstrate applications of the proposed method and effects of different component parameters on the system reliability. (IoT) is an internetworking of myriad of "smart" objects and devices augmented with sensors and actuators (such as cell phones, smart appliances, electrical devices, etc.). [1][2][3] In other words, an IoT smart system incorporates sensing, actuation, and control functions for monitoring and analyzing a situation, and Abbreviations: EMS, Energy management system; FCE, Failure competition event; FDEP, Functional dependence; HSP, Hot spare; IFP, Isolation factor pair; IoT, Internet of Things; LF, Local failure; LS, Local sensing failure; LT, Local transmitting failure; MDD, Multi-valued decision diagram; PDEP, Probabilistic function dependence; PDF, Probability density function; PFDC, Probabilistic function dependence case; PFGE, Propagated failure with global effect; PMS, Phased mission system; PT, Propagation time. Notations: h, Phase number; f iP (t), f iLS (t), f iLT (t), PDF of time-to-PFGE/LS/LT of component i; f iPT (t), PDF of time-to-propagation of component i; FCE j , Failure competition event j, j = 1,2,3; ψ i , The failure function of the i-th phase in the physical layer; ψ xi;h , Unreliability of component i at the end of h; I, Union of set of components causing PFGE and set of components being isolated under an FCE; P FCEj t ð Þ, Probability of no PFGE to components in I; q iLS (t), q iLT (t), Occurrence probability of LS, LT to component i; q iP (t), Occurrence probability of PFGE to component i; q iS (t), q iT (t), Occurrence probability of LS, LT given that no PFGE to i; Q FCEj t ð Þ, Failure probability given that no PFGE happens to components in I; T h , Duration of phase h; x i = 0, Component i functions in all the phases; x i = h, Component i fails during h given that i is operational at the beginning of h; X iP , X iLS , X iLT , Event that component i has a PFGE, LS, LT; X iPT , Event that the propagation time is less than the time difference between the relay LT and the component i PFGE; U comm (t), Unreliability of the communicat...

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