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...
Functional dependence (FDEP) exists in many real‐world systems, where the failure of one component (trigger) causes other components (dependent components) within the same system to become isolated (inaccessible or unusable). The FDEP behavior complicates the system reliability analysis because it can cause competing failure effects in the time domain. Existing works have assumed noncascading FDEP, where each system component can be a trigger or a dependent component, but not both. However, in practical systems with hierarchical configurations, cascading FDEP takes place where a system component can play a dual role as both a trigger and a dependent component simultaneously. Such a component causes correlations among different FDEP groups, further complicating the system reliability analysis. Moreover, the existing works mostly assume that any failure propagation originating from a system component instantaneously takes effect, which is often not true in practical scenarios. In this work, we propose a new combinatorial method for the reliability analysis of competing systems subject to cascading FDEP and random failure propagation time. The method is hierarchical and flexible without limitations on the type of time‐to‐failure distributions for system components. A detailed case study is performed on a sensor system used in smart home applications to illustrate the proposed methodology.
Function dependence takes place in systems where the malfunction of certain trigger component(s) causes other system components (referred to as dependent components) to become unusable or inaccessible. Systems undergoing function dependence often exhibit diverse statuses due to competitions in the time domain between propagated failure from a dependent component and local failure of the corresponding trigger component. If the former wins (ie, occurring first), a failure propagation effect is induced, crashing the entire system. If the latter wins, a failure isolation effect may be induced quarantining the damage from the propagated failure (the isolation effect can occur in a deterministic or probabilistic manner depending on applications). Existing models addressing such competitions have restrictive assumptions such as uncorrelated competitions from multiple function dependence groups, zero or negligible failure propagation time, and deterministic failure isolation effect. This paper advances the state of the art by proposing a combinatorial reliability model for systems undergoing correlated, probabilistic competitions and random failure propagation time for dependent components. A case study of a wireless body area network system for patient monitoring is performed to illustrate the proposed methodology and effects of different model parameters on the system reliability.
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