Efficient exploration of availability models guided by failure distances

Recently, a method to bound the steady-state availability using the failure distance concept has been proposed. In this paper we refine that method by introducing state space exploration techniques. In the methods proposed here, the state space is incrementally generated based on the contributions to the steady-state availability band of the states in the frontier of the currently generated state space. Several state space exploration algorithms are evaluated in terms of bounds quality and memory and CPU time requirements. The more efficient seems to be a waved algorithm which expands transition groups. We compare our new methods with the method based on the failure distance concept without state exploration and a method proposed by Souza e Silva and Ochoa which uses state space exploration but does not use the failure distance concept. Using typical examples we show that the methods proposed here can be significantly more efficient than any of the previous methods.Postprint (published version

Failure distance based bounds for steady-state availability without the kwnowledge of minimal cuts

We propose an algorithm to compute bounds for the steady-state unavailability using continuous-time Markov chains, which is based on the failure distance concept. The algorithm generates incrementally a subset of the state space until the tightness of the bounds is the specified one. In contrast with a previous algorithm also based on the failure distance concept, the proposed algorithm uses lower bounds for failure distances which are computed on the fault tree of the system, and does not require the knowledge of the minimal cuts. This is advantageous when the number of minimal cuts is large or their computation is time-consuming.Postprint (published version

Bounding steady-state availability models with group repair and phase type repair distributions

We propose an algorithm to obtain bounds for the steady-state availability using Markov models in which only a small portion of the state space is generated. The algorithm is applicable to models with group repair and phase type repair distributions and involves the solution of only four linear systems of the size of the generated state space, independently on the number of “return” states. Numerical examples are presented to illustrate the algorithm and compare it with a previous bounding algorithm.Postprint (published version

Failure distance based bounds of dependability measures

El tema d'aquesta tesi és el desenvolupament de mètodes de fitació per a una classe de models de confiabilitat basats en cadenes de Markov de temps continu (CMTC) de sistemes tolerants a fallades.Els sistemes considerats a la tesi es conceptualitzen com formats per components (hardware o software) que fallen i, en el cas de sistemes reparables, són reparats. Els components s'agrupen en classes de forma que els components d'una mateixa classe són indistingibles. Per tant, un component és considerat com a una instància d'una classe de components i el sistema inclou un bag de classes de components definit sobre un cert domini. L'estat no fallada/fallada del sistema es determina a partir de l'estat no fallada/fallada dels components mitjançant una funció d'estructura coherent que s'especifica amb un arbre de fallades amb classes d'esdeveniments bàsics. (Una classe d'esdeveniment bàsic és la fallada d'un component d'una classe de components.)La classe de models basats en CMTC considerada a la tesi és força àmplia i permet, per exemple, de modelar el fet que un component pot tenir diversos modes de fallada. També permet de modelar fallades de cobertura mitjançant la introducció de components ficticis que no fallen per ells mateixos i als quals es propaguen les fallades d'altres components. En el cas de sistemes reparables, la classe de models considerada admet polítiques de reparació complexes (per exemple, nombre limitat de reparadors, prioritats, inhibició de reparació) així com reparació en grup (reparació simultània de diversos components). Tanmateix, no és possible de modelar la reparació diferida (és a dir, el fet de diferir la reparació d'un component fins que una certa condició es compleixi).A la tesi es consideren dues mesures de confiabilitat: la no fiabilitat en un instant de temps donat en el cas de sistemes no reparables i la no disponibilitat en règim estacionari en el cas sistemes reparables.Els mètodes de fitació desenvolupats a la tesi es basen en el concepte de "distància a la fallada", que es defineix com el nombre mínim de components que han de fallar a més dels que ja han fallat per fer que el sistema falli.A la tesi es desenvolupen quatre mètodes de fitació. El primer mètode dóna fites per a la no fiabilitat de sistemes no reparables emprant distàncies a la fallada exactes. Aquestes distàncies es calculen usant el conjunt de talls mínims de la funció d'estructura del sistema. El conjunt de talls mínims s'obté amb un algorisme desenvolupat a la tesi que obté els talls mínims per a arbres de fallades amb classes d'esdeveniments bàsics. El segon mètode dóna fites per a la no fiabilitat usant fites inferiors per a les distàncies a la fallada. Aquestes fites inferiors s'obtenen analitzant l'arbre de fallades del sistema, no requereixen de conèixer el conjunt de talls mínims i el seu càlcul és poc costós. El tercer mètode dóna fites per a la no disponibilitat en règim estacionari de sistemes reparables emprant distàncies a la fallada exactes. El quart mètode dóna fites per a la no disponibilitat en règim estacionari emprant les fites inferiors per a les distàncies a la fallada.Finalment, s'il·lustren les prestacions de cada mètode usant diversos exemples. La conclusió és que cada un dels mètodes pot funcionar molt millor que altres mètodes prèviament existents i estendre de forma significativa la complexitat de sistemes tolerants a fallades per als quals és possible de calcular fites ajustades per a la no fiabilitat o la no disponibilitat en règim estacionari.The subject of this dissertation is the development of bounding methods for a class of continuous-time Markov chain (CTMC) dependability models of fault-tolerant systems.The systems considered in the dissertation are conceptualized as made up of components (hardware or software) that fail and, for repairable systems, are repaired. Components are grouped into classes, the components of the same class being indistinguishable. Thus, a component is regarded as an instance of some component class and the system includes a bag of component classes defined over a certain domain. The up/down state of the system is determined from the unfailed/failed state of the components through a coherent structure function specified by a fault tree with basic event classes. (A basic event class is the failure of a component of a component class.)The class of CTMC models considered in the dissertation is quite wide and allows, for instance, to model the fact that a component may have different failure modes. It also allows to model coverage failures by means of introducing fictitious components that do not fail by themselves and to which uncovered failures of other components are propagated. In the case of repairable systems, the considered class of models supports very complex repair policies (e.g., limited repairpersons, priorities, repair preemption) as well as group repair (i.e., simultaneous repair of several components). However, deferred repair (i.e., the deferring of repair until some condition is met) is not allowed.Two dependability measures are considered in the dissertation: the unreliability at a given time epoch for non-repairable systems and the steady-state unavailability for repairable systems.The bounding methods developed in the dissertation are based on the concept of "failure distance from a state," which is defined as the minimum number of components that have to fail in addition to those already failed to take the system down.We develop four bounding methods. The first method gives bounds for the unreliability of non-repairable fault-tolerant systems using (exact) failure distances. Those distances are computed using the set of minimal cuts of the structure function of the system. The set of minimal cuts is obtained using an algorithm developed in the dissertation that obtains the minimal cuts for fault trees with basic event classes. The second method gives bounds for the unreliability using easily computable lower bounds for failure distances. Those lower bounds are obtained analyzing the fault tree of the system and do not require the knowledge of the set of minimal cuts. The third method gives bounds for the steady-state unavailability using (exact) failure distances. The fourth method gives bounds for the steady-state unavailability using the lower bounds for failure distances.Finally, the performance of each method is illustrated by means of several large examples. We conclude that the methods can outperform significantly previously existing methods and extend significantly the complexity of the fault-tolerant systems for which tight bounds for the unreliability or steady-state unavailability can be computed

Efficient exploration of availability models guided by failure distances

Recently, a method to bound the steady-state availability using the failure distance concept has been proposed. In this paper we refine that method by introducing state space exploration techniques. In the methods proposed here, the state space is incrementally generated based on the contributions to the steady-state availability band of the states in the frontier of the currently generated state space. Several state space exploration algorithms are evaluated in terms of bounds quality and memory and CPU time requirements. The more efficient seems to be a waved algorithm which expands transition groups. We compare our new methods with the method based on the failure distance concept without state exploration and a method proposed by Souza e Silva and Ochoa which uses state space exploration but does not use the failure distance concept. Using typical examples we show that the methods proposed here can be significantly more efficient than any of the previous methods