Minimal repair of failed components in coherent systems

The minimal repair replacement is a reasonable assumption in many practical systems. Under this assumption a failed component is replaced by another one whose reliability is the same as that of the component just before the failure, i.e., a used component with the same age. In this paper we study the minimal repair in coherent systems. We consider both the cases of independent and dependent components. Three replacement policies are studied. In the first one, the first failed component in the system is minimally repaired while, in the second one, we repair the component which causes the system failure. A new technique based on the relevation transform is used to compute the reliability of the systems obtained under these replacement policies. In the third case, we consider the replacement policy which assigns the minimal repair to a fixed component in the system. We compare these three options under different stochastic criteria and for different system structures. In particular, we provide the optimal strategy for all the coherent systems with 1-4 independent and identically distributed components

Linking component importance to optimisation of preventive maintenance policy

In reliability engineering, time on performing preventive maintenance (PM) on a component in a system may affect system availability if system operation needs stopping for PM. To avoid such an availability reduction, one may adopt the following method: if a component fails, PM is carried out on a number of the other components while the failed component is being repaired. This ensures PM does not take system’s operating time. However, this raises a question: Which components should be selected for PM? This paper introduces an importance measure, called Component Maintenance Priority (CMP), which is used to select components for PM. The paper then compares the CMP with other importance measures and studies the properties of the CMP. Numerical examples are given to show the validity of the CMP

Understanding the shape of the mixture failure rate (with engineering and demographic applications)

Mixtures of distributions are usually effectively used for modeling heterogeneity. It is well known that mixtures of DFR distributions are always DFR. On the other hand, mixtures of IFR distributions can decrease, at least in some intervals of time. As IFR distributions often model lifetimes governed by ageing processes, the operation of mixing can dramatically change the pattern of ageing. Therefore, the study of the shape of the observed (mixture) failure rate in a heterogeneous setting is important in many applications. We study discrete and continuous mixtures, obtain conditions for the mixture failure rate to tend to the failure rate of the strongest populations and describe asymptotic behavior as t tends to infty. Some demographic and engineering examples are considered. The corresponding inverse problem is discussed.

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

Analysis of non-coherent fault trees using ternary decision diagrams

Risk and safety assessments performed on potentially hazardous industrial systems commonly utilise Fault Tree Analysis (FTA) to forecast the probability of system failure. The type of logic for the top event is usually limited to AND and OR gates which leads to a coherent fault tree structure. In non-coherent fault trees components’ working states as well as components’ failures contribute to the failure of the system. The qualitative and quantitative analyses of non-coherent fault trees can introduce further difficulties over and above those seen in the coherent case. It is shown that the Binary Decision Diagram (BDD) method can be used for this type of assessment. The BDD approach can improve the accuracy and efficiency of the quantitative analysis of non-coherent fault trees. This article demonstrates the value of the Ternary Decision Diagram method (TDD) for the qualitative analysis of non-coherent fault trees. Such analysis can be used to provide information to a decision making process for future actions of an autonomous system and therefore it must be performed in real time. In these circumstances fast processing and small storage requirements are very important. The TDD method provides a fast processing capability and small storage is achieved when a single structure is used for both qualitative and quantitative analyses. The efficiency of the TDD method is discussed and compared to the performance of the established methods for analysis of non-coherent fault trees

Importance measures for non-coherent-system analysis

Component importance analysis is a key part of the system reliability quantification process. It enables the weakest areas of a system to be identified and indicates modifications, which will improve the system reliability. Although a wide range of importance measures have been developed, the majority of these measures are strictly for coherent system analysis. Non-coherent systems can occur and accurate importance analysis is essential. This paper extends four commonly used measures of importance, using the noncoherent extension of Birnbaum’s measure of component reliability importance. Since both component failure and repair can contribute to system failure in a noncoherent system, both of these influences need to be considered. This paper highlights that it is crucial to choose appropriate measures to analyze component importance. First the aims of the analysis must be outlined and then the roles that component failures and repairs can play in system state deterioration can be considered. For example, the failure/repair of components in safety systems can play only a passive role in system failure, since it is usually inactive, hence measures that consider initiator importance are not appropriate to analyze the importance of these components. Measures of importance must be chosen carefully to ensure analysis is meaningful and useful conclusions can be drawn

ASTRA 3.x: Theoretical Manual

This report describes the main algorithms implemented in ASTRA 3.x to analyse coherent and non-coherent fault trees. ASTRA 3.x is fully based on the state-of-the-art of Binary Decision Diagrams (BDD) approach. In case of non-coherent fault trees ASTRA 3.x dynamically assigns to each node of the graph a label that identifies the type of the associated variable in order to drive the application of the most suitable analysis algorithms. The resulting BDD is referred to as Labelled BDD (LBDD). Exact values of the unavailability, expected number of failure and repair are calculated; the unreliability upper bound is automatically determined under given conditions. Several importance measures of basic events are also provided. From the LBDD a ZBDD embedding all MCS is obtained from which a subset of Significant Minimal Cut Sets (SMCS) is determined through the application of the cut-off techniques. An important issue is related to the analysis of safety related systems according to the IEC 61508 international standard. In order to simplify the fault tree modelling and analysis a new component type has been defined allowing determining, for any configuration, the PFDavg and PFHavg values. The Staggered testing policy is also applicable besides the Sequential testing implicitly considered by the IEC standardJRC.G.6-Security technology assessmen

ASTRA 3.0: Logical and Probabilistic Analysis Methods

This report contains the description of the main methods, implemented in ASTRA 3.0, to analyse coherent and non-coherent fault trees. ASTRA 3.0 is fully based on the Binary Decision Diagrams (BDD) approach. In case of non-coherent fault trees ASTRA 3.0 dynamically assigns to each node of the graph a label that identifies the type of the associated variable in order to drive the application of the most suitable analysis algorithms. The resulting BDD is referred to as Labelled BDD (LBDD). Exact values of the unavailability, expected number of failure and repair are calculated; the unreliability upper bound is automatically determined under given conditions. Five different importance measures of basic events are also provided. From the LBDD a ZBDD embedding all the MCS is obtained from which a subset of Significant Minimal Cut Sets (SMCS) is determined through the application of the cut-off techniques. With very complex trees it may happen that the working memory is not sufficient to store the large LBDD structure. In these cases ASTRA 3.0 completes the analysis by constructing a Reduced ZBDD embedding the SMCS - using cut-off techniques - thus by-passing the construction of the LBDD. The report also contains few tutorials on the usefulness of non-coherent fault trees, on the BDD approach, and on the determination of failure and repair frequencies.JRC.DG.G.7-Traceability and vulnerability assessmen

Reliability of Systems Using Event Occurrence Networks

The study of a system\u27s reliability has played a crucial role in business and industry since the dawn of modern technology. Current graphical models utilized in reliability theory are limited in that no one model or technique allows for a thorough analysis of system reliability. This research introduces a new graphical model and methodology to be used in the field of reliability that addresses this concern. Event Occurrence Networks (EONs) and their solution methodologies provide an all-inclusive graphical model that allows for the manipulation of several important reliability measures. An EON is a probabilistic network that represents the superposition of several terminating counting processes and is an efficient tool in both non-repairable and repairable systems. Current methodologies are also restricted in the distributions that characterize component life and repair times. This concern is alleviated via EONs coupled with piecewise polynomial approximation