Markovian Reliability Analysis of Dynamic Systems

In engineering practice, structural system with dynamic output performance has gained more and more attention. Reliability analysis of these dynamic systems based on the real performance function is normally time-consuming, which is hard to accept in engineering. An SVR-NARX (Support vector machine regression-Nonlinear autoregressive with exogenous input) model is, therefore, established in this paper to replace the real performance function for reliability analysis. To further improve the efficiency for dynamic systems with small failure probability, importance sampling is combined with SVR-NARX model. Two nonlinear examples in this paper show that the established SVR-NARX model can accurately describe the dynamic behavior of the systems, and the proposed method is efficient and accurate for the reliability analysis of dynamic systems.

Dynamic reliability analysis using the extended support vector regression (X-SVR)

Classical combinatorial fault trees can be used to assess combinations of failures but are unable to capture sequences of faults, which are important in complex dynamic systems. A number of proposed techniques extend fault tree analysis for dynamic systems. One of such technique, Pandora, introduces temporal gates to capture the sequencing of events and allows qualitative analysis of temporal fault trees. Pandora can be easily integrated in model-based design and analysis techniques. It is, therefore, useful to explore the possible avenues for quantitative analysis of Pandora temporal fault trees, and we identify Bayesian Networks as a possible framework for such analysis. We describe how Pandora fault trees can be translated to Bayesian Networks for dynamic dependability analysis and demonstrate the process on a simplified fuel system model. The conversion facilitates predictive reliability analysis of Pandora fault trees, but also opens the way for post-hoc diagnostic analysis of failures.

Reliability assessment in structural dynamics

Solving dynamic flowgraph methodology models using binary decision diagrams

The scope of this paper is to apply a model-correction-based strategy for efficient reliability analysis of uncertain dynamical systems based on a low-fidelity (LF) model whose outcomes are corrected in a probabilistic sense to represent the more realistic outcomes of a high-fidelity (HF) model. In the model-correction approach utilized, the LF model is calibrated to the HF model close to the so-called most probable point in standard normal space, which allows a more realistic assessment of the considered complex dynamical system. Since only few expensive limit state function evaluations of the HF model are required, an efficient reliability analysis is enabled. In an application example, the LF model describes an existing single-span railway bridge modelled as simply supported Euler–Bernoulli beam subjected to moving single forces representing the axle loads of a moving train. The HF modelling approach accounts for the bridge–train interaction by modelling the passing train as mass-spring-damper system, however increasing the computational effort of the limit state function evaluations. Failure probabilities evaluated with the model-correction approach are contrasted and discussed with failure probabilities of the sophisticated bridge–train interaction model evaluated with the first-order reliability method (FORM). It is demonstrated that the efficiency of the method depends on the correlation between the LF and the HF model. A comparison of the results of FORM and the model-correction-based approach shows that the latter provides reliable failure probability prediction of the HF model while leading to a significant reduction in computational effort.

Two unrepairable series structure systems with k-out-of-m:G subsystems and spares are investigated. The first one consists of a k-out-of-m:G subsystem and a series subsystem while the other consists of two k-out-of-m:G subsystems. The systems have identical components with identical lifetime distributions and the working components are suspended as soon as the systems are down. Two Markov models are proposed for the reliability analysis of such systems and closed form results on the reliability and the mean time to failure (MTTF) are presented. Numerical examples are given to illustrate the impact of several parameters on the reliability of the systems.

PurposeDegraded failures and sudden critical failures are quite prevalent in industries. Degradation processes commonly belong to Weibull family and critical failures are found to follow exponential distribution. Therefore, it becomes important to carry out reliability and availability analysis of such systems. From the reported literature, it is learnt that models are available for the situations where the degraded failures as well as critical failures follow exponential distribution. The purpose of this paper is to present models suitable for reliability and availability analysis of systems where the degradation process follows Weibull distribution and critical failures follow exponential distribution.Design/methodology/approachThe research uses Semi-Markov modeling using the approach of method of stages which is suitable when the failure processes follow Weibull distribution. The paper considers various states of the system and uses state transition diagram to present the transition of the system among good state, degraded state and failed state. Method of stages is used to convert the semi-Markov model to Markov model. The number of stages calculated in Method of stages is usually not an integer value which needs to be round off. Method of stages thus suffers from the rounding off error. A unique approach is proposed to arrive at failure rates to reduce the error in method of stages. Periodic inspection and repairs of systems are commonly followed in industries to take care of system degradation. This paper presents models to carry out reliability and availability analysis of the systems including the case where degraded failures can be arrested by appropriate inspection and repair.FindingsThe proposed method for estimating the degraded failure rate can be used to reduce the error in method of stages. The models and the methodology are suitable for reliability and availability analysis of systems involving degradation which is very common in systems involving moving parts. These models are very suitable in accurately estimating the system reliability and availability which is very important in industry. The models conveniently cover the cases of degraded systems for which the model proposed by Hokstad and Frovig is not suitable.Research limitations/implicationsThe models developed consider the systems where the repair phenomenon follows exponential and the failure mechanism follows Weibull with shape parameter greater than 1.Practical implicationsThese models can be suitably used to deal with reliability and availability analysis of systems where the degradation process is non-exponential. Thus, the models can be practically used to meet the industrial requirement of accurately estimating the reliability and availability of degradable systems.Originality/valueA unique approach is presented in this paper for estimating degraded failure rate in the method of stages which reduces the rounding error. The models presented for reliability and availability analyses can deal with degradable systems where the degradation process follows Weibull distribution, which is not possible with the model presented by Hokstad and Frovig.

This paper presents a novel and simple approach to reliability analysis of phased-mission systems. The technique presented in this paper transforms a phased-mission system into several non-phased-mission systems, and thus allows each phase to be modeled separately. The mission succeeds as long as every phase successively executes its requirements, and failed component(s) of any phase is(are) repaired so that the system is in a successful state before as well as after it begins the next phase. Alternative mission success scenarios are also readily definable within this context. The benefit of this simplified approach is that it provides a practical implementation for the reliability analysis of phased-mission systems. The different phases of the system are computed independently, and the duration and the structure of the phases are left to the designer or manager. If the requirements of the mission change during execution of the mission (duration of a phase or the sequence of phases), the impact of the change in mission objectives is easily found without recomputing the applicable or operative Markov model. This is due to the fact that all of the reliability analysis data are presented over the entire mission duration consisting for all phases, and the initial and final probabilities can easily be found by examining the output reliability data instead of recomputing the model

Many practical systems are phased-mission systems (PMSs), where the mission consists of multiple, consecutive, and non-overlapping phases of operation. An accurate reliability analysis of a PMS must consider statistical dependence of component states across phases, as well as dynamics in system configurations, success criteria, and component behavior. This paper proposes a new method based on multiple-valued decision diagrams (MDDs) for the reliability analysis of a non-repairable binary-state PMS. Due to its multi-valued logic nature, the MDD model has recently been applied to the reliability analysis of multistate systems. In this work, we present a novel way to adapt MDDs for the reliability analysis of systems with multiple phases. Examples show how the MDD models are generated and evaluated to obtain the mission reliability measures. Performance of the MDD-based method is compared with an existing binary decision diagram (BDD)-based method for PMS analysis. Empirical results show that the MDD-based method can offer lower computational complexity as well as a simpler model construction and improved evaluation algorithms over those used in the BDD-based method.

The study and analysis of repairable systems is an important topic in reliability. Analytical techniques become very complicated and unrealistic especially for modern complex systems. There have been attempts in the literature to evolve more realistic techniques using simulation approach for reliability analysis of systems. The purpose of this paper is to develop a novel Markov system dynamics (MSD) simulation framework for the reliability modeling and analysis of a repairable system. This paper proposes a hybrid approach called as MSD approach which combines the Markov approach with system dynamics simulation approach for reliability modeling. This approach will have the advantages of both Markov as well as system dynamics methodologies. The proposed framework is illustrated for a repairable two component system. The results of the simulation obtained in this work when compared with that obtained by traditional Markov analysis clearly validate that this novel MSD approach is an alternative approach for reliability modeling and analysis.

Performance and Reliability Analysis of Computer Systems: An Example-Based Approach Using the SHARPE Software Package provides a variety of probabilistic, discrete-state models used to assess the reliability and performance of computer and communication systems. The models included are combinatorial reliability models (reliability block diagrams, fault trees and reliability graphs), directed, acyclic task precedence graphs, Markov and semi-Markov models (including Markov reward models), product-form queueing networks and generalized stochastic Petri nets. A practical approach to system modeling is followed; all of the examples described are solved and analyzed using the SHARPE tool. In structuring the book, the authors have been careful to provide the reader with a methodological approach to analytical modeling techniques. These techniques are not seen as alternatives but rather as an integral part of a single process of assessment which, by hierarchically combining results from different kinds of models, makes it possible to use state-space methods for those parts of a system that require them and non-state-space methods for the more well-behaved parts of the system. The SHARPE (Symbolic Hierarchical Automated Reliability and Performance Evaluator) package is the `toolchest' that allows the authors to specify stochastic models easily and solve them quickly, adopting model hierarchies and very efficient solution techniques. All the models described in the book are specified and solved using the SHARPE language; its syntax is described and the source code of almost all the examples discussed is provided. Audience: Suitable for use in advanced level courses covering reliability and performance of computer and communications systems and by researchers and practicing engineers whose work involves modeling of system performance and reliability.

An efficient simulation method for reliability analysis of linear dynamical systems using simple additive rules of probability

Computation of bounds for transient measures of large rewarded Markov models using regenerative randomization

In this paper, the authors demonstrate how fault tree analysis could be used to perform reliability analysis of hardware-software systems. The functional dependency of the hardware components on the interfacing software components is appropriately modeled using fault trees. The MIT (Massachusetts Institute of Technology)-CSR's (Center for Space Research) ACIS (Advanced X-ray Astrophysics Facility Imaging Charge Couple Device Imaging Spectrometer) system is used to illustrate the fault tree analysis method in reliability analysis of complex hardware-software systems. The ACIS science instrument system is a space borne system to acquire and process X-ray images over the sky, and sends them to earth. It has hardware and software components with interfaces between them making it a very good example of a complex hardware software system. This approach could be used in analyzing other complex systems being designed today and in identifying the critical components to make the system safe and more reliable.