Cold Spare Research Articles

Reliability analysis of dynamic fault trees with Priority-AND gates using conditional binary decision diagrams

The conditional binary decision diagram (CBDD) is an extension of the BDD by introducing the conditioning event node, which has been applied to analyze the reliability of the dynamic fault tree (DFT). However, the previous CBDD-based method is limited to the DFT with spare gates since the Boolean conditioning event only describes the replacement state in spare gates. Hence, it cannot be available for the DFT with Priority-AND (PAND) gates. To address this issue, a novel Boolean conditioning event is proposed to describe the sequence-dependence failure in the dynamic system modeled by the DFT with PAND gates. A DFT with complex PAND gates can be converted into a conditional fault tree (CFT) by recursively applying derived rules that are based on the proposed conditioning event. As a result, the minimal cut set replaces the minimal cut sequence for qualitative analysis, which can reduce the average space complexity in a general case. Then, the CBDD can be generated based on the CFT and it can be used for evaluation. Finally, case studies demonstrate an extension of the cold spare gate and the advantages of our method.

Reliability Analysis of Cold-standby Systems with Subsystems Using Conditional Binary Decision Diagrams

<p>Cold-standby systems have been widely used for conditions with limited power, which achieve fault tolerance and high-reliability systems. The cold spare (CSP) gate is a common dynamic gate in the dynamic fault tree (DFT). DFT with CSP gates is typically used to model a cold-standby system for reliability analysis. In general, inputs of the CSP gate are considered to be basic events. However, with the requirement of the current system design, the inputs of the CSP gate may be either basic events or top events of subtrees. Hence, the sequence-dependency among basic events in CSP gates becomes much more complex. However, the early conditional binary decision diagram (CBDD) used for the reliability analysis of spare gates does not consider it well. To address this problem, the conditioning event rep is improved to describe the replacement behavior in CSP gates with subtrees inputs, and the related formulae are derived. Further, a combinatorial method based on the CBDD is demonstrated to evaluate the reliability of cold-standby systems modeled by CSP gates with subtrees inputs. The case study is presented to show the advantage of using our method.</p> <p> </p>

Optimization Methods for Redundancy Allocation in Hybrid Structure Large Binary Systems

This paper addresses the issue of optimal redundancy allocation in hybrid structure large binary systems. Two aspects of optimization are considered: (1) maximizing the reliability of the system under the cost constraint, and (2) obtaining the necessary reliability at a minimum cost. The complex binary system considered in this work is composed of many subsystems with redundant structure. To cover most of the cases encountered in practice, the following kinds of redundancy are considered: active redundancy, passive redundancy, hybrid standby redundancy with a hot or warm reserve and possibly other cold ones, triple modular redundancy (TMR) structure with control facilities and cold spare components, static redundancy: triple modular redundancy or 5-modular redundancy (5MR), TMR/Simplex with cold standby redundancy, and TMR/Duplex with cold standby redundancy. A classic evolutionary algorithm highlights the complexity of this optimization problem. To master the complexity of this problem, two fundamentally different optimization methods are proposed: an improved evolutionary algorithm and a zero-one integer programming formulation. To speed up the search process, a lower bound is determined first. The paper highlights the difficulty of these optimization problems for large systems and, based on numerical results, shows the effectiveness of zero-one integer programming.

Optimization on Preventive Maintenance and Spare Unit Number for Multi-unit Parallel System

Preventive maintenance (PM) for multi-unit parallel system with limited production resource is a crucial issue. To find a solution for the issue, this study focused on a multi-unit parallel system with one repairman and some spare units, and developed an optimization model for the system. In the model, PM policy and cold spare unit number were jointly considered. After optimization, an optimal PM policy with PM interval of running and spare units, PM number and cold spare unit number were obtained. Then, a numerical example was analyzed to illustrate the proposed model, and some results were attained based on the sensitive analysis.

An investigation of reliability optimization in standby systems

Due to the limitations of space or extra costs incurred, the reliability optimization problem of a spare system is of great interest and importance. In this article, we devote our efforts into the investigation of reliability optimization problem of the warm spare gate and cold spare gate. For a spare gate with fixed components, we first examine the relationship between the component order and the corresponding reliability; then, the equivalence of a cascaded model with a multiple-input spare gate is further presented. We find that for a warm spare gate, the corresponding reliability value is anticipated to be affected by the adopted component replacing order; nevertheless, the reliability is a fixed value once the components are provided for a cold spare gate. This finding indicates that reliability is irrespective of the component order for a cold spare gate. Therefore, for the warm spare gate, the component order can be varied to improve the corresponding system reliability, whereas for the cold spare gate, we should attempt to improve the reliabilities of the spare components aiming to obtain a higher reliability. These findings are potentially useful in the design process of a system consisting of spare gates.

Operation-oriented reliability and availability evaluation for onboard high-speed train control system with dynamic Bayesian network

The reliability and availability of the onboard high-speed train control system are important to guarantee operational efficiency and railway safety. Failures occurring in the onboard system may result in serious accidents. In the analysis of the effects of failure, it is significant to consider the operation of an onboard system. This article presents a systemic approach to evaluate the reliability and availability for the onboard system based on dynamic Bayesian network, with taking into account dynamic failure behaviors, imperfect coverage factors, and temporal effects in the operational phase. The case studies are presented and compared for onboard systems with different redundant strategies, that is, the triple modular redundancy, hot spare double dual, and cold spare double dual. Dynamic fault trees of the three kinds of onboard system are constructed and mapped into dynamic Bayesian networks. The forward and backward inferences are conducted not only to evaluate the reliability and availability but also to recognize the vulnerabilities of the onboard systems. A sensitivity analysis is carried out for evaluating the effects of failure rates subject to uncertainties. To improve the reliability and availability, the recovery mechanism should be paid more attention. Finally, the proposed approach is validated with the field data from one railway bureau in China and some industrial impacts are provided.

Optimal Design of Redundant Structures by Incorporating Various Costs

Redundant systems, which usually consist of a number of same/similar components (or modules), have been used in various critical infrastructures to ensure the system's normal function. Usually, system reliability can be improved with the adoption of additional components or redundancies. Typically, two types are mainly included, i.e., majority voters and standby redundancies (referred to as SPARE gates for simplicity). Nevertheless, with the increment of redundancies, the consumed cost or space requirement also grows. This study considers a tradeoff between cost and reliability in order to pursue the cost-effective optimal design. The relationships between the total cost and corresponding parameters are discussed thoroughly. Besides, in order to determine the cost-effective design at the expense of a unit of cost, a revised evaluation standard is proposed (referred to as ${\rm{R}\_\rm{per}\_\rm{Cost}}$ ). In this paper, we perform a cost-effective analysis of majority voters with different implementations; and we also perform the analyses of SPARE gates (here, a warm spare gate and a cold spare gate are mainly focused). For deriving corresponding total cost, algorithms are presented to predict the necessary failure time of components. In this line, cost-effective analyses of several case studies are performed.

Reliability Modeling of Redundant Systems Considering CCF Based on DBN

Common cause failure (CCF) has become a hot topic in reliability and availability analysis of redundant systems. Aiming at the shortage of $$\beta $$ -factor model in distinguishing three or more failures, multiple error shock theory is put forward. Having the problem in determining minimal cut sets and structure functions for dynamic fault tree (DFT), dynamic Bayesian network (DBN) is applied to transit DFT events to corresponding nodes and express causal relations between the nodes. On the base of explicit modeling for CCF, DBN models for hot spare (HSP) gate, cold spare (CSP) gate and warm spare (WSP) gate are established considering CCF processes. For a HSP gate, all failure processes are listed in the stress event layer for each component. For a CSP gate and a WSP gate, CCF node and intermediate nodes are introduced to express causal relations. At last, a control unit and its improved type are taken as examples. The DBN models are built by referring to corresponding DFT structures when taking CCFs into consideration. From the results, it is obvious that the modern unit has a relative higher reliability and availability. And it is less easily influenced by uncertainty such as failure rates and coverage factor through sensitivity analysis.

Risk-based design of process systems using discrete-time Bayesian networks

Temporal Bayesian networks have gained popularity as a robust technique to model dynamic systems in which the components' sequential dependency, as well as their functional dependency, cannot be ignored. In this regard, discrete-time Bayesian networks have been proposed as a viable alternative to solve dynamic fault trees without resort to Markov chains. This approach overcomes the drawbacks of Markov chains such as the state-space explosion and the error-prone conversion procedure from dynamic fault tree. It also benefits from the inherent advantages of Bayesian networks such as probability updating. However, effective mapping of the dynamic gates of dynamic fault trees into Bayesian networks while avoiding the consequent huge multi-dimensional probability tables has always been a matter of concern. In this paper, a new general formalism has been developed to model two important elements of dynamic fault tree, i.e., cold spare gate and sequential enforcing gate, with any arbitrary probability distribution functions. Also, an innovative Neutral Dependency algorithm has been introduced to model dynamic gates such as priority-AND gate, thus reducing the dimension of conditional probability tables by an order of magnitude. The second part of the paper is devoted to the application of discrete-time Bayesian networks in the risk assessment and safety analysis of complex process systems. It has been shown how dynamic techniques can effectively be applied for optimal allocation of safety systems to obtain maximum risk reduction.

Reliability importance analysis of Markovian systems at steady state using perturbation analysis

Sensitivity analysis has been primarily defined for static systems, i.e. systems described by combinatorial reliability models (fault or event trees). Several structural and probabilistic measures have been proposed to assess the components importance. For dynamic systems including inter-component and functional dependencies (cold spare, shared load, shared resources, etc.), and described by Markov models or, more generally, by discrete events dynamic systems models, the problem of sensitivity analysis remains widely open. In this paper, the perturbation method is used to estimate an importance factor, called multi-directional sensitivity measure, in the framework of Markovian systems. Some numerical examples are introduced to show why this method offers a promising tool for steady-state sensitivity analysis of Markov processes in reliability studies.

Development Effort of the Lunar Orbiter Laser Altimeter Laser Transmitter

ABSTRACTThe Lunar Orbiter Laser Altimeter (LOLA) is one of six instruments on the Lunar Reconnaissance Orbiter (LRO) with the objectives to determine the global topography of the lunar surface at high resolution, measure landing site slopes and search for polar ices in shadowed regions. The LOLA laser transmitter is a passively q-switched cross-Porro resonator. The flight laser beryllium bench houses two oscillators (a primary oscillator and a cold spare). The two oscillators are designed to operate sequentially during the mission. The secondary laser will be turned on if the primary laser can no longer provide adequate scientific data products. All components used in the laser have space flight heritage. In this paper we will summarize the development effort of the LOLA laser including the material choice, design criteria and contamination control as applied to the flight laser build.

Fault-Tolerant Memory Architecture Against Radiation-Dependent Errors: A Mixed Error Control Approach

We present a high qualitative reconfigurability method for fault-tolerant memory systems against radiation influence on semiconductors. Its novelty lies in a joint failure repair mechanism. It uses a concurrent on-line technique based on asynchronous built-in current sensors (BICS), parity check and cold spare modules against electrical abnormal behaviour due to latch-up (LU), and the Hamming SEC code to counterattack single error upset (SEU), manifested in logical failures. Complete reliability computations, which underlie the proposed scheme, search for a 99.902% tolerance, thought to meet typical spatial irradiation conditions, to the cost of a small hardware overhead (2 spare (additional) 1K1 modules for each 1K16 of a memory system of 512K16, and Mean Time To Failure e 10−7 h−1). Finally, as we envisage a 2.4 μm CMOS implementation, we performed complexity estimations, which show that the supplementary self-tolerance ensuring circuitry involves an overhead of 0.0094% for a 512K16 memory. The recovering latency is minimised. For SEU in DRAM it requires zero latency and no more than the duration of an equivalent refresh cycle in SRAM. LU reflects a locality property, as only the affected module is submitted to the recovering algorithm.

Mean time to first failure of repairable systems with one cold spare : Winfrid G. Schneeweiss. IEEE Transactions on Reliability, 44 (4), 567 (1995)

Mean time to first failure of repairable systems with one cold spare : Winfrid G. Schneeweiss. IEEE Transactions on Reliability, 44 (4), 567 (1995)

Mean time to first failure of repairable systems with one cold spare

A general (nonMarkov) 1-out-of-2:G system with statistically-identical components, repair, and cold standby is reviewed. Coverage is considered, viz, failures of the switching mechanism for activating the spare. The explicit derivation of the mean time-to-first-failure and its in-depth discussion appear to be new. The state transition graph and the Petri net both show the way to general (n-1)-out-of-n:G systems of this category. However, for n>2, results are given only for statistically-identical components which are all as good as new, when a repaired component is put to use. This limits applicability of results to electronic systems.