Liudong Xing

Analysis of generalized phased-mission system reliability, performance, and sensitivity

This paper proposes a generalized phased-mission system (GPMS) analysis methodology called GPMS-CPR that has high computation efficiency and is easy to implement. GPMS-CPR can evaluate a wider range of more practical systems with less restrictive mission requirements, while offering more human-friendly performance indices such as multilevel grading as compared to the previous PMS approaches. GPMS-CPR also accounts for imperfect coverage. This method implements an exciting synthesis of several approaches into a single methodology. Further, it extends the methodology to allow for the analysis of sensitivity of each component for each phase as well as for the entire phased mission, with respect to the multilevel reliability for the GPMS. The conventional phase-OR PMS appear as a special case this GPMS. The advantages of this approach are in the low computational complexity, broad applicability, easy implementation, and high integration (reliability, performance, and sensitivity for GPMS). The methodology is illustrated with examples.

Reliability Evaluation of Phased-Mission Systems With Imperfect Fault Coverage and Common-Cause Failures

This paper proposes efficient methods to assess the reliability of phased-mission systems (PMS) considering both imperfect fault coverage (IPC), and common-cause failures (CCF). The IPC introduces multimode failures that must be considered in the accurate reliability analysis of PMS. Another difficulty in analysis is to allow for multiple CCF that can affect different subsets of system components, and which can occur s-dependently. Our methodology for resolving the above difficulties is to separate the consideration of both IPC and CCF from the combinatorics of the binary decision diagram-based solution, and adjust the input and output of the program to generate the reliability of PMS with IPC and CCF. According to the separation order, two equivalent approaches are developed. The applications and advantages of the approaches are illustrated through examples. PMS without IPC and/or CCF appear as special cases of the approaches

A New Decision-Diagram-Based Method for Efficient Analysis on Multistate Systems

Multistate systems can model many practical systems in a wide range of real applications. A distinct characteristic of these systems is that the systems and their components may assume more than two levels of performance (or states), varying from perfect operation to complete failure. The nonbinary property of multistate systems and their components makes the analysis of multistate systems difficult. This paper proposes a new decision-diagram-based method, called multistate multivalued decision diagrams (MMDD), for the analysis of multistate systems with multistate components. Examples show how the MMDD models are generated and evaluated to obtain the system-state probabilities. The MMDD method is compared with the existing binary decision diagram (BDD)-based method. Empirical results show that the MMDD method can offer less computational complexity and simpler model evaluation algorithm than the BDD-based method.

An Efficient Binary-Decision-Diagram-Based Approach for Network Reliability and Sensitivity Analysis

Reliability and sensitivity analysis is a key component in the design, tuning, and maintenance of network systems. Tremendous research efforts have been expended in this area, but two practical issues, namely, imperfect coverage (IPC) and common-cause failures (CCF), have generally been missed or have not been fully considered in existing methods. In this paper, an efficient approach for fully incorporating both IPC and CCF into network reliability and sensitivity analysis is proposed. The challenges are to allow multiple failure modes introduced by IPC and to cope with multiple dependent faults caused by CCF simultaneously in the analysis. Our methodology for addressing the aforementioned challenges is to separate the consideration of both IPC and CCF from the combinatorics of the solution, which is based on reduced ordered binary decision diagrams (ROBDD). Due to the nature of the ROBDD and the separation of IPC and CCF from the solution combinatorics, our approach has a low computational complexity and is easy to implement. A sample network system is analyzed to illustrate the basics and advantages of our approach. A software tool that we developed for fault-tolerant network reliability and sensitivity analysis is also presented.

Reliability and performance of multi-state systems with propagated failures having selective effect

The paper presents an algorithm for evaluating performance distribution of complex series-parallel multi-state systems with common cause failures caused by propagation of failures in system elements. The failure propagation can have a selective effect, which means that the failures originated from different elements can cause failures of different subsets of system elements. The suggested algorithm is based on the universal generating function approach and a generalized reliability block diagram method (recursive aggregation of pairs of elements and their replacement by an equivalent one). The performance distribution evaluation procedure is repeated for each combination of common cause failures. Illustrative examples are provided.

Automated Modeling of Dynamic Reliability Block Diagrams Using Colored Petri Nets

Computer system reliability is conventionally modeled and analyzed using techniques such as fault tree analysis and reliability block diagrams (RBDs), which provide static representations of system reliability properties. A recent extension to RBDs, called dynamic RBDs (DRBD), defines a framework for modeling the dynamic reliability behavior of computer-based systems. However, analyzing a DRBD model in order to locate and identify design errors, such as a deadlock error or faulty state, is not trivial when done manually. A feasible approach to verifying it is to develop its formal model and then analyze it using programmatic methods. In this paper, we first define a reliability markup language that can be used to formally describe DRBD models. Then, we present an algorithm that automatically converts a DRBD model into a colored Petri net. We use a case study to illustrate the effectiveness of our approach and demonstrate how system properties of a DRBD model can be verified using an existing Petri net tool. Our formal modeling approach is compositional; thus, it provides a potential solution to automated verification of DRBD models.

Reliability Analysis of Nonrepairable Cold-Standby Systems Using Sequential Binary Decision Diagrams

Many real-world systems, particularly those with limited power resources, are designed with cold-standby redundancy for achieving fault tolerance and high reliability. Cold-standby units are unpowered and, thus, do not consume any power until needed to replace a faulty online component. Cold-standby redundancy creates sequential dependence between the online component and standby components; in particular, a standby component can start to work and then fail only after the online component has failed. Traditional approaches to handling the cold-standby redundancy are typically state-space-based or simulation-based or inclusion/exclusion-based methods. Those methods, however, have the state-space explosion problem and/or require long computation time particularly when results with a high degree of accuracy are desired. In this paper, we propose an analytical method based on sequential binary decision diagrams (SBDD) for combinatorial reliability analysis of nonrepairable cold-standby systems. Different from the simulation-based methods, the proposed approach can generate exact system reliability results. In addition, the system SBDD model and reliability evaluation expression, once generated, are reusable for the reliability analysis with different component failure parameters. The approach has no limitation on the type of time-to-failure distributions for the system components or on the system structure. Application and advantages of the proposed approach are illustrated through several case studies.

BDD-based reliability evaluation of phased-mission systems with internal/external common-cause failures

Phased-mission systems (PMS) are systems in which multiple non-overlapping phases of operations (or tasks) are accomplished in sequence for a successful mission. Examples of PMS abound in applications such as aerospace, nuclear power, and airborne weapon systems. Reliability analysis of a PMS must consider statistical dependence across different phases as well as dynamics in system configuration, failure criteria, and component behavior. This paper proposes a binary decision diagrams (BDD) based method for the reliability evaluation of non-repairable binary-state PMS with common-cause failures (CCF). CCF are simultaneous failure of multiple system elements, which can be caused by some external factors (e.g., lightning strikes, sudden changes in environment) or by propagated failures originating from some elements within the system. Both the external and internal CCF is considered in this paper. The proposed method is combinatorial, exact, and is applicable to PMS with arbitrary system structures and component failure distributions. An example with different CCF scenarios is analyzed to illustrate the application and advantages of the proposed method.

Reliability of demand-based phased-mission systems subject to fault level coverage

In many real-world applications, a mission may consist of several different tasks or phases that have to be accomplished in sequence. Such systems are referred to as phased-mission systems (PMS). In this paper we consider the demand-based PMS with parallel structure, where the system components function in parallel with different capacities in each phase of the mission and the mission is successful if and only if the total system capacity meets the predetermined mission demand in each phase. The reliability of the demand-based PMS (DB-PMS) with parallel structure subject to fault-level coverage (FLC) is first studied using a multi-valued decision diagram (MDD) based technique. The traditional MDD is modified to accommodate the FLC mechanism and new MDD construction and evaluation procedures are proposed for DB-PMS. To reduce the size of the MDD, an alternative construction procedure applying the branching truncation method and new reduction rules are further proposed. An upwards algorithm is put forward to evaluate the reliability of DB-PMS subject to FLC. The proposed approaches are illustrated through examples.

Reliability of k-out-of-n systems with phased-mission requirements and imperfect fault coverage

In this paper, an efficient method is proposed for the exact reliability evaluation of k-out-of-n systems with identical components subject to phased-mission requirements and imperfect fault coverage. The system involves multiple, consecutive, and non-overlapping phases of operation, where the k values and failure time distributions of system components can change from phase to phase. The proposed method considers statistical dependencies of component states across phases as well as dynamics in system configuration and success criteria. It also considers the time-varying and phase-dependent failure distributions and associated cumulative damage effects for the system components. The proposed method is based on the total probability law, conditional probabilities and an efficient recursive formula to compute the overall mission reliability with the consideration of imperfect fault coverage. The main advantages of this method are that both its computational time and memory requirements are linear in terms of the system size, and it has no limitation on the type of time-to-failure distributions for the system components. Three examples are presented to illustrate the application and advantages of the proposed method.