Multi-state Multi-valued Decision Diagram Research Articles

Reliability assessment of non-repairable multi-state phased mission systems with backup missions

Recently, the reliability of the multi-state phased mission systems (MS-PMSs) have been widely studied, which is used in the aerospace industry. Except for the phase dependency, the considering of the components/system multi-state behaviors in the PMSs also makes the reliability modeling more complicated. Meanwhile, the redundancy design can ensure high system reliability for the aerospace industry. The mission back-up design is always designed except for the redundant components, which can be reactivated when the working components fail. With the mission backup mechanism, some critical missions could be re-executed. To deal with these complicated situations, a new model based on multi-state multi-valued decision diagram (MMDD) is developed for the reliability modeling of MS-PMSs considering phase backups and multi-results. By using the PMS-MMDD method, the system reliability can be assessed efficiently. The correctness of the proposed method is verified by comparing with the MC simulation method. At last, the reliability of the propulsion system in a spacecraft is assessed to illustrate the proposed method.

Reliability assessment of multi-state phased mission system with non-repairable multi-state components

• A MMDD algorithm for PMS and a PMS-MMDD model are proposed to model the non-repairable multi-state phased-mission system. • A Markov renewal equation-based method is proposed to evaluate system probabilities with non-exponential distributions. • The comparison to the Monte Carlo simulation method illustrate the computation accuracy and efficiency of the proposed methods. • An attitude and orbit control system in spacecraft is studied as a practical example to illustrate the proposed methods. Phased mission systems (PMSs) like satellites and spacecraft perform their functions over non-overlapping mission periods, called phases. One of the challenges in assessing reliability of PMSs comes from considering the s -dependence among phases, and the consideration on the multi-state behavior of components and systems makes the reliability analysis even more difficult. To effectively address this problem, a multi-state multivalued decision diagram algorithm for PMS and a multi-state multi-valued decision diagram model for phased mission system (PMS-MMDD) method is developed for the reliability modelling of non-repairable multi-state components. Based on the Semi-Markov process, a Markov renewal equation-based method is developed to deal with non-exponential multi-state components and a numerical method, the trapezoidal integration method, is used to compute the complex integrals in the path probability evaluation. A case study of a multi-state attitude and orbit control system in a spacecraft is analyzed to illustrate the proposed PMS-MMDD model and the Markov renewal equation-based evaluation method. The accuracy and computation efficiency of the proposed method are verified by the Monte Carlo simulation method.

Research of mission success importance for a multi-state repairablek-out-of-nsystem

For the reliability analysis of complex equipment system, one of the key objectives is that the equipment can complete the specified mission as expected. First of all, this article presents the analysis method of mission success importance for a multi-state k-out-of-n repairable system based on multi-state multi-valued decision diagram as well as the implementation procedure. Second, the engineering significance of mission success importance for a multi-state repairable 2-out-of-3 system is discussed by comparing the component order of mission success importance with multi-state Birnbaum importance, multi-state Fussell–Vesely importance, performance achievement worth, and performance reduction worth. Finally, the change rule of mission success importance is presented for a multi-state 2-out-of-3 repairable system when the reliability of a component is changed. The analysis results show that the engineering significance and change rule of mission success importance could provide effective support for missi...

Reliability analysis of multi-state systems subject to failure mechanism dependence based on a combination method

A multi-state system is a kind of system in which both the system and its components may display multiple performance levels, and it can be utilized to model more complicated and practical systems. As one kind of multi-state object, the performance degradation of a system and its components can be analyzed in terms of failure mechanism dependence. Some coupling relationships of these failure mechanisms exhibit multi-state properties as well. This paper merged the primary failure mechanism correlations proposed in our previous research and provided a combinational method that proposes a modified binary decision diagram (BDD) and a multi-state multi-valued decision diagram (MMDD) models for the state-probability evaluation and reliability analysis of the multi-state system. The method consists of four steps: generation of BDD models for components, calculation of state-probability for components, generation of MMDD models for the system and calculation of reliability for the system. As a study case, the reliability and state-probability of a multi-state sensor system are evaluated using this combinational method. Finally, a comparison between the binary-state and the multi-state are given as well.

Decision diagram based methods and reliability analysis for k-out-of-n: G systems

Binary k-out-of-n systems are commonly used reliability models in engineering practice. Many authors have extended the concept of k-out-of-n system to multi-state k-out-of-n systems. This paper proposes a binary decision diagram (BDD) based approach for binary k-out-of-n: G system and a multi-state multi-valued decision diagram (MMDD) based approach for multi-state k-out-of-n: G system. BDD and MMDD have been extensively used for representing and manipulating logic functions in many areas, including reliability modeling and analysis. In this paper, patterns of BDD/MMDD for binary/multi-state k-out-of-n: G system are summarized and proved, a two-step algorithmic process is proposed for modeling the BDD/MMDD and three case studies are implemented to demonstrate the presented methods. Complexity analysis shows that the presented method is more computationally efficient than the traditional algorithms for k-out-of-n: G system.

A novel decision diagrams extension method

Binary decision diagram (BDD) is a graph-based representation of Boolean functions. It is a directed acyclic graph (DAG) based on Shannon׳s decomposition. Multi-state multi-valued decision diagram (MMDD) is a natural extension of BDD for the symbolic representation and manipulation of the multi-valued logic functions. This paper proposes a decision diagram extension method based on original BDD/MMDD while the scale of a reliability system is extended. Following a discussion of decomposition and physical meaning of BDD and MMDD, the modeling method of BDD/MMDD based on original BDD/MMDD is introduced. Three case studies are implemented to demonstrate the presented methods. Compared with traditional BDD and MMDD generation methods, the decision diagrams extension method is more computationally efficient as shown through the running time.

Integrated importance of multi-state fault tree based on multi-state multi-valued decision diagram

Integrated importance measures have been developed to study the effect of component state probabilities and state transition rates on the multi-state system performance, identifying the weakest component to facilitate the system maintenance and optimization activities. This article proposes an analytical method based on multi-state multi-valued decision diagram for computing the integrated importance measure values. Following a discussion of decomposition and physical meaning of integrated importance measures, the modeling method of multi-state multi-valued decision diagram based on multi-state fault tree analysis is introduced. A five-step integrated importance measure analysis approach based on multi-state multi-valued decision diagram is then proposed. Two case studies are implemented to demonstrate the presented methods. Complexity analysis shows that the multi-state multi-valued decision diagram–based method is more computationally efficient than the existing method using Markov–Bayesian networks.

An Efficient Multistate Multivalued Decision Diagram-Based Approach for Multistate System Sensitivity Analysis

Multistate systems (MSS) are systems in which the system and its components are characterized by multiple states or performance levels. Component importance or sensitivity analysis facilitates the identification of vulnerabilities within the system, and aids in the quantification of criticalities of the system components. Multistate component importance analysis poses unique challenges to existing methods that are primarily based on binary-state applications. This paper presents an analytical method based on multistate multivalued decision diagrams (MMDD) for multistate component importance analysis. The contribution of this work is two-fold: 1) a novel, efficient algorithm for directly generating an MMDD model from multistate capacity network specifications without inefficient enumeration of multistate minimal path or cut vectors; and 2) an efficient, exact MMDD-based approach for evaluating MSS reliability and importance measures. The advantages of the proposed method are illustrated through a comparison with existing methods, and through detailed analyses of three case studies.

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.

On multistate system analysis : Xue Janan. IEEE Trans. Reliab.R-34(4), 329 (1985)

A multi-state system is a kind of system in which both the system and its components may display multiple performance levels, and it can be utilized to model more complicated and practical systems. As one kind of multi-state object, the performance degradation of a system and its components can be analyzed in terms of failure mechanism dependence. Some coupling relationships of these failure mechanisms exhibit multi-state properties as well. This paper merged the primary failure mechanism correlations proposed in our previous research and provided a combinational method that proposes a modified binary decision diagram (BDD) and a multi-state multi-valued decision diagram (MMDD) models for the state-probability evaluation and reliability analysis of the multi-state system. The method consists of four steps: generation of BDD models for components, calculation of state-probability for components, generation of MMDD models for the system and calculation of reliability for the system. As a study case, the reliability and state-probability of a multi-state sensor system are evaluated using this combinational method. Finally, a comparison between the binary-state and the multi-state are given as well.