Analysis Of Multi-state Systems Research Articles

Availability‐aware virtual network function placement based on multidimensional universal generating functions

AbstractNetwork function virtualization (NFV) implements network functions as software, which enables flexible, resource‐efficient, and rapid provision of network services. In NFV, network services are realized by the service function chain (SFC), which is a chain of virtual network functions (VNFs) linked in the proper order. Both availability and deployment cost are key concerns for network operators providing network services as SFC. This paper proposes a flexible VNF placement model on a per‐VNF instance basis that minimizes deployment costs while satisfying availability requirements that may be placed on SFC. This paper uses a multidimensional universal generating function (MUGF) method, which is a multistate system analysis method, to compute the availability of a multistate SFC system with multiple VNFs coexisting on a server. The MUGF method calculates the performance of the entire SFC by combining the performance of servers as determined by applying a continuous‐time Markov chain. To reduce the time to compute the SFC availability, we introduce operators to be applied to MUGF and develop an availability computing method. In addition, a heuristic algorithm for determining VNF placement targeting the lowest deployment cost possible while meeting availability requirements is presented. Numerical results show that the proposed model obtains VNF placement with lower cost than the conventional model in all examined cases. The proposed model achieves VNF placement at 58.5%–75.0% of the deployment cost of the conventional model for the same SFC availability requirements.

Performance efficiency and cost analysis of multi-state systems with successive damage and maintenance in multiple shock events

Real-world systems are often exposed to shocks likes earthquakes and hurricanes during service life, and these shocks may occur multiple times. However, existing studies lack research on damage and maintenance interacting processes under multiple shocks. In this paper, a new performance efficiency and budget surplus rate model for multi-state systems is developed under the interaction of damage and maintenance. System performance efficiency measures the ability of the system to recover its performance from multiple shocks. The budget surplus rate model is introduced for measuring the system's ability to respond to losses from multiple shocks. Multiple cumulative shocks not only cause the system to transfer from a high-performance state to a low-performance state, but also accelerate the performance degradation of the system bringing successive damage, which is reflected by the reduced transition time between states. Markov processes are used to characterize the state transition process between the system suffering damage and maintenance under multiple shock events. A case study of a nuclear power plant is used to demonstrate the proposed methods. Sensitivity analysis of performance efficiency and budget surplus rate is also performed to reflect the shock resistance and maintenance capability of the nuclear power plant system.

A new method for analysis of Multi-State systems based on Multi-valued decision diagram under epistemic uncertainty

The development of the system's model is an important step in reliability analysis. The system's model in reliability analysis similar to other knowledge areas is used as an explanatory and research tool. In reliability analysis, this model is mathematical and allows us to determine quantitative characteristics to evaluate the behavior of the original system. Typically such a mathematical model approximates the behavior of the initial system and has some uncertainty. However, this uncertainty can increase significantly if the initial data for building the model is uncertain and incompletely specified. The uncertainty of the mathematical model also causes incorrect estimates of the system behavior and its reliability. Therefore, it is important to develop methods that allow us to take into account the uncertain nature of the initial data, first of all, take into account epistemic uncertainty in initial data. A new method for the development of a mathematical model of a Multi-State System (MSS) in the form of a Multi-Valued Decision Diagram based on incompletely specified and uncertain data is proposed. In other words, the proposed method takes into account the epistemic uncertainty of the initial data. The specific of this method is the use of Data Mining based classification procedures, in particular, the Fuzzy Decision Trees.

Reliability analysis of multi-state systems with lag-dependent components

In a multi-state system (MSS) with dependent components, the performance distributions of low priority components (LPCs) depend on the states of high priority components (HPCs). However, the relationship between LPCs and HPCs is usually considered as the instantaneous dependency (instant-dependency). In practice, the dependency between them is lagging due to the electronic circuits, i.e, the performance distributions of LPCs would be changed after a certain transmission time when one state of HPCs transfers to another. In this paper, the lag-dependency between LPCs and HPCs in a MSS is considered. At the beginning of transfer of each state for HPCs, three kinds of lag threshold values are set to quantify the transmission time from HPCs to corresponding LPCs. Due to the lag-dependency, the sojourn time and probabilities of states of HPCs are reanalyzed. As an important method of reliability analysis, the universal generating function is utilized to analyze the reliability of a MSS with lag-dependent components. The effectiveness of the proposed methods is proved via a comparative analysis of MSSs with instant-dependent components and lag-dependent components. The results show that the reliability of MSS would be underestimated if the lag-dependency is not considered.

Mission aborting and system rescue for multi-state systems with arbitrary structure

Rescue procedures (RP), triggered either by the occurrence of the mission failure or by a certain undesired system state, are usually applied to survive a life-critical or safety-critical system mitigating or avoiding costly consequences. Existing works model either the mission failure-triggered RP or the system state-triggered RP, but not both. This paper makes contributions by co-modeling both types of RPs in the reliability analysis of multi-state systems with arbitrary structure and heterogeneous system elements. The system performs a primary mission (PM) with the specified time duration. System configuration (i.e., required subset of working elements and system functioning criteria) and reliability characteristics of system elements are different during PM and RP. A probabilistic modeling method is proposed to analyze reliability metrics of the considered system in forms of mission success probability (MSP) and system survival probability (SSP). Based on the MSP and SSP evaluation, two types of mission abort rules (performance constraint-based and system state subset-based) are investigated and compared. An example of an electrical heating system is provided to illustrate the proposed method and solutions to the optimal mission aborting policy that maximizes MSP subject to meeting a certain level of SSP.

A testability modeling method based on structure-function-state-test

Aiming at the testability analysis of multi-state system, a testability modeling method based on structure-function-state-test is proposed. Based on the hierarchical structure analysis of the system, taking the function modeling of the structure as the core, the performance, fault and state of the function are described, and the test correlation of the system fault and state is studied. Through the analysis of a typical case, the results show that the model can: 1. Realize the system fault test correlation analysis considering the uncertain factors; 2. Realize the state test correlation analysis of the multi state system; 3. Realize the testability analysis of the multi state system by calculating the fault detection rate, fault isolation rate and state detection rate.

A C++ class for multi-state algebraic reliability computations

We present the design and implementation of a C++ class for reliability analysis of multi-state systems using an algebraic approach based on monomial ideals. The class is implemented within the open-source CoCoALib library and provides functions to compute system reliability and bounds. The algorithms we present may be applied to general systems with independent components having identical or non-identical probability distributions.

Multiple-valued Decision Diagrams for Multi-state System Performability Analysis

Background: In a multi-state system, either the entire system or its components will have more than two states. Different kind of multi-state systems have been investigated, such as multistate series-parallel systems, multi-state k-out-of-n systems and multi-state linear consecutive-k-outof- n systems. Methods: Performability analysis is concerned with the calculation of probability distribution of different system performance levels. In this paper, Multi-valued Decision Diagram (MDD) based approaches are discussed to conduct the performability analysis of multi-state systems. Results: Examples are provided to illustrate the use of MDD approaches for three types of multistate systems, e.g. multi-state series-parallel systems, multi-state k-out-of-n systems and multi-state linear consecutive-k-out-of-n systems. Conclusion: The empirical results show that the MDD approaches have lower computational complexity than the traditional methods in model generation and evaluation.

Resilience analysis of multi-state systems with time-dependent behaviors

Most of existing resilience models assume that system performances are continuous. In this paper, we consider resilience modeling and analysis for multi-state systems, whose performances are characterized by discrete, rather than continuous variables. A non-homogeneous Semi-Markov reward process model is developed for resilience analysis of multi-state systems. In the developed model, system performance changes, caused by either disruptive events or system recoveries, are modeled as state transitions, and rewards are used to model financial losses incurred during and after the disruptions. Four resilience metrics are defined to quantify different aspects of resilience. As the developed model is non-homogeneous, it can capture time-dependent system behaviors and their impact on system resilience. An efficient resilience analysis algorithm is also designed based on linear interpolation and implemented using vectorization. The computational benefits of the developed algorithm are demonstrated through two numerical experiments. We apply the developed method on two practical case studies, an oil tank farm and a re-configurable computing system. The results show that the developed methods can quantify resilience of multi-state systems accurately and efficiently.

Reliability Analysis of Common Cause Failure Multistate System Based on CUGF

This paper addresses the problem of mixed uncertainty in the reliability analysis of multistate systems under common cause failure conditions. Combining the cloud model theory, universal generation function (UGF) method, and common cause failure theory, the universal generation function method is extended based on a probabilistic cloud model, i.e., the cloud universal generation function (CUGF) analysis method. The cloud model represents the random and cognitive uncertainty of the state probability, i.e., mixed uncertainty. Next, through CUGF, according to the calculation rules of cloud operators, we provide steps to obtain the reliability of a multistate system under independent failure and common cause failure conditions and obtain cloud digital features for reliability. The accuracy and feasibility of the method are verified by a numerical example. This paper solves the problem of reliability analysis of multistate systems with mixed uncertainty in unit state probability information under common cause failure conditions. We integrate system multistate, information uncertainty, and common cause failure for reliability analysis to avoid large errors, more in line with a project’s actual situation. We propose new ideas and methods to process randomness and fuzzy information or data in multistate system reliability analysis.

Probabilistic model-checking based reliability analysis for failure correlation of multi-state systems

Many conventional reliability analysis methods for multi-state systems assume independence among the various subsystems. To avoid this, we propose a probabilistic model checking-based approach for failure correlation analysis of multi-state systems. First, an improved Apriori algorithm is used to determine the effect of a subsystem failure on the associated subsystems. Next, a copula function is applied to establish the relationship between failures of the associated subsystems. Finally, probabilistic model-checking is used to analyze the reliability of the entire system and all its subsystems. The effectiveness of the proposed method is verified using an application involving offshore wind turbines. The results show that the proposed method can be used flexibly and effectively for multi-state system reliability analysis. Moreover, the proposed method lays the foundation for system maintenance strategy formulation and other engineering applications.

Reliability analysis of multi-state systems with common cause failures based on Bayesian network and fuzzy probability

Multi-state components, common cause failures (CCFs) and data uncertainty are the general problems for reliability analysis of complex engineering systems. In this paper, a method incorporating fuzzy probability and Bayesian network (BN) into multi-state systems (MSSs) with CCFs is proposed. In particular, basic theories of multi-state BN and fuzzy probability are developed. Moreover, a model integrating CCFs with BN has also been illustrated. In order to incorporate fuzzy probability into MSSs reliability evaluation considering common parent node generated by CCFs, fuzzy probability has to be translated into accurate probability through defuzzification and normalization methods which are both elaborated. In addition, quantitative analysis based on BN is carried out. In this paper, feed system of boring spindle in computer numerical control machine is analyzed as an example to validate the feasibility of the proposed method. It can improve the ability of BN on reliability evaluation of complex system with uncertainty issues.

Reliability Analysis of Multi-State Systems based on EUGF Method using Common Cause Failure Components

Reliability Analysis of Multi-State Systems based on EUGF Method using Common Cause Failure Components

Stress–strength reliability analysis of multi-state system based on generalized survival signature

The stress–strength model has been widely used in reliability design of system. In the traditional stress–strength reliability theory, the system and each component are assumed to be only in one of two possible states being either working or failed, and the notion of stress–strength reliability is the probability that the strength is larger than the stress. In this paper, we study the stress–strength reliability of multi-state system based on generalized survival signature. It is supposed that the state of multi-state system is defined by using the ratio between strength and stress random variables. The definitions of generalized survival signature for a certain class of multi state systems with multi-state components in both discrete and continuous cases are given. In addition, the expressions of stress–strength reliability in both discrete and continuous situations are derived. In the case of continuous multi-state system, it is assumed that the random strength and stress are both from the Weibull distributions with different scale parameters, and the two different continuous kernel functions are Pareto and generalized half logistic distribution functions, respectively. Based on the assumptions, the stress–strength reliability is estimated by using both classical and Bayesian statistical theories. The uniformly minimum variance unbiased estimator and maximum likelihood estimator for the stress–strength reliability of the continuous multi-state system are derived. Under the squared error loss function, the exact expression of Bayes estimator for the stress–strength reliability of the continuous multi-state system is developed by using Gauss hypergeometric function. Finally, the Monte Carlo simulations are performed to compare the performances of the proposed stress–strength reliability estimators, and a real data set is also analyzed for an illustration of the findings. • The definitions of the generalized survival signature (GSS) are given. • We study the stress–strength reliability (SSR) of multi-state system based on GSS. • The multi-state system in both discrete and continuous cases are considered. • Classical and Bayesian statistical theories are used to estimate the SSR.

Dynamic Fuzzy Reliability Analysis of Multistate Systems Based on Universal Generating Function

Considering the fuzziness of load, strength, operational states, and state probability, reliability models of multistate systems are developed based on universal generating function (UGF). The fuzzy UGF of load and the fuzzy UGF of strength are proposed in this paper, which are used to derive the fuzzy component UGF and the fuzzy system UGF. By defining the decomposition operator and the inner product operator, failure dependence and effects of multiple load applications are taken into account in the established reliability models. Moreover, dynamic fuzzy reliability models of multistate systems are constructed considering the strength degradation of components. The results show that failure dependence and the effects of multiple load applications have significant impacts on system reliability, which considerably decrease system reliability and increase the fuzziness of system reliability under low performance requirements. Besides, in the dynamic reliability analysis of multistate systems, strength degradation dependence could lead to large computational error.

Reliability analysis of multi-state system with three-state components and its application to wind energy

In most real life situations, the system’s components contribute differently in different performance levels. Such a situation can be modeled by systems with multi-state components having more than one working status, e.g. perfect functioning, and partial working. In this paper, a multi-state system that consists of two types of three-state components is defined and studied. An explicit formula for the probability that the performance of the system is at least a given level is obtained for the most general case when the components are statistically dependent. The model is applied to evaluate the wind power system that consists of two wind plants in different regions. An optimization problem is formulated to find the optimal number of wind turbines that must be installed in the wind plants by minimizing the total cost under specific power production.

How combined performance and propagation of failure dependencies affect the reliability of a MSS

Reliability assessment of systems with multiple components is often analyzed on the assumption of component independency. This assumption can be overcome by considering component interactions and is useful for assessing the reliability of technical systems. This paper presents a reliability assessment analysis of multi-state systems (MSS) considering the combination of two types of dependencies: performance and propagation of failure. Performance dependency occurs in sub-systems sharing performance distribution, whereas propagation of failures dependence consists of failures originating in one sub-system causing failures in other sub-systems. The proposed method is based on the extended universal generating approach used for the analysis of MSS with dependencies. This method was applied to wind turbine multi-state system. The results show how sub-system interactions influence the reliability.

Reliability analysis of multi-state system with application of multiple-valued logic

PurposeThe purpose of this paper is to develop a new mathematical method for the reliability analysis and evaluation of multi-state system (MSS) reliability that agrees with specifics of such system. It is possible based on the application of multiple-valued logic (MVL) that is a natural extension of Boolean algebra used in reliability analysis.Design/methodology/approachSimilar to Boolean algebra, MVL is used for the constriction of the structure function of the investigated system. The interpretation of the structure function of the MSS in terms of MVL allows using mathematical methods and approaches of this logic for the analysis of the structure function.FindingsThe logical differential calculus is one of mathematical approaches in MVL. The authors develop new method for MSS reliability analysis based on logical differential calculus, in particular direct partial logical derivatives, for the investigation of critical system states (CSSs). The proposed method allows providing the qualitative and quantitative analyses of MSS: the CSS can be defined for all possible changes of any system component or group of components, and probabilities of this state can also be calculated.Originality/valueThe proposed method permits representing the MSS in the form of a structure function that is interpreted as MVL function and provides the system analyses without special transformation into Boolean interpretation and with acceptable computational complexity.

Importance analysis of multi-state systems based on tools of logical differential calculus

Importance analysis deals with the investigation of influence of individual system components on system operation. This investigation can be qualitative or quantitative. The qualitative analysis focuses on finding scenarios in which a degradation/improvement of a specific component or a group of components results in a degradation/improvement of the whole system, while the quantitative one deals with numerical estimation of components importance. In this paper, we propose a new approach for importance analysis of Multi-State Systems (MSSs). The qualitative or quantitative importance analysis is based on the identification of critical states. The new approach can be used for calculation of all types of critical states. It is based on the application of direct partial logic derivatives. These derivatives are one of the methods of logical differential calculus. In this paper, the specifics of these derivatives for importance analysis of MSSs are considered in detail.

Reliability analysis of multi-state emergency detection system using simulation approach based on fuzzy failure rate

Fault tree analysis is one of the most useful techniques in reliability analysis of multistate systems that analyze and handle complex systems via Monte Carlo simulations or mathematical approaches. Traditional fault tree cannot depict the exact evaluation of components and systems failures with respect to simplex analysis. On the other hand, the exact evaluation of system reliability with unknown data owning to components and elements is still difficult. Therefore, in this paper, in order to overcome this problem as for the quantitative analysis of fault trees, the reliability analysis of a multistate system (i.e. Launch Emergency Detection System) based on fault tree analysis and fuzzy failure rates is studied. Accordingly, using fuzzy arithmetic, events time-to-failure are generated and then the Top Event time to failure is calculated. Finally, the results of the analytical solution are compared with the results attained by presented approach and shows that, in spite of less effort and time consuming, this method has more accuracy and suitable for all real industrial and complex systems. This paper has further developed the method of FTA for the most generic case where both the system and the components have multiple failure states.