Binary-state System Research Articles

Reliability of consecutive-[formula omitted]-out-of-[formula omitted]: F systems with shared components under non-homogeneous Markov dependence

Multi-state system models are more practical and valuable when describing complex engineering structures than binary-state system models. Modelling of linear consecutive-(k,l)-out-of-n: F systems with shared components under non-homogeneous Markov dependence is discussed in this work. The proposed model is an extension of both “consecutive-k-out-of-n: F system” and “consecutive-k-out-of-n: F system with shared components between adjacent subsystems”. All the components in the system are assumed to have three states and are non-homogeneous Markov-dependent. Using the method of sum of disjoint products (SDP), the system reliability formula is derived by summing the reliability values for all disjoint cases. The well-known finite Markov chain imbedding approach (FMCIA) is used for deriving the reliability formula for each disjoint case. For the special cases of systems with homogeneous Markov-dependent or independent components, the corresponding results are deduced. Finally, some numerical examples are presented to illustrate all the results developed here.

A generalized model selection framework for multi-state failure data analysis

PurposeThe purpose of this paper is to carry out a reliability analysis of a mechanical system considering the degraded states to get a proper understanding of system behavior and its propagation towards complete failure.Design/methodology/approachThe reliability analysis of computerized numerical control machine tools (CNCMTs) using a multi-state system (MSS) approach that considers various degraded states rather than a binary approach is carried out. The failures of the CNCMT are classified into five states: one fully operational state, three degraded states and one failed state.FindingsThe analysis of failure data collected from the field and tests conducted in the laboratory provided detailed understandings about the quality of the material and its failure behavior used in designing and the capability of the manufacturing system. The present work identified that Class II (major failure) is critical from a maintainability perspective whereas Class III (moderate failure) and Class IV (minor failure) are critical from a reliability perspective.Research limitations/implicationsThis research applies to reliability data analysis of systems that consider various degraded states.Practical implicationsMSS reliability analysis approach will help to identify various degraded states of the system that affect the performance and productivity and also to improve system reliability, availability and performance.Social implicationsIndustrial system designers recognized that reliability and maintainability is a critical design attribute. Reliability studies using the binary state approach are insufficient and incorrect for the systems with degraded failures states, and such analysis can give incorrect results, and increase the cost. The proposed MSS approach is more suitable for complex systems such as CNCMT rather than the binary-state system approach.Originality/valueThis paper presents a generalized framework MSS's failure and repair data analysis has been developed and applied to a CNCMT.

Survival signature for reliability evaluation of a multi-state system with multi-state components

Survival signature technology has recently attracted increasing attention for its merits on quantifying reliability of systems with multiple types of components. In order to implement reliability evaluation of multi-state system (MSS), computing methods of survival signature are studied for reliability analysis of several different systems in this paper. For an MSS consisting of multi-state components, its survival signature can be developed based on the different state definition of system. For the binary-state system with multi-state components, its survival signature is based on the generalization of survival signature for multi-state components. For a real life engineering MSS consisting of subsystems, the computing method of survival signature of system has also been derived based on the survival signature of subsystems and mapping of subsystems’ states to system's states. This enables consecutive application of the new method to substantial realistic MSS, with no theoretical limit on the size of the systems. Examples illustrate the applicability of the analysis approach for systems reliability.

Reliability analysis and selective maintenance for multistate queueing system

The reliability theory of the multi-state system (MSS) has received considerable attention in recent years, as it is able to characterize the multi-state property and complicated deterioration process of systems in a finer way than that of binary-state system. In general, the performance of the task processing type MSS is typically measured by an operation time (processing speed). Whereas, considering the queueing phenomenon caused by the random arrival and processing of tasks, some other criteria should be taken into account to evaluate the quality of service (QoS) and the profit of stakeholders, such as waiting time, service and abandon rate of tasks and consequent profit rate. In this article, we focus on the queueing process of tasks and analyse the performance and reliability of MSS in an M/M/2 queueing model, which is referred to as a multi-state queueing system (MSQS). Two kinds of deterioration are studied including the gradual degradation of servers and the sudden breakdown of the whole system. A performance assessment function is defined to obtain the profit rate of MSQS in different performance states. Based on the proposed performance function, the selective maintenance method is studied to optimize the accumulated profit under the constraint of maintenance resource and time.

Reliability Modeling for Sparsely Connected Homogeneous Multistate Consecutive-k-Out-of-n: GSystems

Compared to binary-state system models, multistate (MS) system models are more practical and useful when describing complex systems in applications, such as communication systems, oil pipeline systems, and grid or cloud computing infrastructures. This paper models a generalized sparsely connected MS consecutive- ${k}$ -out-of- ${n}$ : ${G}$ system. The proposed model is regarded as a natural extension of the consecutive- ${k}$ -out-of- ${n}$ system. Moreover, the proposed system model could cover three special MS submodels, i.e., a decreasing MS: ${G}$ system model, an increasing MS: ${G}$ system model, and a nonmonotonic MS: ${G}$ system model. Three corresponding real-world examples are given to illustrate the applications of the model. Meanwhile, by utilizing the well-known finite Markov chain imbedding method, the explicit system reliability and state distribution for the three kinds of submodels are presented, respectively. Finally, the developed indexes and analysis method are demonstrated by numerical examples.

Parameter inference for non-repairable multi-state system reliability models by multi-level observation sequences

Multi-state system reliability theory has received considerable attention in recent years, as it is able to characterize the multi-state nature and complicated deterioration process of systems in a finer fashion than that of binary-state system models. Parameter inference for multi-state system reliability models, which is a task that precedes reliability evaluation and optimization, is an interesting topic to be investigated. In this paper, a new parameter inference method, which aggregates observation sequences from multiple levels of a system, is developed. The proposed inference method generally consists of two stages: (1) compute the sequences of the posterior state probability distributions of units based on multi-level observation sequences by dynamic Bayesian network models and (2) estimate the unknown transition probabilities of units by converting the sequences of posterior state probability distributions into a least squares problem. Two illustrative examples, together with a set of comparative studies, are presented to demonstrate the effectiveness and efficiency of the proposed method.

GENERALIZATION OF THE MEAN-FIELD METHOD FOR POWER-LAW DISTRIBUTIONS

Recently much attention has been paid to the nonextensive canonical distributions: the α-families. Such distributions have been found in many real-world systems such as fully developed turbulence and financial markets. In this paper, a generalized mean-field method to approximate the expectations of the α-families is proposed. We calculate the α′-projection of a probability distribution to find that the computational complexity to approximate the expectations is greatly reduced with a proper choice of the projection-index α′. We apply this method to a simple binary-state system and compare the results with direct numerical calculations.

A conditional simulation method for estimating the critical component of networks

The critical component of a network system is defined as the component that has the largest Birnbaum importance in this paper. We show that, so far as the critical component is concerned, the only parameter needed to be estimated is the average state of every component given that the whole system is operational This paper also proposes a new simulation algorithm to estimate the critical component of a binary-state network system. Comparing with the crude simulation method, the proposed method saves 90 percent to 99 percent computation time in the simulation experiment of this paper. The performance may be even better when the size of the network grows.

STOCHASTIC BOUNDS FOR GENERALIZED SYSTEMS IN RELIABILITY THEORY

Practically, it is not feasible to obtain the precise reliability of systems in a reasonable time, when the systems are large and complex. In this paper, we present some stochastic bounds on generalized systems of which state spaces are mathematically partially ordered sets. In the first place we introduce a notion of generalized systems and then present some stochastic bounds on the system reliability by using maximal and minimal elements of the structures of the systems. The bounds are generalization of the well-known max-min bounds on binary-state system reliability. Furthermore, we present the other stochastic bounds when systems are decomposed into several modules and satisfy a condition which is called MC (Maximal Coincidence) condition. We show that these bounds are tighter than the former. For a few simple systems, we give numerical examples and estimations of computational complexity for obtaining these stochastic bounds.

On Multistate System Analysis

Discrete function theory, which extends switching function theory and multiple-valued logic function theory, is introduced into multistate system analysis. Some theoretical conclusions and algorithms which play key roles in multistate system analysis are presented. The concepts of s-coherence and duality in binary-state system analysis are generalized. The set of minimal upper (maximum lower) vectors for level j, which play the role of min path (cut) set, is introduced to represent the states of a monotonic multistate system. Two approaches to computing state probability of multistate systems are given, one is based on inclusion-exclusion, the other is based on enumeration. Binary-state fault-tree is extended to multistate fault-tree. A computer code (MSTA1) has been programmed and is used to evaluate a multistate fault-tree. Multistate fault-tree and the computer code have been applied to paper-making industry; the results are consistent with the field data.