Reliability Assessment Of Multi-state Systems Research Articles

Multisource Imprecise Information Calibration for Reliability Assessment of Multistate Systems: A Consensus Reaching Perspective

Multisource Imprecise Information Calibration for Reliability Assessment of Multistate Systems: A Consensus Reaching Perspective

Intuitionistic fuzzy approach to reliability assessment of multi-state systems

One of the major problems that one encounters within an engineering system is the assessment of its quality, or in other words, reliability. However, conventional reliability tends to ignore the fuzziness in the system, i.e., the lack of precision, vagueness, inaccuracy, or inadequacy in the information obtained. As a result, the integration of fuzzy sets into reliability theory has proven to be incredibly vital. Similarly, the universal generating function (UGF) technique has also been an asset in reliability assessment ever since its inception due to its simplicity. Here, a novel technique involving the intuitionistic fuzzy sets (IFS), specifically using the triangular intuitionistic fuzzy numbers (TIFN) and the UGF method, has been created for the reliability assessment of a fuzzy multi-state system (FMSS). This method is then applied to a system of wireless communication and its intuitionistic fuzzy reliability and availability are evaluated where each performance state and its probability are characterized by a TIFN. The obtained results are also represented graphically for better insights. This work is helpful in getting a clear picture of FMSS and thus, making them more reliable.

Fusing Conflicting Multisource Imprecise Information for Reliability Assessment of Multistate Systems: A Two-Stage Optimization Approach

Expert knowledge is an important information source for system reliability assessment, especially when historical data are limited. However, when elicited, expert knowledge is often imprecise with large uncertainty. Moreover, as experts usually own different expertise and knowledge, the elicited knowledge from different experts might be conflicting. In this article, a two-stage optimization model is put forth to fuse the imprecise and conflicting information from multiple sources to assess reliability of multistate systems. The degradation of the components in the multistate system is modeled via imprecise Markov models. Then, in the first-stage optimization, upper and lower bounds of the degradation model parameters are determined by minimizing the conflict between the prediction of the model and the multisource imprecise information elicited from experts. A particle swarm optimization algorithm is tailored to solve the computational problems brought by the presence of high-dimensional decision variables and resolve the optimization problem. The second-stage optimization is, then, conducted to identify the upper and lower bounds of the system reliability function given that the degradation model parameters are constrained in the bounds obtained from the first-stage optimization. A numerical example, along with a radar display and control system, is used to demonstrate the effectiveness and applicability of the proposed method.

Measuring Conflicts of Multisource Imprecise Information in Multistate System Reliability Assessment

In engineering scenarios, expert judgments play an essential role in reliability assessment, especially for those systems with few historical data. To achieve a rational result, experts from different areas should be involved, and the uncertainties in their assessments should be properly addressed. Such information is often referred to as multisource imprecise information (MSII) and might contain high degree of conflicts, as different experts usually have different expertise and knowledge. Properly quantifying the conflicts among the MSII, then, becomes a critical issue, as the subsequent processing of MSII (e.g., combination and calibration), depends on the degree of conflict in the MSII. To this end, a new conflict measure is put forth based on the Dempster–Shafer theory (DST) to quantify and visualize the conflict in the MSII from a group of experts. In the first place, the MSII from each expert is used to construct the basic belief assignment (BBA) of the reliability estimates for the corresponding expert under the DST. A 2-D conflict measure, which combines the conflict factor and Jousselme distance in DST, is, then, proposed to measure the conflict between the experts’ BBAs. The conflict is quantified from two perspectives, viz., mutual conflict and total conflict. Finally, a Bhattacharyya distance-based method is developed to further quantify the informativeness of each expert's MSII to the system reliability estimate. A numerical example along with an engineering case is used to validate the effectiveness of the proposed approach.

A generic physics-informed neural network-based framework for reliability assessment of multi-state systems

In this paper, we develop a generic physics-informed neural network (PINN)-based framework to assess the reliability of multi-state systems (MSSs). The proposed framework follows a two-step procedure. In the first step, we recast the reliability assessment of MSS as a machine learning problem using the framework of PINN. A feedforward neural network with two individual loss groups is constructed to encode the initial condition and the state transitions governed by ordinary differential equations in MSS, respectively. Next, we tackle the problem of high imbalance in the magnitudes of back-propagated gradients from a multi-task learning perspective and establish a continuous latent function for system reliability assessment. Particularly, we regard each element of the loss function as an individual learning task and project a task’s gradient onto the norm plane of any other task with a conflicting gradient by taking the projecting conflicting gradients (PCGrad) method. We demonstrate the applications of the proposed framework for MSS reliability assessment in a variety of scenarios, including time-independent or dependent state transitions, where system scales increase from small to medium. The computational results indicate that PINN-based framework reveals a promising performance in MSS reliability assessment and incorporation of PCGrad into PINN substantially improves the solution quality and convergence speed of the algorithm.

Reliability assessment for multi-state systems with state transition dependency

As multi-state system reliability models are capable of characterizing the multi-state nature of engineered systems in deteriorating process, they have received considerable concerns in the past few decades. Most reported works on multi-state system reliability modeling are, however, based on the premise that transitions among states of a system/component are stochastically independent. Sometimes, a system may experience the same environmental/working conditions when deteriorating from a better state to worse ones, and thus, state transitions of a system/component could be stochastically dependent. In this paper, a new reliability model for multi-state systems/components with state transition dependency is put forth. The dependency among state transitions is implicitly characterized by copula functions which offer a great flexibility of linking arbitrary marginal distributions together to construct a multivariate distribution. The reliability function of a population of multi-state systems/components and the conditional reliability function of each individual multi-state system/component given a set of observations are derived. The likelihood functions for model parameter estimation are formulated for two cases, i.e., continuous and discontinuous inspection strategies, and model selection criteria are customized to identify the most preferable model among candidates. Two illustrative examples, together with comparative studies, are presented to demonstrate the effectiveness of the proposed method.

Hybrid uncertainty model for multi-state systems and linear programming-based approximations for reliability assessment

This article studies reliability assessment for Multi-State Systems (MSSs) with components states that are uncertain in both probability and performance realizations. First, we propose a model of (discrete) Hybrid Uncertainty Variable (HUV) for modeling the hybrid uncertainty of the MSS, in which both state performance levels and associated probability level are described by uncertain values. The HUV can be regarded as a generalization of random variable whose realizations and corresponding probabilities are both uncertain values. Especially the uncertain probabilities are controlled by the probability law. Leveraging the HUV-based hybrid uncertainty model, the primitive probability law is considered throughout the whole process from modeling component state probabilities, through the resulting system state probabilities, to the final reliability computations. Therefore, the information loss is reduced to a minimum. Furthermore, we develop a framework for assessing the reliability of the MSS with hybrid uncertainty. In particular, due to hybrid uncertainty considered together with the primitive probability law constraints, the reliability bound computations essentially require solving a pair of multi-linear optimization problems, which in general are non-convex and non-concave and therefore belong to a class of difficult optimization problems. Therefore, we develop a linear programming‐based cut-generation approach for solving the reliability bound assessment problem which achieves a computationally attractive approximation. Finally, the effectiveness of our approaches is validated in the case study with the comparisons to the published results.

Dynamic Reliability Assessment for Multi-State Systems Utilizing System-Level Inspection Data

Traditional time-based reliability assessment methods evaluate the reliability of a multi-state system (MSS) from a population or a statistical perspective that the reliability of a system is computed purely based upon historical time-to-failure data collected from a large population of identical components or systems. These methods, however, fail to characterize the stochastic behaviors of a specific individual system. In this paper, by utilizing system-level observation history, a dynamic reliability assessment method for MSSs is put forth. The proposed recursive Bayesian formula is able to dynamically update the reliability function of a specific MSS over time by incorporating system-level inspection data. The dynamic reliability function, state probabilities, and remaining useful life distribution of an MSS in residual lifetime are derived for two common cases: the degradation of components follows a homogeneous continuous time Markov process, and a non-homogeneous continuous time Markov process. The effectiveness and accuracy of the proposed method are demonstrated via two numerical examples.

Random Fuzzy Extension of the Universal Generating Function Approach for the Reliability Assessment of Multi-State Systems Under Aleatory and Epistemic Uncertainties

Many engineering systems can perform their intended tasks with various levels of performance, which are modeled as multi-state systems (MSS) for system availability and reliability assessment problems. Uncertainty is an unavoidable factor in MSS modeling, and it must be effectively handled. In this work, we extend the traditional universal generating function (UGF) approach for multi-state system (MSS) availability and reliability assessment to account for both aleatory and epistemic uncertainties. First, a theoretical extension, named hybrid UGF (HUGF), is made to introduce the use of random fuzzy variables (RFVs) in the approach. Second, the composition operator of HUGF is defined by considering simultaneously the probabilistic convolution and the fuzzy extension principle. Finally, an efficient algorithm is designed to extract probability boxes ( p-boxes) from the system HUGF, which allow quantifying different levels of imprecision in system availability and reliability estimation. The HUGF approach is demonstrated with a numerical example, and applied to study a distributed generation system, with a comparison to the widely used Monte Carlo simulation method.

Reliability assessment for multi-state systems under uncertainties based on the Dempster–Shafer theory

This article presents an original method for evaluating reliability indices for Multi-State Systems (MSSs) in the presence of aleatory and epistemic uncertainties. In many real- world MSSs, an insufficiency of data makes it difficult to estimate precise values for component state probabilities. The proposed approach applies the transferable belief model interpretation of the Dempster–Shafer theory to represent component state beliefs and to evaluate the MSS reliability indices. The example of an oil transmission system is used to demonstrate the proposed approach and it is compared with the universal generating function method. The value of the Dempster–Shafer theory lies in its ability to use several combination rules in order to evaluate reliability indices for MSSs that depend on the reliability of the experts’ opinions as well as their independence.

Fully Bayesian reliability assessment of multi-state systems with overlapping data

The failure data at the system level are often limited,resulting in high uncertainty to system reliability assessment. Integrating data drawn from various structural levels of the target system (e.g. the system, subsystems, assemblies and components),i.e. the multi-level data, through Bayesian analysis can improve the precision of system reliability assessment. However, if the multi-level data are overlapping, it is challenging for Bayesian integration to develop the likelihood function. Especially for multistate systems (MSS), the Bayesian integration with overlapping data is even more difficult. The major disadvantage of previous approaches is the intensive computation for the development of the likelihood function caused by the workload to opt the appropriate combinations of the vectors of component states consistent with the overlapping data. An improved fully Bayesian integration approach from a geometric perspective is proposed for the reliability assessment of MSS with overlapping data. In this method, a specific combination of component states is regarded as a state vector, which leads to a specific system state of the MSS, and all state vectors generate a system state space. The overlapping data are regarded as the constraints which create hyperplanes in the system state space. And a point in a hyperplane corresponds to a particular combination of the state vectors. In the light of the features of the constraints, the proposed approach introduces space partition and hyperplane segmentation, which reduces the selection workload significantly and simplifies the likelihood function for overlapping data. Two examples demonstrate the feasibility and efficiency of the proposed approach.

The Markov Reward Model for a Multi-State System Reliability Assessment with Variable Demand

This paper considers reliability measures for a multi-state system where the system and its components can have different performance levels ranging from perfect functioning to complete failure. The suggested approach presents a generalized reliability measure as a functional of trajectories of two stochastic processes — output performance of the entire multi-state system and the corresponding demand. It shows how the commonly used reliability measures 120 can be derived from this functional and how they can be computed by using the developed Markov reward model. Corresponding procedures for rewards definition are suggested for different reliability measures. A numerical example is presented in order to illustrate the approach.