Reliability modeling in a predictive maintenance context: A margin-based approach

Current reliability approaches were designed to assess and quantify the reliability associated with complex systems such as nuclear power plants (NPPs). These approaches are generally based on classical Boolean logic structures such as event trees (ETs) and fault trees (FTs) [Rausand, 2020]. The outcome obtained by combining FTs and ETs is the set of minimal cuts sets (MCSs), with each MCS representing a unique combination of BEs that leads to an undesired outcome (e.g., core damage). Probabilistic evaluation of a MCS is performed by evaluating the product of the probability values associated with each BE. A relevant factor here is that the probability values associated with BEs used in the plant models are updated at least every 4 years based on past operational experience and through the use of a Bayesian statistical process [Siu, 1998]. Hence, the probability value of a BE associated with a physical asset (e.g., a centrifugal pump or motor-operated valve) in no way reflects that asset’s actual condition and performance.
 This fact plays a major role in the application of plant reliability models to support risk-informed decisions. With the particular goal of reducing operation and maintenance costs, existing NPPs are moving from corrective and periodic maintenance toward new types of predictive maintenance strategies [Agarwal, 2021]. This transition is designed such that maintenance is conducted only when the asset requires it (i.e., prior to undergoing imminent failure). And though these benefits cannot be achieved through actual reliability modelling methods and currently employed reliability data, they can be achieved by employing asset-monitoring sensors, automated data acquisition systems, data analysis methods, and improved decision-making processes. Combined, these resources can provide precise information on the health of an asset, track its degradation trends, and estimate its expected failure time. Based on such information, maintenance operations can be scheduled and performed for each asset on an as-needed basis. This dynamic context of predictive maintenance operations requires new methods of data analysis, the propagation of asset health information from the asset level to the system level, and the optimization of plant resources.
 This paper provides an alternative reliability approach designed for a predictive maintenance context in which a direct link is created between monitoring data and decision-making. Rather than thinking of reliability in terms of system/asset probability of failure, we propose a reliability mindset based on the concept of margin [Mandelli, 2023]. An asset’s health is quantified by determining its margin, based on the asset’s current and historical monitoring data. The margin values of the monitored asset are then propagated through system reliability models (e.g., FTs or reliability block diagrams) to identify the assets that are more critical to guarantee system operation. We show how a margin-based approach can be used assess asset health, based solely on current and historic monitoring data (e.g., condition-based, anomaly detection, diagnostic, and prognostic data) [Xingang, 2021]. A margin-based approach directly addresses the limitations of classical reliability modelling approaches and provides a snapshot of system health—given the availability of monitoring data. These two different approaches are designed to address different types of decisions: classical reliability models support static decisions (e.g., a set frequency of periodic maintenance or surveillance operations) based on past operational experience, whereas a margin-based approach directly supports dynamic decisions involving maintenance operations that should only be performed when necessary, based on monitoring data (i.e., a predictive maintenance context).

Established reliability modelling and analysis techniques are not readily extended to address whole systems which include software — it is difficult to incorporate software elements of a system within reliability block diagrams and no means of predicting the reliability of software elements has become established. An approach has been developed based on the technique of functional thread analysis — borrowed from software structured analysis and design methods — which allows reliability modelling and analyses of entire software intensive systems to be initiated from early in the system development.

Degradation of multi-component system exists widely in the field of engineering. And the degradation failure of multi-component system is due to the overall degradation of the system to a certain extent, or the degradation of component. In this paper, we focus on the reliability model of multi-component degradation system, which failure caused by degradation of component failure, was simplified and applied to the optimization model of maintenance policy. For each component of the degraded system, pure degradation and degradation increment can cause irreversible damage to it. The continuous degradation process was considered to be linear. And the degradation increment caused by the shock was considered to be cumulative. The shock was random, so that subject to Poisson distribution. The reliability model of the multi-component degradation system under the cumulative Poisson shock is complex and not easy to be applied to the maintenance model optimization model of the multi-component system. From that, this paper simplified the reliability model of multi-component degradation system under the cumulative Poisson shock. And the simplified reliability function was used as the constraint to improve the optimization model of multi-objective maintenance policy based on the reliability theory so as to facilitate its application in engineering. The feasibility of the simplified reliability model and the correctness of the improved multi-objective maintenance policy was verified by case. The influence of the change of the reliability constraint value on the whole maintenance policy was analyzed.

Performance and Reliability Analysis of Computer Systems: An Example-Based Approach Using the SHARPE Software Package provides a variety of probabilistic, discrete-state models used to assess the reliability and performance of computer and communication systems. The models included are combinatorial reliability models (reliability block diagrams, fault trees and reliability graphs), directed, acyclic task precedence graphs, Markov and semi-Markov models (including Markov reward models), product-form queueing networks and generalized stochastic Petri nets. A practical approach to system modeling is followed; all of the examples described are solved and analyzed using the SHARPE tool. In structuring the book, the authors have been careful to provide the reader with a methodological approach to analytical modeling techniques. These techniques are not seen as alternatives but rather as an integral part of a single process of assessment which, by hierarchically combining results from different kinds of models, makes it possible to use state-space methods for those parts of a system that require them and non-state-space methods for the more well-behaved parts of the system. The SHARPE (Symbolic Hierarchical Automated Reliability and Performance Evaluator) package is the `toolchest' that allows the authors to specify stochastic models easily and solve them quickly, adopting model hierarchies and very efficient solution techniques. All the models described in the book are specified and solved using the SHARPE language; its syntax is described and the source code of almost all the examples discussed is provided. Audience: Suitable for use in advanced level courses covering reliability and performance of computer and communications systems and by researchers and practicing engineers whose work involves modeling of system performance and reliability.

In consideration of some drawbacks of stochastic reliability method in theoretical and practical aspects, as well as the existence of insufficient and vague data in actual equipments design, the possbilistic reliability models of typically general systems are constructed in this paper. Characterizing the systems(components) failure behavior by possibility measures in place of probability measures, treating the systems (components) lifetime as fuzzy variables in the possibility space, and introducing possibilistic approaches into system reliability modeling and analysis, the possibilistic reliability theories are advanced based on possibilistic measurements. By expanding the universe of discourse, the derivation of system reliability models is simplified without loss of the nature of the problems to be solved, and proofs and calculations of possibilistic reliability of typical systems including series, parallel, series-parallel, parallel-series, and cold standby systems are much more straightforward than the traditional ones. The detailed application examples in system reliability analysis verify a possibilistic design framework on the general reliability models background, which provide some technical supports and guarantees for possibilistic reliability design and possibilistic reliability management in the case of limited statistical data.

Asset health monitoring has traditionally relied on data from inspections, tests, sensors and monitoring systems. However, the use of digital models has increased. Within a digital twin (DT) framework, digital models of the most relevant degradation mechanisms can be used to estimate an asset's current health and to predict its future status. A DT can provide support for decision-making aiming at optimizing inspection planning, prioritizing the most critical assets and evaluating relevant parameters to health management, such as assets remaining useful lives (RUL) and inspection timing and spots [1]. From a DT perspective, all information is underpinned by data and digital models [2]. Therefore, data and model uncertainties play a very important role in model estimates and predictions. These uncertainties are related to several issues, such as data quality, process variations, asset design specifications, fabrication tolerances, measurement uncertainties and the representativeness of the degradation model [1,3]. This paper addresses how these uncertainties influence the RUL assessment and impact the reliability of inspection planning for model-based health monitoring. Focusing on O&G subsea assets, the influence of uncertainties on models’ estimates is addressed, as well as its impact on the evaluation of assets RUL, which supports maintenance and inspection planning. This paper emphasizes the importance of considering uncertainties when using DTs for decision-making on asset health monitoring.

The seven papers included in this special section focus on reliability, resilience, and prognostics modeling of complex engineering systems. This topic has become very challenging due to factors such as complex physical interdependence and functional interactions among mechanical, electrical, software, and control subsystems, as well as the interactions with external environments. The difficulties of modeling the reliability and resilience as well as system performance prognostics of complex engineering system have been observed from many perspectives, e.g., 1) the schedule delays and cost overruns of major government and industry commercial programs, and 2) the challenges when planning and managing recovery activities of critical infrastructure damaged due to extreme events. When multiple sources of information and disparate data are available, how to monitor, model, and predict the system resilience and reliability over time of complex engineering systems becomes essential and critical for safe, reliable, resilient, and economic operations of most cyber-physical systems.

The traditional system reliability model for complex system exhibits deviation due to the overlook of failure correlation directionality among components. In order to rectify this problem, a new reliability modeling method for complex system is proposed based on failure network digraph technique. First, the failure network digraph is built with related failure mechanism analysis, and the component reliability models are built based on mean rank order. Then, taking the component reliability models as the marginal distribution, the system joint reliability function is developed with the introduction of the Copula function. Third, the parameter of Copula function is estimated with the aid of Kendall rank correlation coefficient obtained by samples. Finally, the method is applied to a machining center, the result shows that the new Copula function model considering failure correlation directionality is more rational and effective compared with the traditional Copula function model, which provides a theoretical basis for reliability evaluation and allocation of complex system.

Using Reliability Modeling and Accelerated Life Testing to Formulate a Cost Model of Photovoltaic Systems with Different Architectures

Systems with protective auxiliary component are common in engineering industry. The auxiliary components in these systems play an essential role to protect the main components from severe environment impact, however, dependence between the main and auxiliary components are usually ignored in most existing literatures. Besides, failures of auxiliary components are hidden in most systems since they do not halt the system. Therefore, inspections are necessary. In most existing studies, inspections are assumed to be perfect, which is not consistent with the reality. In this paper, a new reliability model is developed for systems with dependent main and auxiliary components under imperfect inspections. Some important indexes, such as system reliability and availability, are derived by the recursive and matrix methods, respectively. Thereafter, a numerical example is presented to illustrate the results and verify the correctness of the proposed method, in which influences of imperfect inspections are also studied by conducting sensitivity analysis on the inspection accuracy parameter.

The current research of reliability allocation of CNC lathes always treat CNC lathes as independent series systems. However, CNC lathes are complex systems in the actual situation. Failure correlation is rarely considered when reliability allocation is conducted. In this paper, drawbacks of reliability model based on failure independence assumption are illustrated, after which, reliability model of CNC lathes considering failure correlation of subsystems is established based on Copula theory, which is an improvement of traditional reliability model of series systems. As the failure time of CNC lathes often obeys Weibull or exponential distribution, Gumbel Copula is selected to build correlation model. After that, a reliability allocation method considering failure correlation is analyzed based on the model established before. Reliability goal is set first and then failure rates are allocated to subsystems according to the allocation vector through solving the correlation model. Reliability allocation is conducted for t = 1. A real case of a CNC lathe and a numerical case are presented together to illustrate the advantages of the reliability model established considering failure correlation and the corresponding allocation method. It shows that the model accords to facts and real working condition more, and failure rates allocated to all the subsystems are increased to some extent. This research proposes a reliability allocation method which takes failure correlation among subsystems of CNC lathes into consideration, and costs for design and manufacture could be decreased.

Reliability modeling and optimal random preventive maintenance policy for parallel systems with damage self-healing

This paper uses two modeling tools to analyze the reliability of real-time expert systems: (1) a stochastic Petri net (SPN) for computing the conditional response time distribution given that a fixed number of expert system match-select-act cycles are executed, and (2) a simulation search tree for computing the distribution of expert system match-select-act cycles for formulating a control strategy in response to external events. By modeling the intrinsic match-select-act cycle of expert systems and associating rewards rates with markings of the SPN, the response time distribution for the expert system to reach a decision can be computed as a function of design parameters, thereby facilitating the assessment of reliability of expert systems in the presence of real-time constraints. The utility of the reliability model is illustrated with an expert system characterized by a set of design conditions under a real-time constraint. This reliability model allows the system designers to: (1) experiment with a range of selected parameter values; and (2) observe their effects on system reliability.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Reliability and hybrid maintenance modeling for competing failure systems with multistage periods

Modern complex systems of responsible purposes are built as fault-tolerant systems, i.e. such systems have the ability to function while some of their separate elements have a fault. This feature is achieved by introduction of different kinds of redundancy (structural, algorithmic, time, etc.), which leads to complications of the algorithm of system internal behavior due to the introduction of the functions of monitoring, fault localization, switching and performance recovery system, resulting in the significant complication of the model of system reliability. The complexity of such fault-tolerant systems makes their reliability of greater dimension (of the order of tens till hundreds of thousand equations), which is almost impossible for their formation and analysis by hand. Therefore, the requires a high level of credibility and an appropriate level of formalization to built models are imposed on these models, which allows to implement the automation of their building and analysis of reliability using modern computer tools. The combination of analytical methods for the research of reliability and computing capability of modern computers is a promising direction for further development of methods of reliability theory. Experience shows that the manual building the state space of fault-tolerant systems even with a small number of elements (up to 10) without the use of software is a time-consuming process. This article describes the procedure of automated development of the reliability models of complex technical systems, implemented in software module ASNA, which developed at the chair Theoretical Radioengineering and Radiomeasurement of Lviv National Polytechnic University