Reliability modeling of multi‐state degraded repairable systems and its applications to automotive systems

In this paper, we presented a continuous‐time Markov process‐based model for evaluating time‐dependent reliability indices of multi‐state degraded systems, particularly for some automotive subsystems and components subject to minimal repairs and negative repair effects. The minimal repair policy, which restores the system back to an “as bad as old” functioning state just before failure, is widely used for automotive systems repair because of its low cost of maintenance. The current study distinguishes with others that the negative repair effects, such as unpredictable human error during repair work and negative effects caused by propagated failures, are considered in the model. The negative repair effects may transfer the system to a degraded operational state that is worse than before due to an imperfect repair. Additionally, a special condition that a system under repair may be directly transferred to a complete failure state is also considered. Using the continuous‐time Markov process approach, we obtained the general solutions to the time‐dependent probabilities of each system state. Moreover, we also provided the expressions for several reliability measures include availability, unavailability, reliability, mean life time, and mean time to first failure. An illustrative numerical example of reliability assessment of an electric car battery system is provided. Finally, we use the proposed multi‐state system model to model a vehicle sub‐frame fatigue degradation process. The proposed model can be applied for many practical systems, especially for the systems that are designed with finite service life.     

A Risk‐based Approach to Managing Performance‐based Maintenance Contracts

The global trend towards performance‐based maintenance contracting has presented new challenges to maintenance service providers as they are compensated or penalized based on performance outcomes instead of time and materials consumed during maintenance service. The problem becomes more complex when uncertainties exist in reliability performance and maintenance activities of technical systems. In this paper, a general framework for managing performance‐based maintenance contract under risks is proposed. We illustrate our approach with an application in a multi‐echelon multi‐system spare parts control problem. Several different performance measures are considered and a probabilistic constrained optimization problem is formulated from the perspective of the service provider. Hybrid simulation/analytic heuristics are proposed to solve the problem based on the monotonic properties of performance measures. This approach is flexible and can be applied to a wide range of problems with similar properties. Numerical example shows that the probability of violating performance requirements is high if the risk is overlooked. We also provide guidelines on how to apply this approach in practice. Copyright © 2016 John Wiley & Sons, Ltd.     

Opportunistic maintenance of multi‐equipment system: a case study

A case study on preventive maintenance (PM) of a multi‐equipment system is presented in this paper. Each equipment of the system consists of many components/subsystems connected in series. Because of the series structure, opportunistic maintenance (OM) policies are more effective for the components of the equipment. A new OM policy based on the classification of opportunities has been proposed. Various OM policies have been evaluated using simulation modeling, and the new policy has been found to be more effective than the existing OM policies. The impact of this policy on the overall system has also been simulated. Copyright © 2000 John Wiley & Sons, Ltd.     

Reliability analysis of standby systems with multi‐state elements subject to constant transition rates

Standby redundancy has been extensively applied to critical engineering systems to enhance system reliability. Researches on reliability evaluation for standby systems focus more on systems with binary‐state elements. However, multi‐state elements with different performances have played a significant role in engineering systems. This paper presents an approach for reliability analysis of standby systems composed of multi‐state elements with constant state transition rates and absorbing failure states. The approach allows modelling different standby systems beyond cold, warm and hot ones by taking into account differences in possible maintenance of elements in standby and operation modes and dependence of elements' operational behavior on their initial state at the time of activation. An iterative algorithm for reliability evaluation based on element state probabilities is suggested. Illustrating examples of evaluating reliability of different types of homogeneous and heterogeneous standby systems are demonstrated.     

Condition based maintenance in the context of opportunistic maintenance

Condition based maintenance (CBM) uses the operating condition of a component to predict a failure event. Compared to age based replacement (ABR), CBM usually results in higher availability and lower maintenance costs, since it tries to prevent unplanned downtime and avoid unnecessary preventive maintenance activities for a component. However, the superiority of CBM remains unclear in multi‐component systems, in which opportunistic maintenance strategies can be applied. Opportunistic maintenance aims to group maintenance activities of two or more components in order to reduce maintenance costs. In a serial system, this may also result in less downtime of the production line. The aim of this paper is to examine the impact of opportunistic maintenance on the effectiveness of CBM. We simulate a small system consisting of three components in series and vary the number of components under a CBM policy, the length of the opportunistic maintenance zone, the cost benefits of grouping maintenance activities, and the chance of a failure occurrence within a preventive maintenance (PM) interval. The results show that within the current experimental settings, CBM remains cost effective in the multi‐component serial system, but is less effective than ABR in grouping maintenance activities. When the chance of failure is small and the length of the opportunistic maintenance zone is large, ABR may even be a better option if line productivity is important.     

A joint reliability-redundancy optimization approach for multi-state series-parallel systems

In this paper, we present a practical approach for the joint reliability-redundancy optimization of multi-state series-parallel systems. In addition to determining the optimal redundancy level for each parallel subsystem, this approach also aims at finding the optimal values for the variables that affect the component state distributions in each subsystem. The key point is that technical and organizational actions can affect the state transition rates of a multi-state component, and thus affect the state distribution of the component and the availability of the system. Taking this into consideration, we present an approach for determining the optimal versions and numbers of components and the optimal set of technical and organizational actions for each subsystem of a multi-state series-parallel system, so as to minimize the system cost while satisfying the system availability constraint. The approach might be considered to be the multi-state version of the joint system reliability-redundancy optimization methods.     

Transient behavior of time‐between‐failures of complex repairable systems

It is well known for complex repairable systems (with as few as four components), regardless of the time‐to‐failure (TTF) distribution of each component, that the time‐between‐failures (TBFs) tends toward the exponential. This is a long‐term or ‘steady‐state’ property. Aware of this property, many of those modeling such systems tend to base spares provisioning, maintenance personnel availability and other decisions on an exponential TBFs distribution. Such a policy may suffer serious drawbacks. A non‐homogeneous Poisson process (NHPP) accounts for these intervals for some time prior to ‘steady‐state’. Using computer simulation, the nature of transient TBF behavior is examined. The number of system failures until the exponential TBF assumption is valid is of particular interest. We show, using a number of system configurations and failure and repair distributions, that the transient behavior quickly drives the TBF distribution to the exponential. We feel comfortable with achieving exponential results for the TBF with 30 system failures. This number may be smaller for configurations with more components. However, at this point, we recommend 30 as the systems failure threshold for using the exponential assumption. Copyright © 2002 John Wiley & Sons, Ltd.     

Epileptic seizure detection by combining robust‐principal component analysis and least square‐support vector machine

The feature extraction from electroencephalogram (EEG) signals is widely used for computer‐aided epileptic seizure detection. However, multiple channels of EEG signals and their correlations have not been completely harnessed. In this article, a novel automatic seizure detection approach is proposed by analyzing the spatiotemporal correlation of multi‐channel EEG signals. This approach combines the maximum cross‐correlation, robust‐principal component analysis, and least square‐support vector machine to detect the events. Our proposed method delivers higher detection sensitivity, specificity, and accuracy than the state‐of‐the‐art approaches based on the 19 channels’ EEG signals of 37 absence epilepsy patients experiencing 57 seizure events.     

On‐line reliability estimation for individual components using statistical degradation signal models

With very few exceptions, most contemporary reliability engineering methods are geared towards estimating a population characteristic(s) of a system, subsystem or component. The information so extracted is extremely valuable for manufacturers and others that deal with product in relatively large volumes. In contrast, end users are typically more interested in the behavior of a ‘particular’ component used in their system to arrive at optimal component replacement or maintenance strategies leading to improved system utilization, while reducing risk and maintenance costs. The traditional approach to addressing this need is to monitor the component through degradation signals and ‘classifying’ the state of a component into discrete classes, say ‘good’, ‘bad’ and ‘in‐between’ categories. In the event, one can develop effective degradation signal forecasting models and precisely define component failure in the degradation signal space, then, one can move beyond the classification approach to a more vigorous reliability estimation and forecasting scheme for the individual unit. This paper demonstrates the feasibility of such an approach using ‘general’ polynomial regression models for degradation signal modeling. The proposed methods allow first‐order autocorrelation in the residuals as well as weighted regression. Parametric bootstrap techniques are used for calculating confidence intervals for the estimated reliability. The proposed method is evaluated on a cutting tool monitoring problem. In particular, the method is used to monitor high‐speed steel drill‐bits used for drilling holes in stainless‐steel metal plates. A second study involves modeling and forecasting fatigue‐crack‐growth data from the literature. The task involved estimating and forecasting the reliability of plates expected to fail due to fatigue‐crack‐growth. Both studies reveal very promising results. Copyright © 2002 John Wiley & Sons, Ltd.     

A human‐like numerical technique for design of engineering systems

Because of the necessity for considering various creative and engineering design criteria, optimal design of an engineering system results in a highly‐constrained multi‐objective optimization problem. Major numerical approaches to such optimal design are to force the problem into a single objective function by introducing unjustifiable additional parameters and solve it using a single‐objective optimization method. Due to its difference from human design in process, the resulting design often becomes completely different from that by a human designer. This paper presents a novel numerical design approach, which resembles the human design process. Similar to the human design process, the approach consists of two steps: (1) search for the solution space of the highly‐constrained multi‐objective optimization problem and (2) derivation of a final design solution from the solution space. Multi‐objective gradient‐based method with Lagrangian multipliers (MOGM‐LM) and centre‐of‐gravity method (CoGM) are further proposed as numerical methods for each step. The proposed approach was first applied to problems with test functions where the exact solutions are known, and results demonstrate that the proposed approach can find robust solutions, which cannot be found by conventional numerical design approaches. The approach was then applied to two practical design problems. Successful design in both the examples concludes that the proposed approach can be used for various design problems that involve both the creative and engineering design criteria. Copyright © 2005 John Wiley & Sons, Ltd.     

Feature selection and fault‐severity classification–based machine health assessment methodology for point machine sliding‐chair degradation

In this paper, we propose an offline and online machine health assessment (MHA) methodology composed of feature extraction and selection, segmentation‐based fault severity evaluation, and classification steps. In the offline phase, the best representative feature of degradation is selected by a new filter‐based feature selection approach. The selected feature is further segmented by utilizing the bottom‐up time series segmentation to discriminate machine health states, ie, degradation levels. Then, the health state fault severity is extracted by a proposed segment evaluation approach based on within segment rate‐of‐change (RoC) and coefficient of variation (CV) statistics. To train supervised classifiers, a priori knowledge about the availability of the labeled data set is needed. To overcome this limitation, the health state fault‐severity information is used to label (eg, healthy, minor, medium, and severe) unlabeled raw condition monitoring (CM) data. In the online phase, the fault‐severity classification is carried out by kernel‐based support vector machine (SVM) classifier. Next to SVM, the k‐nearest neighbor (KNN) is also used in comparative analysis on the fault severity classification problem. Supervised classifiers are trained in the offline phase and tested in the online phase. Unlike to traditional supervised approaches, this proposed method does not require any a priori knowledge about the availability of the labeled data set. The proposed methodology is validated on infield point machine sliding‐chair degradation data to illustrate its effectiveness and applicability. The results show that the time series segmentation‐based failure severity detection and SVM‐based classification are promising.     

Preventive maintenance policy of single‐unit systems based on shot‐noise process

This paper develops reliability and maintenance models for a single‐unit system subject to hard failures under random environment of external shocks. Motivated by the observations of shot‐noise process in practice, the impact of shock damage on system failure behavior is characterized by random hazard rate increments. To remove such negative impact, imperfect preventive repair is performed periodically, and preventive replacement is performed after several repairs. Considering the joint effects of both random shocks and imperfect repair on the system hazard rate, we derive recursive equations for the system reliability function. Furthermore, we investigate the optimal maintenance policy that minimizes the expected cost per unit time of the system. The applicability of the reliability and maintenance model is validated by a case study on a wind turbine system.     

Service‐level assurance in high‐availability multi‐unit systems using the M‐for‐N backup scheme

In this paper, we investigate service‐level assurance in high‐availability multi‐unit systems using the M‐for‐N backup scheme. M‐for‐N shared protection (backup) systems with priority control (i.e. prioritized protection switching and prioritized re‐housing of repaired units) can be applied to actual telecommunication devices that are subject to service‐level agreement (SLA) involving reliability measures. A priority level is assigned to each end user in such a system and the switching and unit re‐housing process is subject to the priority. The main contribution of this paper is to give a practical computation method of the user‐perceived availability under the priority control. Our case studies for real telecommunication systems reveal the effect of priority control on the user‐perceived availability. Copyright © 2011 John Wiley & Sons, Ltd.     

Reliability‐based Optimal Maintenance Scheduling by Considering Maintenance Effect to Reduce Cost

A new reliability‐based optimal maintenance scheduling method is presented that considers the effect of maintenance in reducing costs. An ordering list of element maintenance effects with various maintenance‐interval types is constructed. By means of this ordering list, reliability‐based optimal maintenance scheduling for simple reliability structures and composite reliability systems is then carried out. The properties of the proposed method, such as the evaluation of maintenance cost reduction, the simplicity of the proposed method by sacrificing system availability within the allowance method, the operation decision based on the optimal maintenance schedule, etc., are discussed. With simulations, the effectiveness of the proposed method is verified. Copyright © 2005 John Wiley & Sons, Ltd.     

Short communication optimal replacement scheduling in multi‐state series–parallel systems

The paper generalizes a replacement schedule optimization problem to multi‐state systems, where the system and its components have a range of performance levels—from perfect functioning to complete failure. The multi‐state system reliability is defined as the ability to satisfy a demand which is represented as a required system performance level. The reliability of system elements is characterized by their lifetime distributions with hazard rates increasing in time and is specified as expected number of failures during different time intervals. The optimal number of element replacements during the study period is defined as that which provides the desired level of the system reliability by minimum sum of maintenance cost and cost of unsupplied demand caused by failures. To evaluate multi‐state system reliability, a universal generating function technique is applied. A genetic algorithm (GA) is used as an optimization technique. Examples of the optimal replacement schedule determination are demonstrated. Copyright © 2000 John Wiley & Sons, Ltd.     

Control Method for Multiple‐Input Multiple‐Output Non‐Gaussian Random Vibration Test

A control method for multi‐input multi‐output non‐Gaussian random vibration test based on an improved zero‐memory nonlinear transformation and an inverse system method is proposed. Compared with the classic zero‐memory nonlinear transformation method, the improved one can overcome the defect of the dynamic range loss. The inverse system method is put forward in order to control the kurtoses and the spectra for multi‐input multi‐output non‐Gaussian random vibration test simultaneously. The main idea of inverse system method is to generate the Gaussian reference response signals first from the reference spectra, and the improved zero‐memory nonlinear transformation method is utilized to obtain the non‐Gaussian reference response signals with the reference kurtoses, then the continuous and stationary coupled driving signals can be derived from the relationship between the inputs and outputs of the test system. Thus, the difficulty in generation of driving signals in multi‐input multi‐output non‐Gaussian random vibration test can be overcome. The matrix power control algorithm is introduced for the spectrum control, and a kurtosis control algorithm is set up similarly. A simulation example and an experimental test are provided in the paper, and the results illustrate the effectiveness and feasibility of the proposed control method. Copyright © 2017 John Wiley & Sons, Ltd.     

Availability optimisation for stochastic degrading systems under imperfect preventive maintenance

This paper deals with imperfect preventive maintenance (PM) optimisation problem. The system to be maintained is typically a production system assumed to be continuously monitored and subject to stochastic degradation. To assess such degradation, the proposed maintenance model takes into account both corrective maintenance (CM) and PM. The system undergoes PM whenever its reliability reaches an appropriate value, while CM is performed at system failure. After a given number of maintenance actions, the system is preventively replaced by a new one. Both CM as well as PM are considered imperfect, i.e. they bring the system to an operating state which lies between two extreme states, namely the as bad as old state and as good as new state. The imperfect effect of CM and PM is modelled on the basis of the hybrid hazard rate model. The objective of the proposed PM optimisation model consists on finding the optimal reliability threshold together with the optimal number of PM actions to maximise the average availability of the system. A mathematical model is then proposed. To solve this problem an algorithm is provided. A numerical example is presented to illustrate the proposed maintenance optimisation model.     

Optimum Maintenance and Availability of Series Systems Subject to Imperfect Repair

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Condition‐based Maintenance Optimization Using Neural Network‐based Health Condition Prediction

Artificial neural network (ANN)‐based methods have been extensively investigated for equipment health condition prediction. However, effective condition‐based maintenance (CBM) optimization methods utilizing ANN prediction information are currently not available due to two key challenges: (i) ANN prediction models typically only give a single remaining life prediction value, and it is hard to quantify the uncertainty associated with the predicted value; (ii) simulation methods are generally used for evaluating the cost of the CBM policies, while more accurate and efficient numerical methods are not available, which is critical for performing CBM optimization. In this paper, we propose a CBM optimization approach based on ANN remaining life prediction information, in which the above‐mentioned key challenges are addressed. The CBM policy is defined by a failure probability threshold value. The remaining life prediction uncertainty is estimated based on ANN lifetime prediction errors on the test set during the ANN training and testing processes. A numerical method is developed to evaluate the cost of the proposed CBM policy more accurately and efficiently. Optimization can be performed to find the optimal failure probability threshold value corresponding to the lowest maintenance cost. The effectiveness of the proposed CBM approach is demonstrated using two simulated degradation data sets and a real‐world condition monitoring data set collected from pump bearings. The proposed approach is also compared with benchmark maintenance policies and is found to outperform the benchmark policies. The proposed CBM approach can also be adapted to utilize information obtained using other prognostics methods. Copyright © 2012 John Wiley & Sons, Ltd.     

Interface Jacobian‐based Co‐Simulation

Co‐simulation is a prominent method to solve multi‐physics problems. Multi‐physics simulations using a co‐simulation approach have an intrinsic advantage. They allow well‐established and specialized simulation tools for different fields and signals to be combined and reused with minor adaptations in contrast to the monolithic approach. However, the partitioned treatment of the coupled system poses the drawback of stability and accuracy challenges. If several different subsystems are used to form the co‐simulation scenario, these issues are especially important. In this work, we propose a new co‐simulation algorithm based on interface Jacobians. It allows for the stable and accurate solution of complex co‐simulation scenarios involving several different subsystems. Furthermore, the Interface Jacobian‐based Co‐Simulation Algorithm is formulated such that it enables parallel execution of the participating subsystems. This results in a high‐efficient procedure. Furthermore, the Interface Jacobian‐based Co‐Simulation Algorithm handles algebraic loops as the co‐simulation scenario is defined in residual form. Copyright © 2014 John Wiley & Sons, Ltd.