Residual-life distributions from component degradation signals: A Bayesian approach

Real-time condition monitoring is becoming an important tool in maintenance decision-making. Condition monitoring is the process of collecting real-time sensor information from a functioning device in order to reason about the health of the device. To make effective use of condition information, it is useful to characterize a device degradation signal, a quantity computed from condition information that captures the current state of the device and provides information on how that condition is likely to evolve in the future. If properly modeled, the degradation signal can be used to compute a residual-life distribution for the device being monitored, which can then be used in decision models. In this work, we develop Bayesian updating methods that use real-time condition monitoring information to update the stochastic parameters of exponential degradation models. We use these degradation models to develop a closed-form residual-life distribution for the monitored device. Finally, we apply these degradation and residual-life models to degradation signals obtained through the accelerated testing of bearings.     

A condition monitoring approach for real-time monitoring of degrading systems using Kalman filter and logistic regression

We present a new model for reliability analysis that is able to employ condition monitoring data in order to simultaneously monitor the latent degradation level and track failure progress over time. The method presented in this paper is a bridge between Bayesian filtering and classical binary classification, both of which have been employed successfully in various application domains. The Kalman filter is used to model a discrete-time continuous-state degradation process that is hidden and for which only indirect information is available through a multi-dimensional observation process. Logistic regression is then used to connect the latent degradation state with the failure process that is itself a discrete-space stochastic process. We present a closed-form solution for the marginal log-likelihood function and provide formulas for few important reliability measures. A dynamic cost-effective maintenance policy is finally introduced that can employ sensor signals for real-time decision-making. We finally demonstrate the accuracy and usefulness of our framework via numerical experiments.     

Optimal maintenance decisions under imperfect inspection

The process industry is increasingly making use of Risk Based Inspection (RBI) techniques to develop cost and/or safety optimal inspection plans. This paper proposes an adaptive Bayesian decision model to determine these optimal inspection plans under uncertain deterioration. It uses the gamma stochastic process to model the corrosion damage mechanism and Bayes’ theorem to update prior knowledge over the corrosion rate with imperfect wall thickness measurements. This is very important in the process industry as current non-destructive inspection techniques are not capable of measuring the exact material thickness, nor can these inspections cover the total surface area of the component. The decision model finds a periodic inspection and replacement policy, which minimizes the expected average costs per year. The failure condition is assumed to be random and depends on uncertain operation conditions and material properties. The combined deterioration and decision model is illustrated by an example using actual plant data of a pressurized steel vessel.     

Long-term predictive opportunistic replacement optimisation for a small multi-component system using partial condition monitoring data to date

The advanced condition monitoring tools and sensors have changed the decision making on maintenance in modern manufacturing. To face the change, an integrated ‘prognostics-replacement’ framework is proposed to optimise the replacement decision from component-level layer into production system-level layer by using condition monitoring data in this paper. Some special situations such as no failure or suspension histories of many of same or similar components for prognosis, etc., are considered. A novel degradation prediction model is introduced and the failure risk of a component is estimated based on its degradation level and service time. A total current-term cost rate function is defined to determine the replacement clusters and time for performing replacement from an integrated and economic view. A conservative window is used to adjust the replacement time and overcome the prognostic results varying at different inspection time in a long task. To optimise the replacement clusters effectively, a random-keys genetic algorithm (GA) based on convex set theory is developed. The proposed framework is validated by different small systems. Two commonly adopted replacement policies are compared. Sensitive analysis is conducted and the results show the outperformance of our proposed framework.     

Time-based replacement policies for a fault tolerant system subject to degradation and two types of shocks

A single component nonrepairable system suffering from both an internal stochastic degradation process and external random shocks is investigated in this paper. More specifically, the Wiener process with a positive drift coefficient is introduced to describe the gradual deterioration and the arrival number of external shocks is counted with a nonhomogeneous Poisson process (NHPP). Meanwhile, fault tolerant design is incorporated into the stochastically deterioration system so as to protect it from shock failures to some extent and is consummately addressed via a generalized m − δ shock model. From the actual engineering point of view, external shocks are typically classified into two distinct categories in this current research, that is, a minor shock (Type I shock) increasing the damage load on current degradation level and a traumatic shock (Type II shock) resulting in system catastrophic failure immediately. The closed-form expression of system survival function is derived analytically and is viewed as the generalization of existing reliability function for systems subject to dependent and competing failure processes. Based on which, two time-based maintenance (TBM) policies including an age replacement model and a block replacement model are scheduled, where the expected long-run cost rate (ELRCR) in each model is, respectively, optimized to seek the optimal replacement interval. In the illustrative example part, a subsea blowout preventer (BOP) control system is arranged to validate the theoretical results numerically. To compare which policy is more profitable under different conditions, the relative gain on optimal maintenance cost rate of the two TBM policies is presented.     

Condition based maintenance optimization for multi-component systems using proportional hazards model

The objective of condition based maintenance (CBM) is typically to determine an optimal maintenance policy to minimize the overall maintenance cost based on condition monitoring information. The existing work reported in the literature only focuses on determining the optimal CBM policy for a single unit. In this paper, we investigate CBM of multi-component systems, where economic dependency exists among different components subject to condition monitoring. The fixed preventive replacement cost, such as sending a maintenance team to the site, is incurred once a preventive replacement is performed on one component. As a result, it would be more economical to preventively replace multiple components at the same time. In this work, we propose a multi-component system CBM policy based on proportional hazards model (PHM). The cost evaluation of such a CBM policy becomes much more complex when we extend the PHM based CBM policy from a single unit to a multi-component system. A numerical algorithm is developed in this paper for the exact cost evaluation of the PHM based multi-component CBM policy. Examples using real-world condition monitoring data are provided to demonstrate the proposed methods.     

Model-based Monte Carlo state estimation for condition-based component replacement

This paper presents a model-based Monte Carlo method, also called particle filtering, for estimating the failure probability of a component subject to degradation. The estimations are embedded within an optimal policy of condition-based component replacement, in which both replacement upon failure and preventive replacement are considered, and the decision variable is the expected cost per unit time. An application is reported with regards to a component subject to fatigue degradation, modeled by the well-known Paris-Erdogan law. The possibility of predicting accurately the component remaining life with the associated uncertainty and of updating the prediction on the basis of observations of the degradation process, opens the door for effective condition-based replacement planning and risk-informed life-extension for hazardous technologies, such as the nuclear, aerospace and chemical ones.     

A periodic inspection and replacement policy for systems subject to competing failure modes due to degradation and traumatic events

This paper deals with the condition-based maintenance of single-unit systems which are subject to the competing and dependent failures due deterioration and traumatic shock events. The main aim is to provide a model to assess the value of condition monitoring information for the maintenance decision-making. A condition-based periodic inspection/replacement policy is developed and compared with a benchmark time-based block replacement policy.Numerical results show that it is indeed useful to follow closely the actual evolution of the system to adapt the maintenance decisions to the true system state to improve the performance of maintenance policies. The analysis of the maintenance costs savings can be used to justify or not the choice to implement a policy based on condition monitoring information and to invest in condition monitoring devices.     

Measurement of the resistive leakage current in surge arresters under artificial rain test and impulse voltage subjection

Surge arresters are installed on transmission and distribution lines and in substations between phase and earth in order to improve the lightning performance and reduce the failure rates. High-energy stresses and housing deterioration are the main factors of degradation and damage of surge arresters. Thus, there is need for testing and monitoring the electrical network?s arresters, in order to verify their good condition and their ability to effectively protect the lines. The most common method used, is the measurement of the arresters? total leakage current (with the isolation of the resistive part), which is an indicator of the arrester?s condition, since every change, deterioration or damage leads to an increase of the resistive leakage current. In the current work, the total leakage current of two 20 kV ZnO surge arresters without gaps is measured and the resistive component for three different cases (brand new arresters, measurements under artificial rain and measurements after impulse voltage subjection) is computed. The analysis of the produced results can be useful in correct diagnosis of arresters? condition and in more effective schedule maintenance, since any recorded high-resistive currents do not necessarily result arrester?s repair or replacement.     

On-line tool adjustment with adaptive tool wear function identification

This paper proposes a systematic approach for on-line tool management, including tool wear process monitoring, average tool wear function identification, and optimal tool adjustment/replacement decision making. The proposed method is ideal when some prior information is available regarding the upcoming tool wear process, although the prior information may be inaccurate or the working condition of the upcoming process may change.     

基于Gamma退化过程的直升机主减速器行星架剩余寿命预测模型

鉴于Gamma过程具有平稳、独立增量等退化建模所需的属性,将其用于描述设备退化过程,并针对缺乏故障数据时难以进行剩余寿命预测的问题,利用设备运行中采集的表征其退化状态的大量间接状态参数和少量直接状态参数,建立了基于Gamma退化过程的剩余寿命预测模型;针对经验最大化算法中似然函数难以解析求解的问题,引入粒子滤波算法实现了模型参数估计;最后将模型应用于直升机主减速器行星架的剩余寿命预测,得到了不同时刻的预测结果及95%置信区间,验证了预测模型的有效性和准确性。     

基于剩余寿命预测的维修与备件订购联合策略优化

利用设备健康状态信息预测剩余使用寿命,并进行维修和备件订购决策以达到降低设备检修成本和备件成本的目的。针对单部件系统提出基于剩余寿命预测的维修与备件订购联合策略,其中维修决策遵循控制限原则,即根据系统退化量判断是预防性更换还是故障更换,同时基于历史退化信息预测系统剩余寿命,引入订货阈值判断是否订货。通过分析更换时刻备件状态确定所有可能更新事件,推导各事件发生概率进而计算各事件更新成本和更新长度,采用更新报酬理论构建最小化单位时间内期望费用的联合策略模型,设计离散事件仿真算法求解模型。最后,通过实例验证模型和算法,得到最小的单位时间内期望费用14.656 3,最优预防性更换阈值8,最优订货阈值1 000。     

Missing data methods in PCA and PLS: Score calculations with incomplete observations

A very important problem in industrial applications of PCA and PLS models, such as process modelling or monitoring, is the estimation of scores when the observation vector has missing measurements. The alternative of suspending the application until all measurements are available is usually unacceptable. The problem treated in this work is that of estimating scores from an existing PCA or PLS model when new observation vectors are incomplete. Building the model with incomplete observations is not treated here, although the analysis given in this paper provides considerable insight into this problem. Several methods for estimating scores from data with missing measurements are presented, and analysed: a method, termed single component projection, derived from the NIPALS algorithm for model building with missing data; a method of projection to the model plane; and data replacement by the conditional mean. Expressions are developed for the error in the scores calculated by each method. The error analysis is illustrated using simulated data sets designed to highlight problem situations. A larger industrial data set is also used to compare the approaches. In general, all the methods perform reasonable well with moderate amounts of missing data (up to 20% of the measurements). However, in extreme cases where critical combinations of measurements are missing, the conditional mean replacement method is generally superior to the other approaches.     

Component replacement policies for re workable assemblies

In an assembly process, test operations are often introduced to ensure product quality. After having been rejected by a test operation due to a bad component, a product may be sent to a rework station for component replacement. Some products, however, may have two or more identical components for better reliability or higher capacity. For example, a rack holds a number of identical magnetic storage devices or a computer has multiple processors. Under this situation, different replacement policies may be considered. Bad components can be replaced by either untested ones or known good ones. In the latter case, the assembly line must keep an inventory of good components. Contingent on the condition of replacement components and the method of inventory replenishment, three different policies are identified. Under the first policy, all bad components will be replaced by untested ones, and therefore, the product must be retested. The second policy will replace all bad components with good ones if available. In this case, no additional test is required. However, if the number of bad components is greater than the inventory level, all components ( both good and bad) will be replaced by untested ones. Then the product is sent for retest and good components are placed in inventory. Policy III always replaces the bad ones with good ones. It is assumed that all (good) replacement components come from an independent source. If there are not enough good components for replacement, the product must wait. This paper investigates all three policies, using stochastic models. The performance of a policy is dependent on yield, test time, product configuration, and production demand. A good choice should consider the tradeoff between production lead time and inventory cycle. Numerical results, derived from a real-life case, are presented.     

A study of availability-centered preventive maintenance for multi-component systems

This paper studies preventive maintenance (PM) in simultaneously considering three actions, mechanical service, repair and replacement for a multi-components system based on availability. Mechanical service denotes the activities including lubricating, cleaning, checking and adjusting, etc. which is set to alleviate strength degradation. Repair is defined on that not only slow down the degraded velocity but also restore the degraded strength partly. Replacement is settled to recover a component to its original condition. According to the definitions, the degradation of components is analyzed from its failure mechanisms and the improvements of various actions to it in reliability were measured by using two improved factors. Following the proposed model of reliability, the mean-up and mean-down times of each component are also investigated and the replacement intervals of components are determined based on availability maximization. Here, the minimum one among the intervals is chosen as the PM interval of system for programming the periodical PM policy. The selection of action for the components on every PM stage is decided by maximizing system benefit in maintenance. Repeatedly, the scheduling is progressed step by step and is terminated until the system extended life reaching to its expected life. The complete schedule provides the information, the actions adopted for the components, the availability and the total cost of system on each stage. Validly, a multi-components system is used as an example to describe the proposed algorithm.     

Condition monitoring strategy—a risk based interval selection

Condition monitoring (CM) has been widely applied in most of the modern process as well as manufacturing industries as a predictive maintenance tool for incipient fault detection and trouble shooting but the interval at which the measurements are to be taken to achieve the best results has not yet been rationally discussed. This paper suggests a method for designing condition monitoring measurement intervals for all types of machines, from commissioning to replacement, by considering various factors such as risk, interval availability, debugging, useful life and wear-out regions of the failure rate curve, as well as economic factors governing the replacement prospects of the machine     

Uncertain process–based reliability and maintenance modeling for systems under mutually dependent degradation and shock processes

For the systems that experience competing failure processes, an uncertain process–based degradation model is developed to describe the systems. The competing degradation process is composed of internal continuous degradation and external shocks, and the mutual dependence between them is considered. When the magnitude of the internal degradation exceeds the threshold, the soft failure occurs. While for the shock processes involving the randomness and the subjective information, we adopt the uncertain random renewal reward process to characterize it. Hard failure occurs when the damage of the shock process exceeds the strength threshold of the system. By using the belief reliability metric, the reliability of the degraded system is defined as the chance measure that neither soft failure nor hard failure occurs. And the effect of the degradation-shock dependence on the system reliability is performed by the parametric studies. Then the proposed degradation model is introduced into the preventive maintenance strategy to minimize the average maintenance cost. Using the microelectromechanical systems as an example, the effectiveness of the constructed degradation model and maintenance strategy is illustrated, and the proposed model can characterize the system degradation process in a superior way to the stochastic process model. These methods can be applied to other similar degraded systems and provide support for maintenance decisions.     

Optimal control limit for degradation process of a unit modelled as a Markov chain

An optimal maintenance problem of a plain bearing is discussed where the bearing is a critical unit of a piece of metallurgical equipment. The bearing shell wear process is investigated as a degradation one; maximum bearing degradation results in the whole unit and system in general break-down. The restoration cost of the failed system is definitely higher than the inspection and preventive replacement cost. To describe the degradation process a Markov chain model is used on the basis of statistical inference methods. To estimate the system operation cost a mathematical expectation of losses per unit time in a steady-state regime is evaluated. Linear algebraic equations are developed to assess the losses depending on a control limit value for the degradation process; for the given operation condition the optimal limit of degradation has been found.     

Real‐time Reliability Evaluation for an Individual Product Based on Change‐point Gamma and Wiener Process

Reliability evaluation based on degradation data has received significant attentions in recent years. However, existing works often assume that the degradation evolution over time is governed by a single stochastic process, which may not be realistic if change points exist. Here, for cases of degradation with change points, this paper attempts to capture the degradation process with a multi‐phase degradation model and find the method to evaluate the real‐time reliability of the product being monitored. Once new degradation information becomes available, the evaluation results are adaptively updated through the Bayesian method. In particular, for a two‐stage degradation process of liquid coupling devices (LCDs), a model named as change‐point gamma and Wiener process is developed, after which issues of real‐time reliability evaluation and parameters’ estimation are addressed in detail. Finally, the proposed method is illustrated by a case study of LCDs, and the corresponding results indicate that trustful evaluation results depend on the fitting accuracy in cases of multi‐phase degradation process. Copyright © 2013 John Wiley & Sons, Ltd.     

Ableitung von Festigkeitsforderungen für PKW unter Berücksichtigung statistischer Kriterien

Establishment of strength design requirements for passenger cars based on stochastic criteria For an establishment of strength design requirements of passenger cars the definition of characteristic levels of both the loading environment and the (fatigue) strength is needed. Both quantities exhibit partly considerable scatter and have to be treated as stochastic variables. In this paper, related quantities, methods and procedures are discussed. With regard to loading, “severe” profiles are aimed for based on measurements on test tracks and actual customer usage. Typical scatter values of component fatigue strength are derived on the basis of data collections backed up by specific in‐house experience. This is accomplished using recent literature information.design requirements, strength, load assumptions, component fatigue strength, statistics