A review on degradation models in reliability analysis

With increasingly complex engineering assets and tight economic requirements, asset reliability becomes more crucial in Engineering Asset Management (EAM). Improving the reliability of systems has always been a major aim of EAM. Reliability assessment using degradation data has become a significant approach to evaluate the reliability and safety of critical systems. Degradation data often provide more information than failure time data for assessing reliability and predicting the remnant life of systems. In general, degradation is the reduction in performance, reliability, and life span of assets. Many failure mechanisms can be traced to an underlying degradation process. Degradation phenomenon is a kind of stochastic process; therefore, it could be modelled in several approaches. Degradation modelling techniques have generated a great amount of research in reliability field. While degradation models play a significant role in reliability analysis, there are few review papers on that. This paper presents a review of the existing literature on commonly used degradation models in reliability analysis. The current research and developments in degradation models are reviewed and summarised in this paper. This study synthesises these models and classifies them in certain groups. Additionally, it attempts to identify the merits, limitations, and applications of each model. It provides potential applications of these degradation models in asset health and reliability prediction.

Reliability analysis with suspended items

Reliability analysis has several important engineering applications. Designers and operators of equipment are often interested in the probability of the equipment operating successfully to a given age - this probability is known as the equipment's reliability at that age. Reliability information is also important to those charged with maintaining an item of equipment, as it enables them to model and evaluate alternative maintenance policies for the equipment. In each case, information on failures and survivals of a typical sample of items is used to estimate the required probabilities as a function of the item's age, this process being one of many applications of the statistical techniques known as distribution fitting. In most engineering applications, the estimation procedure must deal with samples containing survivors (suspensions or censorings); this thesis focuses on several graphical estimation methods that are widely used for analysing such samples. Although these methods have been current for many years, they share a common shortcoming: none of them is continuously sensitive to changes in the ages of the suspensions, and we show that the resulting reliability estimates are therefore more pessimistic than necessary. We use a simple example to show that the existing graphical methods take no account of any service recorded by suspensions beyond their respective previous failures, and that this behaviour is inconsistent with one's intuitive expectations. In the course of this thesis, we demonstrate that the existing methods are only justified under restricted conditions. We present several improved methods and demonstrate that each of them overcomes the problem described above, while reducing to one of the existing methods where this is justified. Each of the improved methods thus provides a realistic set of reliability estimates for general (unrestricted) censored samples. Several related variations on these improved methods are also presented and justified. - i

Reliability analysis of transform-based stereo matching techniques, and a new matching constraint

Stereo vision is a method of depth perception, in which depth information is inferred from two (or more) images of a scene, taken from different perspectives. Practical applications for stereo vision include aerial photogrammetry, autonomous vehicle guidance, robotics and industrial automation. The initial motivation behind this work was to produce a stereo vision sensor for mining automation applications. For such applications, the input stereo images would consist of close range scenes of rocks. A fundamental problem faced by matching algorithms is the matching or correspondence problem. This problem involves locating corresponding points or features in two images. For this application, speed, reliability, and the ability to produce a dense depth map are of foremost importance. This work implemented a number of areabased matching algorithms to assess their suitability for this application. Area-based techniques were investigated because of their potential to yield dense depth maps, their amenability to fast hardware implementation, and their suitability to textured scenes such as rocks. In addition, two non-parametric transforms, the rank and census, were also compared. Both the rank and the census transforms were found to result in improved reliability of matching in the presence of radiometric distortion - significant since radiometric distortion is a problem which commonly arises in practice. In addition, they have low computational complexity, making them amenable to fast hardware implementation. Therefore, it was decided that matching algorithms using these transforms would be the subject of the remainder of the thesis. An analytic expression for the process of matching using the rank transform was derived from first principles. This work resulted in a number of important contributions. Firstly, the derivation process resulted in one constraint which must be satisfied for a correct match. This was termed the rank constraint. The theoretical derivation of this constraint is in contrast to the existing matching constraints which have little theoretical basis. Experimental work with actual and contrived stereo pairs has shown that the new constraint is capable of resolving ambiguous matches, thereby improving match reliability. Secondly, a novel matching algorithm incorporating the rank constraint has been proposed. This algorithm was tested using a number of stereo pairs. In all cases, the modified algorithm consistently resulted in an increased proportion of correct matches. Finally, the rank constraint was used to devise a new method for identifying regions of an image where the rank transform, and hence matching, are more susceptible to noise. The rank constraint was also incorporated into a new hybrid matching algorithm, where it was combined a number of other ideas. These included the use of an image pyramid for match prediction, and a method of edge localisation to improve match accuracy in the vicinity of edges. Experimental results obtained from the new algorithm showed that the algorithm is able to remove a large proportion of invalid matches, and improve match accuracy.

Reliability analysis and economic equipment replacement appraisal for substation and sub-transmission systems with explicit inclusion of non-repairable failures

The modern society has come to expect the electrical energy on demand, while many of the facilities in power systems are aging beyond repair and maintenance. The risk of failure is increasing with the aging equipments and can pose serious consequences for continuity of electricity supply. As the equipments used in high voltage power networks are very expensive, economically it may not be feasible to purchase and store spares in a warehouse for extended periods of time. On the other hand, there is normally a significant time before receiving equipment once it is ordered. This situation has created a considerable interest in the evaluation and application of probability methods for aging plant and provisions of spares in bulk supply networks, and can be of particular importance for substations. Quantitative adequacy assessment of substation and sub-transmission power systems is generally done using a contingency enumeration approach which includes the evaluation of contingencies, classification of the contingencies based on selected failure criteria. The problem is very complex because of the need to include detailed modelling and operation of substation and sub-transmission equipment using network flow evaluation and to consider multiple levels of component failures. In this thesis a new model associated with aging equipment is developed to combine the standard tools of random failures, as well as specific model for aging failures. This technique is applied in this thesis to include and examine the impact of aging equipments on system reliability of bulk supply loads and consumers in distribution network for defined range of planning years. The power system risk indices depend on many factors such as the actual physical network configuration and operation, aging conditions of the equipment, and the relevant constraints. The impact and importance of equipment reliability on power system risk indices in a network with aging facilities contains valuable information for utilities to better understand network performance and the weak links in the system. In this thesis, algorithms are developed to measure the contribution of individual equipment to the power system risk indices, as part of the novel risk analysis tool. A new cost worth approach was developed in this thesis that can make an early decision in planning for replacement activities concerning non-repairable aging components, in order to maintain a system reliability performance which economically is acceptable. The concepts, techniques and procedures developed in this thesis are illustrated numerically using published test systems. It is believed that the methods and approaches presented, substantially improve the accuracy of risk predictions by explicit consideration of the effect of equipment entering a period of increased risk of a non-repairable failure.

Intelligent reliability analysis with incomplete covariates

The reliability analysis is crucial to reducing unexpected down time, severe failures and ever tightened maintenance budget of engineering assets. Hazard based reliability methods are of particular interest as hazard reflects the current health status of engineering assets and their imminent failure risks. Most existing hazard models were constructed using the statistical methods. However, these methods were established largely based on two assumptions: one is the assumption of baseline failure distributions being accurate to the population concerned and the other is the assumption of effects of covariates on hazards. These two assumptions may be difficult to achieve and therefore compromise the effectiveness of hazard models in the application. To address this issue, a non-linear hazard modelling approach is developed in this research using neural networks (NNs), resulting in neural network hazard models (NNHMs), to deal with limitations due to the two assumptions for statistical models. With the success of failure prevention effort, less failure history becomes available for reliability analysis. Involving condition data or covariates is a natural solution to this challenge. A critical issue for involving covariates in reliability analysis is that complete and consistent covariate data are often unavailable in reality due to inconsistent measuring frequencies of multiple covariates, sensor failure, and sparse intrusive measurements. This problem has not been studied adequately in current reliability applications. This research thus investigates such incomplete covariates problem in reliability analysis. Typical approaches to handling incomplete covariates have been studied to investigate their performance and effects on the reliability analysis results. Since these existing approaches could underestimate the variance in regressions and introduce extra uncertainties to reliability analysis, the developed NNHMs are extended to include handling incomplete covariates as an integral part. The extended versions of NNHMs have been validated using simulated bearing data and real data from a liquefied natural gas pump. The results demonstrate the new approach outperforms the typical incomplete covariates handling approaches. Another problem in reliability analysis is that future covariates of engineering assets are generally unavailable. In existing practices for multi-step reliability analysis, historical covariates were used to estimate the future covariates. Covariates of engineering assets, however, are often subject to substantial fluctuation due to the influence of both engineering degradation and changes in environmental settings. The commonly used covariate extrapolation methods thus would not be suitable because of the error accumulation and uncertainty propagation. To overcome this difficulty, instead of directly extrapolating covariate values, projection of covariate states is conducted in this research. The estimated covariate states and unknown covariate values in future running steps of assets constitute an incomplete covariate set which is then analysed by the extended NNHMs. A new assessment function is also proposed to evaluate risks of underestimated and overestimated reliability analysis results. A case study using field data from a paper and pulp mill has been conducted and it demonstrates that this new multi-step reliability analysis procedure is able to generate more accurate analysis results.

A review on reliability models with covariates

Modern Engineering Asset Management (EAM) requires the accurate assessment of current and the prediction of future asset health condition. Suitable mathematical models that are capable of predicting Time-to-Failure (TTF) and the probability of failure in future time are essential. In traditional reliability models, the lifetime of assets is estimated using failure time data. However, in most real-life situations and industry applications, the lifetime of assets is influenced by different risk factors, which are called covariates. The fundamental notion in reliability theory is the failure time of a system and its covariates. These covariates change stochastically and may influence and/or indicate the failure time. Research shows that many statistical models have been developed to estimate the hazard of assets or individuals with covariates. An extensive amount of literature on hazard models with covariates (also termed covariate models), including theory and practical applications, has emerged. This paper is a state-of-the-art review of the existing literature on these covariate models in both the reliability and biomedical fields. One of the major purposes of this expository paper is to synthesise these models from both industrial reliability and biomedical fields and then contextually group them into non-parametric and semi-parametric models. Comments on their merits and limitations are also presented. Another main purpose of this paper is to comprehensively review and summarise the current research on the development of the covariate models so as to facilitate the application of more covariate modelling techniques into prognostics and asset health management.

Component reliability estimations without field data

Maintenance activities in a large-scale engineering system are usually scheduled according to the lifetimes of various components in order to ensure the overall reliability of the system. Lifetimes of components can be deduced by the corresponding probability distributions with parameters estimated from past failure data. While failure data of the components is not always readily available, the engineers have to be content with the primitive information from the manufacturers only, such as the mean and standard deviation of lifetime, to plan for the maintenance activities. In this paper, the moment-based piecewise polynomial model (MPPM) are proposed to estimate the parameters of the reliability probability distribution of the products when only the mean and standard deviation of the product lifetime are known. This method employs a group of polynomial functions to estimate the two parameters of the Weibull Distribution according to the mathematical relationship between the shape parameter of two-parameters Weibull Distribution and the ratio of mean and standard deviation. Tests are carried out to evaluate the validity and accuracy of the proposed methods with discussions on its suitability of applications. The proposed method is particularly useful for reliability-critical systems, such as railway and power systems, in which the maintenance activities are scheduled according to the expected lifetimes of the system components.

Applied sub-transmission & distribution reliability assessment of SEQEB network in Queensland

In this paper a combined subtransmission and distribution reliability analysis of SEQEB’s outer suburban network is presented. The reliability analysis was carried out with a commercial software package which evaluates both energy and customer indices. Various reinforcement options were investigated to ascertain the impact they have on the reliability of supply seen by the customers. The customer and energy indices produced by the combined subtransmission and distribution reliability studies contributed to optimise capital expenditure to the most effective areas of the network.

Advances in population surveillance for physical activity and sedentary behavior : reliability and validity of time use surveys

Many countries conduct regular national time use surveys, some of which date back as far as the 1960s. Time use surveys potentially provide more detailed and accurate national estimates of the prevalence of sedentary and physical activity behavior than more traditional self-report surveillance systems. In this study, the authors determined the reliability and validity of time use surveys for assessing sedentary and physical activity behavior. In 2006 and 2007, participants (n = 134) were recruited from work sites in the Australian state of New South Wales. Participants completed a 2-day time use diary twice, 7 days apart, and wore an accelerometer. The 2 diaries were compared for test-retest reliability, and comparison with the accelerometer determined concurrent validity. Participants with similar activity patterns during the 2 diary periods showed reliability intraclass correlations of 0.74 and 0.73 for nonoccupational sedentary behavior and moderate/vigorous physical activity, respectively. Comparison of the diary with the accelerometer showed Spearman correlations of 0.57-0.59 and 0.45-0.69 for nonoccupational sedentary behavior and moderate/vigorous physical activity, respectively. Time use surveys appear to be more valid for population surveillance of nonoccupational sedentary behavior and health-enhancing physical activity than more traditional surveillance systems. National time use surveys could be used to retrospectively study nonoccupational sedentary and physical activity behavior over the past 5 decades.

The explicit hazard model – part 1: theoretical development

Modern Engineering Asset Management (EAM) requires the accurate assessment of current and the prediction of future asset health condition. Appropriate mathematical models that are capable of estimating times to failures and the probability of failures in the future are essential in EAM. In most real-life situations, the lifetime of an engineering asset is influenced and/or indicated by different factors that are termed as covariates. Hazard prediction with covariates is an elemental notion in the reliability theory to estimate the tendency of an engineering asset failing instantaneously beyond the current time assumed that it has already survived up to the current time. A number of statistical covariate-based hazard models have been developed. However, none of them has explicitly incorporated both external and internal covariates into one model. This paper introduces a novel covariate-based hazard model to address this concern. This model is named as Explicit Hazard Model (EHM). Both the semi-parametric and non-parametric forms of this model are presented in the paper. The major purpose of this paper is to illustrate the theoretical development of EHM. Due to page limitation, a case study with the reliability field data is presented in the applications part of this study.

Asset health prediction using the explicit hazard model

The ability to estimate the asset reliability and the probability of failure is critical to reducing maintenance costs, operation downtime, and safety hazards. Predicting the survival time and the probability of failure in future time is an indispensable requirement in prognostics and asset health management. In traditional reliability models, the lifetime of an asset is estimated using failure event data, alone; however, statistically sufficient failure event data are often difficult to attain in real-life situations due to poor data management, effective preventive maintenance, and the small population of identical assets in use. Condition indicators and operating environment indicators are two types of covariate data that are normally obtained in addition to failure event and suspended data. These data contain significant information about the state and health of an asset. Condition indicators reflect the level of degradation of assets while operating environment indicators accelerate or decelerate the lifetime of assets. When these data are available, an alternative approach to the traditional reliability analysis is the modelling of condition indicators and operating environment indicators and their failure-generating mechanisms using a covariate-based hazard model. The literature review indicates that a number of covariate-based hazard models have been developed. All of these existing covariate-based hazard models were developed based on the principle theory of the Proportional Hazard Model (PHM). However, most of these models have not attracted much attention in the field of machinery prognostics. Moreover, due to the prominence of PHM, attempts at developing alternative models, to some extent, have been stifled, although a number of alternative models to PHM have been suggested. The existing covariate-based hazard models neglect to fully utilise three types of asset health information (including failure event data (i.e. observed and/or suspended), condition data, and operating environment data) into a model to have more effective hazard and reliability predictions. In addition, current research shows that condition indicators and operating environment indicators have different characteristics and they are non-homogeneous covariate data. Condition indicators act as response variables (or dependent variables) whereas operating environment indicators act as explanatory variables (or independent variables). However, these non-homogenous covariate data were modelled in the same way for hazard prediction in the existing covariate-based hazard models. The related and yet more imperative question is how both of these indicators should be effectively modelled and integrated into the covariate-based hazard model. This work presents a new approach for addressing the aforementioned challenges. The new covariate-based hazard model, which termed as Explicit Hazard Model (EHM), explicitly and effectively incorporates all three available asset health information into the modelling of hazard and reliability predictions and also drives the relationship between actual asset health and condition measurements as well as operating environment measurements. The theoretical development of the model and its parameter estimation method are demonstrated in this work. EHM assumes that the baseline hazard is a function of the both time and condition indicators. Condition indicators provide information about the health condition of an asset; therefore they update and reform the baseline hazard of EHM according to the health state of asset at given time t. Some examples of condition indicators are the vibration of rotating machinery, the level of metal particles in engine oil analysis, and wear in a component, to name but a few. Operating environment indicators in this model are failure accelerators and/or decelerators that are included in the covariate function of EHM and may increase or decrease the value of the hazard from the baseline hazard. These indicators caused by the environment in which an asset operates, and that have not been explicitly identified by the condition indicators (e.g. Loads, environmental stresses, and other dynamically changing environment factors). While the effects of operating environment indicators could be nought in EHM; condition indicators could emerge because these indicators are observed and measured as long as an asset is operational and survived. EHM has several advantages over the existing covariate-based hazard models. One is this model utilises three different sources of asset health data (i.e. population characteristics, condition indicators, and operating environment indicators) to effectively predict hazard and reliability. Another is that EHM explicitly investigates the relationship between condition and operating environment indicators associated with the hazard of an asset. Furthermore, the proportionality assumption, which most of the covariate-based hazard models suffer from it, does not exist in EHM. According to the sample size of failure/suspension times, EHM is extended into two forms: semi-parametric and non-parametric. The semi-parametric EHM assumes a specified lifetime distribution (i.e. Weibull distribution) in the form of the baseline hazard. However, for more industry applications, due to sparse failure event data of assets, the analysis of such data often involves complex distributional shapes about which little is known. Therefore, to avoid the restrictive assumption of the semi-parametric EHM about assuming a specified lifetime distribution for failure event histories, the non-parametric EHM, which is a distribution free model, has been developed. The development of EHM into two forms is another merit of the model. A case study was conducted using laboratory experiment data to validate the practicality of the both semi-parametric and non-parametric EHMs. The performance of the newly-developed models is appraised using the comparison amongst the estimated results of these models and the other existing covariate-based hazard models. The comparison results demonstrated that both the semi-parametric and non-parametric EHMs outperform the existing covariate-based hazard models. Future research directions regarding to the new parameter estimation method in the case of time-dependent effects of covariates and missing data, application of EHM in both repairable and non-repairable systems using field data, and a decision support model in which linked to the estimated reliability results, are also identified.

Multi-criteria optimization of group replacement schedules for distributed water pipeline assets

This thesis presents a multi-criteria optimisation study of group replacement schedules for water pipelines, which is a capital-intensive and service critical decision. A new mathematical model was developed, which minimises total replacement costs while maintaining a satisfactory level of services. The research outcomes are expected to enrich the body of knowledge of multi-criteria decision optimisation, where group scheduling is required. The model has the potential to optimise replacement planning for other types of linear asset networks resulting in bottom-line benefits for end users and communities. The results of a real case study show that the new model can effectively reduced the total costs and service interruptions.

Remaining useful life prediction of rotating equipment using covariate-based hazard models : industry applications

The ability to estimate the expected Remaining Useful Life (RUL) is critical to reduce maintenance costs, operational downtime and safety hazards. In most industries, reliability analysis is based on the Reliability Centred Maintenance (RCM) and lifetime distribution models. In these models, the lifetime of an asset is estimated using failure time data; however, statistically sufficient failure time data are often difficult to attain in practice due to the fixed time-based replacement and the small population of identical assets. When condition indicator data are available in addition to failure time data, one of the alternate approaches to the traditional reliability models is the Condition-Based Maintenance (CBM). The covariate-based hazard modelling is one of CBM approaches. There are a number of covariate-based hazard models; however, little study has been conducted to evaluate the performance of these models in asset life prediction using various condition indicators and data availability. This paper reviews two covariate-based hazard models, Proportional Hazard Model (PHM) and Proportional Covariate Model (PCM). To assess these models’ performance, the expected RUL is compared to the actual RUL. Outcomes demonstrate that both models achieve convincingly good results in RUL prediction; however, PCM has smaller absolute prediction error. In addition, PHM shows over-smoothing tendency compared to PCM in sudden changes of condition data. Moreover, the case studies show PCM is not being biased in the case of small sample size.

Effect of constitutive material models on seismic response of two-story reinforced concrete frame

This paper focuses on the finite element (FE) response sensitivity and reliability analyses considering smooth constitutive material models. A reinforced concrete frame is modeled for FE sensitivity analysis followed by direct differentiation method under both static and dynamic load cases. Later, the reliability analysis is performed to predict the seismic behavior of the frame. Displacement sensitivity discontinuities are observed along the pseudo-time axis using non-smooth concrete and reinforcing steel model under quasi-static loading. However, the smooth materials show continuity in response sensitivity at elastic to plastic transition points. The normalized sensitivity results are also used to measure the relative importance of the material parameters on the structural responses. In FE reliability analysis, the influence of smoothness behavior of reinforcing steel is carefully noticed. More efficient and reasonable reliability estimation can be achieved by using smooth material model compare with bilinear material constitutive model.