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.

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.

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.

The Explicit Hazard Model – Part 2 : Applications

Hazard and reliability prediction of an engineering asset is one of the significant fields of research in Engineering Asset Health Management (EAHM). In real-life situations where an engineering asset operates under dynamic operational and environmental conditions, the lifetime of an engineering asset can be influenced and/or indicated by different factors that are termed as covariates. The Explicit Hazard Model (EHM) as a covariate-based hazard model is a new approach for hazard prediction which explicitly incorporates both internal and external covariates into one model. EHM is an appropriate model to use in the analysis of lifetime data in presence of both internal and external covariates in the reliability field. This paper presents applications of the methodology which is introduced and illustrated in the theory part of this study. In this paper, the semi-parametric EHM is applied to a case study so as to predict the hazard and reliability of resistance elements on a Resistance Corrosion Sensor Board (RCSB).

Reliability prediction using the non-parametric explicit hazard model : a case study

Survival probability prediction using covariate-based hazard approach is a known statistical methodology in engineering asset health management. We have previously reported the semi-parametric Explicit Hazard Model (EHM) which incorporates three types of information: population characteristics; condition indicators; and operating environment indicators for hazard prediction. This model assumes the baseline hazard has the form of the Weibull distribution. To avoid this assumption, this paper presents the non-parametric EHM which is a distribution-free covariate-based hazard model. In this paper, an application of the non-parametric EHM is demonstrated via a case study. In this case study, survival probabilities of a set of resistance elements using the non-parametric EHM are compared with the Weibull proportional hazard model and traditional Weibull model. The results show that the non-parametric EHM can effectively predict asset life using the condition indicator, operating environment indicator, and failure history.

Asset health prediction using condition indicators and operating environment indicators : a case study

Prognostics and asset life prediction is one of research potentials in engineering asset health management. We previously developed the Explicit Hazard Model (EHM) to effectively and explicitly predict asset life using three types of information: population characteristics; condition indicators; and operating environment indicators. We have formerly studied the application of both the semi-parametric EHM and non-parametric EHM to the survival probability estimation in the reliability field. The survival time in these models is dependent not only upon the age of the asset monitored, but also upon the condition and operating environment information obtained. This paper is a further study of the semi-parametric and non-parametric EHMs to the hazard and residual life prediction of a set of resistance elements. The resistance elements were used as corrosion sensors for measuring the atmospheric corrosion rate in a laboratory experiment. In this paper, the estimated hazard of the resistance element using the semi-parametric EHM and the non-parametric EHM is compared to the traditional Weibull model and the Aalen Linear Regression Model (ALRM), respectively. Due to assuming a Weibull distribution in the baseline hazard of the semi-parametric EHM, the estimated hazard using this model is compared to the traditional Weibull model. The estimated hazard using the non-parametric EHM is compared to ALRM which is a well-known non-parametric covariate-based hazard model. At last, the predicted residual life of the resistance element using both EHMs is compared to the actual life data.

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.

Distinguishing new science from calibration effects in the electron-volt neutron spectrometer VESUVIO at ISIS

The "standard" procedure for calibrating the Vesuvio eV neutron spectrometer at the ISIS neutron source, forming the basis for data analysis over at least the last decade, was recently documented in considerable detail by the instrument’s scientists. Additionally, we recently derived analytic expressions of the sensitivity of recoil peak positions with respect to fight-path parameters and presented neutron–proton scattering results that together called in to question the validity of the "standard" calibration. These investigations should contribute significantly to the assessment of the experimental results obtained with Vesuvio. Here we present new results of neutron–deuteron scattering from D2 in the backscattering angular range (theata > 90 degrees) which are accompanied by a striking energy increase that violates the Impulse Approximation, thus leading unequivocally the following dilemma: (A) either the "standard" calibration is correct and then the experimental results represent a novel quantum dynamical effect of D which stands in blatant contradiction of conventional theoretical expectations; (B) or the present "standard" calibration procedure is seriously deficient and leads to artificial outcomes. For Case(A), we allude to the topic of attosecond quantumdynamical phenomena and our recent neutron scattering experiments from H2 molecules. For Case(B),some suggestions as to how the "standard" calibration could be considerably improved are made.

Sensitivity of peak positions to flight-path parameters in a deep-inelastic scattering neutron TOF spectrometer

The effects of small changes in flight-path parameters (primary and secondary flight paths, detector angles), and of displacement of the sample along the beam axis away from its ideal position, are examined for an inelastic time-of-flight (TOF) neutron spectrometer, emphasising the deep-inelastic regime. The aim was to develop a rational basis for deciding what measured shifts in the positions of spectral peaks could be regarded as reliable in the light of the uncertainties in the calibrated flight-path parameters. Uncertainty in the length of the primary or secondary flight path has the least effect on the positions of the peaks of H, D and He, which are dominated by the accuracy of the calibration of the detector angles. This aspect of the calibration of a TOF spectrometer therefore demands close attention to achieve reliable outcomes where the position of the peaks is of significant scientific interest and is discussed in detail. The corresponding sensitivities of the position of peak of the Compton profile, J(y), to flight-path parameters and sample position are also examined, focusing on the comparability across experiments of results for H, D and He. We show that positioning the sample to within a few mm of the ideal position is required to ensure good comparability between experiments if data from detectors at high forward angles are to be reliably interpreted.

Interrelations between acute and chronic exercise and the immune and endocrine systems

Interaction between the endocrine and immune system is necessary to regulate our health. However, under some conditions, stress hormones can overstimulate or suppress the immune system, resulting in harmful consequences (1). Stress is often considered negative, yet it is an intrinsic part of everyday life. Stress is not clearly defined; it is context-specific and depends on the nature of factors that challenge our body. Internal stimuli will elicit different stress reactions compared with external stimuli (1). Similarly, some stressors will induce responses that may benefit survival, whereas others will cause disturbances that may endanger our health. Stress also depends on how our bodies perceive and respond to stressful stimuli (1).

An accuracy assessment of ASTER stereo images-derived digital elevation model by using rational polynomial coefficient model

The along-track stereo images of Advanced Spaceborne Thermal Emission and Reflection Radiometer (ASTER) sensor with 15 m resolution were used to generate Digital Elevation Model (DEM) on an area with low and near Mean Sea Level (MSL) elevation in Johor, Malaysia. The absolute DEM was generated by using the Rational Polynomial Coefficient (RPC) model which was run on ENVI 4.8 software. In order to generate the absolute DEM, 60 Ground Control Pointes (GCPs) with almost vertical accuracy less than 10 meter extracted from topographic map of the study area. The assessment was carried out on uncorrected and corrected DEM by utilizing dozens of Independent Check Points (ICPs). Consequently, the uncorrected DEM showed the RMSEz of ± 26.43 meter which was decreased to the RMSEz of ± 16.49 meter for the corrected DEM after post-processing. Overall, the corrected DEM of ASTER stereo images met the expectations.

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.

Global, regional, and national disability-adjusted life years (DALYs) for 306 diseases and injuries and healthy life expectancy (HALE) for 188 countries, 1990–2013: Quantifying the epidemiological transition

Background The Global Burden of Disease Study 2013 (GBD 2013) aims to bring together all available epidemiological data using a coherent measurement framework, standardised estimation methods, and transparent data sources to enable comparisons of health loss over time and across causes, age–sex groups, and countries. The GBD can be used to generate summary measures such as disability-adjusted life-years (DALYs) and healthy life expectancy (HALE) that make possible comparative assessments of broad epidemiological patterns across countries and time. These summary measures can also be used to quantify the component of variation in epidemiology that is related to sociodemographic development. Methods We used the published GBD 2013 data for age-specific mortality, years of life lost due to premature mortality (YLLs), and years lived with disability (YLDs) to calculate DALYs and HALE for 1990, 1995, 2000, 2005, 2010, and 2013 for 188 countries. We calculated HALE using the Sullivan method; 95% uncertainty intervals (UIs) represent uncertainty in age-specific death rates and YLDs per person for each country, age, sex, and year. We estimated DALYs for 306 causes for each country as the sum of YLLs and YLDs; 95% UIs represent uncertainty in YLL and YLD rates. We quantified patterns of the epidemiological transition with a composite indicator of sociodemographic status, which we constructed from income per person, average years of schooling after age 15 years, and the total fertility rate and mean age of the population. We applied hierarchical regression to DALY rates by cause across countries to decompose variance related to the sociodemographic status variable, country, and time. Findings Worldwide, from 1990 to 2013, life expectancy at birth rose by 6·2 years (95% UI 5·6–6·6), from 65·3 years (65·0–65·6) in 1990 to 71·5 years (71·0–71·9) in 2013, HALE at birth rose by 5·4 years (4·9–5·8), from 56·9 years (54·5–59·1) to 62·3 years (59·7–64·8), total DALYs fell by 3·6% (0·3–7·4), and age-standardised DALY rates per 100 000 people fell by 26·7% (24·6–29·1). For communicable, maternal, neonatal, and nutritional disorders, global DALY numbers, crude rates, and age-standardised rates have all declined between 1990 and 2013, whereas for non–communicable diseases, global DALYs have been increasing, DALY rates have remained nearly constant, and age-standardised DALY rates declined during the same period. From 2005 to 2013, the number of DALYs increased for most specific non-communicable diseases, including cardiovascular diseases and neoplasms, in addition to dengue, food-borne trematodes, and leishmaniasis; DALYs decreased for nearly all other causes. By 2013, the five leading causes of DALYs were ischaemic heart disease, lower respiratory infections, cerebrovascular disease, low back and neck pain, and road injuries. Sociodemographic status explained more than 50% of the variance between countries and over time for diarrhoea, lower respiratory infections, and other common infectious diseases; maternal disorders; neonatal disorders; nutritional deficiencies; other communicable, maternal, neonatal, and nutritional diseases; musculoskeletal disorders; and other non-communicable diseases. However, sociodemographic status explained less than 10% of the variance in DALY rates for cardiovascular diseases; chronic respiratory diseases; cirrhosis; diabetes, urogenital, blood, and endocrine diseases; unintentional injuries; and self-harm and interpersonal violence. Predictably, increased sociodemographic status was associated with a shift in burden from YLLs to YLDs, driven by declines in YLLs and increases in YLDs from musculoskeletal disorders, neurological disorders, and mental and substance use disorders. In most country-specific estimates, the increase in life expectancy was greater than that in HALE. Leading causes of DALYs are highly variable across countries. Interpretation Global health is improving. Population growth and ageing have driven up numbers of DALYs, but crude rates have remained relatively constant, showing that progress in health does not mean fewer demands on health systems. The notion of an epidemiological transition—in which increasing sociodemographic status brings structured change in disease burden—is useful, but there is tremendous variation in burden of disease that is not associated with sociodemographic status. This further underscores the need for country-specific assessments of DALYs and HALE to appropriately inform health policy decisions and attendant actions.

Global, regional, and national comparative risk assessment of 79 behavioural, environmental and occupational, and metabolic risks or clusters of risks in 188 countries, 1990–2013: a systematic analysis for the Global Burden of Disease Study 2013

Background The Global Burden of Disease, Injuries, and Risk Factor study 2013 (GBD 2013) is the first of a series of annual updates of the GBD. Risk factor quantification, particularly of modifiable risk factors, can help to identify emerging threats to population health and opportunities for prevention. The GBD 2013 provides a timely opportunity to update the comparative risk assessment with new data for exposure, relative risks, and evidence on the appropriate counterfactual risk distribution. Methods Attributable deaths, years of life lost, years lived with disability, and disability-adjusted life-years (DALYs) have been estimated for 79 risks or clusters of risks using the GBD 2010 methods. Risk–outcome pairs meeting explicit evidence criteria were assessed for 188 countries for the period 1990–2013 by age and sex using three inputs: risk exposure, relative risks, and the theoretical minimum risk exposure level (TMREL). Risks are organised into a hierarchy with blocks of behavioural, environmental and occupational, and metabolic risks at the first level of the hierarchy. The next level in the hierarchy includes nine clusters of related risks and two individual risks, with more detail provided at levels 3 and 4 of the hierarchy. Compared with GBD 2010, six new risk factors have been added: handwashing practices, occupational exposure to trichloroethylene, childhood wasting, childhood stunting, unsafe sex, and low glomerular filtration rate. For most risks, data for exposure were synthesised with a Bayesian meta-regression method, DisMod-MR 2.0, or spatial-temporal Gaussian process regression. Relative risks were based on meta-regressions of published cohort and intervention studies. Attributable burden for clusters of risks and all risks combined took into account evidence on the mediation of some risks such as high body-mass index (BMI) through other risks such as high systolic blood pressure and high cholesterol. Findings All risks combined account for 57·2% (95% uncertainty interval [UI] 55·8–58·5) of deaths and 41·6% (40·1–43·0) of DALYs. Risks quantified account for 87·9% (86·5–89·3) of cardiovascular disease DALYs, ranging to a low of 0% for neonatal disorders and neglected tropical diseases and malaria. In terms of global DALYs in 2013, six risks or clusters of risks each caused more than 5% of DALYs: dietary risks accounting for 11·3 million deaths and 241·4 million DALYs, high systolic blood pressure for 10·4 million deaths and 208·1 million DALYs, child and maternal malnutrition for 1·7 million deaths and 176·9 million DALYs, tobacco smoke for 6·1 million deaths and 143·5 million DALYs, air pollution for 5·5 million deaths and 141·5 million DALYs, and high BMI for 4·4 million deaths and 134·0 million DALYs. Risk factor patterns vary across regions and countries and with time. In sub-Saharan Africa, the leading risk factors are child and maternal malnutrition, unsafe sex, and unsafe water, sanitation, and handwashing. In women, in nearly all countries in the Americas, north Africa, and the Middle East, and in many other high-income countries, high BMI is the leading risk factor, with high systolic blood pressure as the leading risk in most of Central and Eastern Europe and south and east Asia. For men, high systolic blood pressure or tobacco use are the leading risks in nearly all high-income countries, in north Africa and the Middle East, Europe, and Asia. For men and women, unsafe sex is the leading risk in a corridor from Kenya to South Africa. Interpretation Behavioural, environmental and occupational, and metabolic risks can explain half of global mortality and more than one-third of global DALYs providing many opportunities for prevention. Of the larger risks, the attributable burden of high BMI has increased in the past 23 years. In view of the prominence of behavioural risk factors, behavioural and social science research on interventions for these risks should be strengthened. Many prevention and primary care policy options are available now to act on key risks.