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 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.

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).

Handling incomplete data in survival analysis with multiple covariates

This paper studies the missing covariate problem which is often encountered in survival analysis. Three covariate imputation methods are employed in the study, and the effectiveness of each method is evaluated within the hazard prediction framework. Data from a typical engineering asset is used in the case study. Covariate values in some time steps are deliberately discarded to generate an incomplete covariate set. It is found that although the mean imputation method is simpler than others for solving missing covariate problems, the results calculated by it can differ largely from the real values of the missing covariates. This study also shows that in general, results obtained from the regression method are more accurate than those of the mean imputation method but at the cost of a higher computational expensive. Gaussian Mixture Model (GMM) method is found to be the most effective method within these three in terms of both computation efficiency and predication accuracy.

Traffic incident clearance time and arrival time prediction based on hazard models

Accurate prediction of incident duration is not only important information of Traffic Incident Management System, but also an ffective input for travel time prediction. In this paper, the hazard based prediction odels are developed for both incident clearance time and arrival time. The data are obtained from the Queensland Department of Transport and Main Roads’ STREAMS Incident Management System (SIMS) for one year ending in November 2010. The best fitting distributions are drawn for both clearance and arrival time for 3 types of incident: crash, stationary vehicle, and hazard. The results show that Gamma, Log-logistic, and Weibull are the best fit for crash, stationary vehicle, and hazard incident, respectively. The obvious impact factors are given for crash clearance time and arrival time. The quantitative influences for crash and hazard incident are presented for both clearance and arrival. The model accuracy is analyzed at the end.

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.

The development and validation of two complementary measures of drivers' hazard perception ability

Hazard perception in driving involves a number of different processes. This paper reports the development of two measures designed to separate these processes. A Hazard Perception Test was developed to measure how quickly drivers could anticipate hazards overall, incorporating detection, trajectory prediction, and hazard classification judgements. A Hazard Change Detection Task was developed to measure how quickly drivers can detect a hazard in a static image regardless of whether they consider it hazardous or not. For the Hazard Perception Test, young novices were slower than mid-age experienced drivers, consistent with differences in crash risk, and test performance correlated with scores in pre-existing Hazard Perception Tests. For drivers aged 65 and over, scores on the Hazard Perception Test declined with age and correlated with both contrast sensitivity and a Useful Field of View measure. For the Hazard Change Detection Task, novices responded quicker than the experienced drivers, contrary to crash risk trends, and test performance did not correlate with measures of overall hazard perception. However for drivers aged 65 and over, test performance declined with age and correlated with both hazard perception and Useful Field of View. Overall we concluded that there was support for the validity of the Hazard Perception Test for all ages but the Hazard Change Detection Task might only be appropriate for use with older drivers.

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.

Ship collision avoidance and COLREGS compliance using simulation-based control behavior selection with predictive hazard assessment

This paper describes a concept for a collision avoidance system for ships, which is based on model predictive control. A finite set of alternative control behaviors are generated by varying two parameters: offsets to the guidance course angle commanded to the autopilot and changes to the propulsion command ranging from nominal speed to full reverse. Using simulated predictions of the trajectories of the obstacles and ship, compliance with the Convention on the International Regulations for Preventing Collisions at Sea and collision hazards associated with each of the alternative control behaviors are evaluated on a finite prediction horizon, and the optimal control behavior is selected. Robustness to sensing error, predicted obstacle behavior, and environmental conditions can be ensured by evaluating multiple scenarios for each control behavior. The method is conceptually and computationally simple and yet quite versatile as it can account for the dynamics of the ship, the dynamics of the steering and propulsion system, forces due to wind and ocean current, and any number of obstacles. Simulations show that the method is effective and can manage complex scenarios with multiple dynamic obstacles and uncertainty associated with sensors and predictions.

Determination of preventive maintenance lead time using hybrid analysis

The time for conducting Preventive Maintenance (PM) on an asset is often determined using a predefined alarm limit based on trends of a hazard function. In this paper, the authors propose using both hazard and reliability functions to improve the accuracy of the prediction particularly when the failure characteristic of the asset whole life is modelled using different failure distributions for the different stages of the life of the asset. The proposed method is validated using simulations and case studies.