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.

Motorway crash duration and its determinants: Do durations vary across motorways?

Traffic congestion has been a growing issue in many metropolitan areas during recent years, which necessitates the identification of its key contributors and development of sustainable strategies to help decrease its adverse impacts on traffic networks. Road incidents generally and crashes specifically have been acknowledged as the cause of a large proportion of travel delays in urban areas and account for 25% to 60% of traffic congestion on motorways. Identifying the critical determinants of travel delays has been of significant importance to the incident management systems which constantly collect and store the incident duration data. This study investigates the individual and simultaneous differential effects of the relevant determinants on motorway crash duration probabilities. In particular, it applies parametric Accelerated Failure Time (AFT) hazard-based models to develop in-depth insights into how the crash-specific characteristic and the associated temporal and infrastructural determinants impact the duration. AFT models with both fixed and random parameters have been calibrated on one year of traffic crash records from two major Australian motorways in South East Queensland and the differential effects of determinants on crash survival functions have been studied on these two motorways individually. A comprehensive spectrum of commonly used parametric fixed parameter AFT models, including generalized gamma and generalized F families, have been compared to random parameter AFT structures in terms of goodness of fit to the duration data and as a result, the random parameter Weibull AFT model has been selected as the most appropriate model. Significant determinants of motorway crash duration included traffic diversion requirement, crash injury type, number and type of vehicles involved in a crash, day of week and time of day, towing support requirement and damage to the infrastructure. A major finding of this research is that the motorways under study are significantly different in terms of crash durations; such that motorway exhibits durations that are on average 19% shorter compared to the durations on motorway. The differential effects of explanatory variables on crash durations are also different on the two motorways. The detailed presented analysis confirms that, looking at the motorway network as a whole, neglecting the individual differences between roads, can lead to erroneous interpretations of duration and inefficient strategies for mitigating travel delays along a particular motorway.

Hedging Options with Different Time Units in the Pricing Models

This study examined the effects of the Greeks of the options and the trading results of delta hedging strategies, with three different time units or option-pricing models. These time units were calendar time, trading time and continuous time using discrete approximation (CTDA) time. The CTDA time model is a pricing model, that among others accounts for intraday and weekend, patterns in volatility. For the CTDA time model some additional theta measures, which were believed to be usable in trading, were developed. The study appears to verify that there were differences in the Greeks with different time units. It also revealed that these differences influence the delta hedging of options or portfolios. Although it is difficult to say anything about which is the most usable of the different time models, as this much depends on the traders view of the passing of time, different market conditions and different portfolios, the CTDA time model can be viewed as an attractive alternative.

Discrete-time modelling of woodwind instrument bores using wave variables

A method for simulation of acoustical bores, useful in the context of sound synthesis by physical modeling of woodwind instruments, is presented. As with previously developed methods, such as digital waveguide modeling (DWM) [Smith, Comput. Music J. 16, pp 74-91 (1992)] and the multi convolution algorithm (MCA) [Martinez et al., J. Acoust. Soc. Am. 84, pp 1620-1627 (1988)], the approach is based on a one-dimensional model of wave propagation in the bore. Both the DWM method and the MCA explicitly compute the transmission and reflection of wave variables that represent actual traveling pressure waves. The method presented in this report, the wave digital modeling (WDM) method, avoids the typical limitations associated with these methods by using a more general definition of the wave variables. An efficient and spatially modular discrete-time model is constructed from the digital representations of elemental bore units such as cylindrical sections, conical sections, and toneholes. Frequency-dependent phenomena, such as boundary losses, are approximated with digital filters. The stability of a simulation of a complete acoustic bore is investigated empirically. Results of the simulation of a full clarinet show that a very good concordance with classic transmission-line theory is obtained.

Forecasting overseas visitors into the United Kingdom using continuous time and autoregressive fractional integrated moving average models with discrete data

This paper applies Gaussian estimation methods to continuous time models for modelling overseas visitors into the UK. The use of continuous time modelling is widely used in economics and finance but not in tourism forecasting. Using monthly data for 1986–2010, various continuous time models are estimated and compared to autoregressive integrated moving average (ARIMA) and autoregressive fractionally integrated moving average (ARFIMA) models. Dynamic forecasts are obtained over different periods. The empirical results show that the ARIMA model performs very well, but that the constant elasticity of variance (CEV) continuous time model has the lowest root mean squared error (RMSE) over a short period.

Time to Left Ventricular Reverse Remodeling after Cardiac Resynchronization Therapy: Better Late than Never

INTRODUCTION: Left ventricular reverse remodeling (LVRR), defined as reduction of end-diastolic and end-systolic dimensions and improvement of ejection fraction, is associated with the prognostic implications of cardiac resynchronization therapy (CRT). The time course of LVRR remains poorly characterized. Nevertheless, it has been suggested that it occurs ≤6 months after CRT. OBJECTIVE: To characterize the long-term echocardiographic and clinical evolution of patients with LVRR occurring >6 months after CRT and to identify predictors of a delayed LVRR response. METHODS: A total of 127 consecutive patients after successful CRT implantation were divided into three groups according to LVRR response: Group A, 19 patients (15%) with LVRR after >6 months (late LVRR); Group B, 58 patients (46%) with LVRR before 6 months (early LVRR); and Group C, 50 patients (39%) without LVRR during follow-up (no LVRR). RESULTS: The late LVRR group was older, more often had ischemic etiology and fewer patients were in NYHA class ≤II. Overall, group A presented LVRR between group B and C. This was also the case with the percentage of clinical response (68.4% vs. 94.8% vs. 38.3%, respectively, p<0.001), and hospital readmissions due to decompensated heart failure (31.6% vs. 12.1% vs. 57.1%, respectively, p<0.001). Ischemic etiology (OR 0.044; p=0.013) and NYHA functional class

Complete longitudinal analyses of the randomized, placebo-controlled, phase III trial of sunitinib in patients with gastrointestinal stromal tumor following imatinib failure.

PURPOSE: To analyze final long-term survival and clinical outcomes from the randomized phase III study of sunitinib in gastrointestinal stromal tumor patients after imatinib failure; to assess correlative angiogenesis biomarkers with patient outcomes. EXPERIMENTAL DESIGN: Blinded sunitinib or placebo was given daily on a 4-week-on/2-week-off treatment schedule. Placebo-assigned patients could cross over to sunitinib at disease progression/study unblinding. Overall survival (OS) was analyzed using conventional statistical methods and the rank-preserving structural failure time (RPSFT) method to explore cross-over impact. Circulating levels of angiogenesis biomarkers were analyzed. RESULTS: In total, 243 patients were randomized to receive sunitinib and 118 to placebo, 103 of whom crossed over to open-label sunitinib. Conventional statistical analysis showed that OS converged in the sunitinib and placebo arms (median 72.7 vs. 64.9 weeks; HR, 0.876; P = 0.306) as expected, given the cross-over design. RPSFT analysis estimated median OS for placebo of 39.0 weeks (HR, 0.505, 95% CI, 0.262-1.134; P = 0.306). No new safety concerns emerged with extended sunitinib treatment. No consistent associations were found between the pharmacodynamics of angiogenesis-related plasma proteins during sunitinib treatment and clinical outcome. CONCLUSIONS: The cross-over design provided evidence of sunitinib clinical benefit based on prolonged time to tumor progression during the double-blind phase of this trial. As expected, following cross-over, there was no statistical difference in OS. RPSFT analysis modeled the absence of cross-over, estimating a substantial sunitinib OS benefit relative to placebo. Long-term sunitinib treatment was tolerated without new adverse events.

MODELING HETEROTACHY IN PHYLOGENETICS

Il a été démontré que l’hétérotachie, variation du taux de substitutions au cours du temps et entre les sites, est un phénomène fréquent au sein de données réelles. Échouer à modéliser l’hétérotachie peut potentiellement causer des artéfacts phylogénétiques. Actuellement, plusieurs modèles traitent l’hétérotachie : le modèle à mélange des longueurs de branche (MLB) ainsi que diverses formes du modèle covarion. Dans ce projet, notre but est de trouver un modèle qui prenne efficacement en compte les signaux hétérotaches présents dans les données, et ainsi améliorer l’inférence phylogénétique. Pour parvenir à nos fins, deux études ont été réalisées. Dans la première, nous comparons le modèle MLB avec le modèle covarion et le modèle homogène grâce aux test AIC et BIC, ainsi que par validation croisée. A partir de nos résultats, nous pouvons conclure que le modèle MLB n’est pas nécessaire pour les sites dont les longueurs de branche diffèrent sur l’ensemble de l’arbre, car, dans les données réelles, le signaux hétérotaches qui interfèrent avec l’inférence phylogénétique sont généralement concentrés dans une zone limitée de l’arbre. Dans la seconde étude, nous relaxons l’hypothèse que le modèle covarion est homogène entre les sites, et développons un modèle à mélanges basé sur un processus de Dirichlet. Afin d’évaluer différents modèles hétérogènes, nous définissons plusieurs tests de non-conformité par échantillonnage postérieur prédictif pour étudier divers aspects de l’évolution moléculaire à partir de cartographies stochastiques. Ces tests montrent que le modèle à mélanges covarion utilisé avec une loi gamma est capable de refléter adéquatement les variations de substitutions tant à l’intérieur d’un site qu’entre les sites. Notre recherche permet de décrire de façon détaillée l’hétérotachie dans des données réelles et donne des pistes à suivre pour de futurs modèles hétérotaches. Les tests de non conformité par échantillonnage postérieur prédictif fournissent des outils de diagnostic pour évaluer les modèles en détails. De plus, nos deux études révèlent la non spécificité des modèles hétérogènes et, en conséquence, la présence d’interactions entre différents modèles hétérogènes. Nos études suggèrent fortement que les données contiennent différents caractères hétérogènes qui devraient être pris en compte simultanément dans les analyses phylogénétiques.

Discrete time representation of continuous time ARMA processes

This paper derives exact discrete time representations for data generated by a continuous time autoregressive moving average (ARMA) system with mixed stock and flow data. The representations for systems comprised entirely of stocks or of flows are also given. In each case the discrete time representations are shown to be of ARMA form, the orders depending on those of the continuous time system. Three examples and applications are also provided, two of which concern the stationary ARMA(2, 1) model with stock variables (with applications to sunspot data and a short-term interest rate) and one concerning the nonstationary ARMA(2, 1) model with a flow variable (with an application to U.S. nondurable consumers’ expenditure). In all three examples the presence of an MA(1) component in the continuous time system has a dramatic impact on eradicating unaccounted-for serial correlation that is present in the discrete time version of the ARMA(2, 0) specification, even though the form of the discrete time model is ARMA(2, 1) for both models.

Improved likelihood inference for the shape parameter in Weibull regression

We obtain adjustments to the profile likelihood function in Weibull regression models with and without censoring. Specifically, we consider two different modified profile likelihoods: (i) the one proposed by Cox and Reid [Cox, D.R. and Reid, N., 1987, Parameter orthogonality and approximate conditional inference. Journal of the Royal Statistical Society B, 49, 1-39.], and (ii) an approximation to the one proposed by Barndorff-Nielsen [Barndorff-Nielsen, O.E., 1983, On a formula for the distribution of the maximum likelihood estimator. Biometrika, 70, 343-365.], the approximation having been obtained using the results by Fraser and Reid [Fraser, D.A.S. and Reid, N., 1995, Ancillaries and third-order significance. Utilitas Mathematica, 47, 33-53.] and by Fraser et al. [Fraser, D.A.S., Reid, N. and Wu, J., 1999, A simple formula for tail probabilities for frequentist and Bayesian inference. Biometrika, 86, 655-661.]. We focus on point estimation and likelihood ratio tests on the shape parameter in the class of Weibull regression models. We derive some distributional properties of the different maximum likelihood estimators and likelihood ratio tests. The numerical evidence presented in the paper favors the approximation to Barndorff-Nielsen`s adjustment.

SAS macros for point and interval estimation of area under the receiver operating characteristic curve for non-proportional and proportional hazards Weibull models

Aims and objectives  For prediction of risk of cardiovascular end points using survival models the proportional hazards assumption is often not met. Thus, non-proportional hazards models are more appropriate for developing risk prediction equations in such situations. However, computer program for evaluating the prediction performance of such models has been rarely addressed. We therefore developed SAS macro programs for evaluating the discriminative ability of a non-proportional hazards Weibull model developed by Anderson (1991) and that of a proportional hazards Weibull model using the area under receiver operating characteristic (ROC) curve.

Method  Two SAS macro programs for non-proportional hazards Weibull model using Proc NLIN and Proc NLP respectively and model validation using area under ROC curve (with its confidence limits) were written with SAS IML language. A similar SAS macro for proportional hazards Weibull model was also written.

Results  The computer program was applied to data on coronary heart disease incidence for a Framingham population cohort. The five risk factors considered were current smoking, age, blood pressure, cholesterol and obesity. The predictive ability of the non-proportional hazard Weibull model was slightly higher than that of its proportional hazard counterpart. An advantage of SAS Proc NLP in terms of the example provided here is that it provides significance level for the parameter estimates whereas Proc NLIN does not.

Conclusion  The program is very useful for evaluating the predictive performance of non-proportional and proportional hazards Weibull models.

Modelagem de dados de falhas de equipamentos de sub-superfície em poços de petróleo da Bacia Potiguar

This master´s thesis presents a reliability study conducted among onshore oil fields in the Potiguar Basin (RN/CE) of Petrobras company, Brazil. The main study objective was to build a regression model to predict the risk of failures that impede production wells to function properly using the information of explanatory variables related to wells such as the elevation method, the amount of water produced in the well (BSW), the ratio gas-oil (RGO), the depth of the production bomb, the operational unit of the oil field, among others. The study was based on a retrospective sample of 603 oil columns from all that were functioning between 2000 and 2006. Statistical hypothesis tests under a Weibull regression model fitted to the failure data allowed the selection of some significant predictors in the set considered to explain the first failure time in the wells

Estimação em modelos de tempo de falha acelerado para dados de sobrevivência correlacionados

We presented in this work two methods of estimation for accelerated failure time models with random e_ects to process grouped survival data. The _rst method, which is implemented in software SAS, by NLMIXED procedure, uses an adapted Gauss-Hermite quadrature to determine marginalized likelihood. The second method, implemented in the free software R, is based on the method of penalized likelihood to estimate the parameters of the model. In the _rst case we describe the main theoretical aspects and, in the second, we briey presented the approach adopted with a simulation study to investigate the performance of the method. We realized implement the models using actual data on the time of operation of oil wells from the Potiguar Basin (RN / CE).

Estimação clássica e Bayesiana em modelos de sobrevida com fração de cura

In Survival Analysis, long duration models allow for the estimation of the healing fraction, which represents a portion of the population immune to the event of interest. Here we address classical and Bayesian estimation based on mixture models and promotion time models, using different distributions (exponential, Weibull and Pareto) to model failure time. The database used to illustrate the implementations is described in Kersey et al. (1987) and it consists of a group of leukemia patients who underwent a certain type of transplant. The specific implementations used were numeric optimization by BFGS as implemented in R (base::optim), Laplace approximation (own implementation) and Gibbs sampling as implemented in Winbugs. We describe the main features of the models used, the estimation methods and the computational aspects. We also discuss how different prior information can affect the Bayesian estimates

Testes em modelos weibull na forma estendida de Marshall-Olkin

In survival analysis, the response is usually the time until the occurrence of an event of interest, called failure time. The main characteristic of survival data is the presence of censoring which is a partial observation of response. Associated with this information, some models occupy an important position by properly fit several practical situations, among which we can mention the Weibull model. Marshall-Olkin extended form distributions other a basic generalization that enables greater exibility in adjusting lifetime data. This paper presents a simulation study that compares the gradient test and the likelihood ratio test using the Marshall-Olkin extended form Weibull distribution. As a result, there is only a small advantage for the likelihood ratio test