Proportional hazards models of infrastructure system recovery

As emphasis is being placed on a system's ability to withstand and to recover from a disruptive event, collectively referred to as dynamic resilience, there exists a need to quantify a system's ability to bounce back after a disruptive event. This work applies a statistical technique from biostatistics, the proportional hazards model, to describe (i) the instantaneous rate of recovery of an infrastructure system and (ii) the likelihood that recovery occurs prior to a given point in time. A major benefit of the proportional hazards model is its ability to describe a recovery event as a function of time as well as covariates describing the infrastructure system or disruptive event, among others, which can also vary with time. The proportional hazards approach is illustrated with a publicly available electric power outage data set.

[1]  P. Allison Survival analysis using the SAS system : a practical guide , 1995 .

[2]  Christopher W. Zobel,et al.  Representing perceived tradeoffs in defining disaster resilience , 2011, Decis. Support Syst..

[3]  P. McCullagh,et al.  Generalized Linear Models , 1972, Predictive Analytics.

[4]  Kash Barker,et al.  Empirical data and regression analysis for estimation of infrastructure resilience, with application to electric power outages , 2013 .

[5]  Seth D. Guikema,et al.  Practical Considerations in Statistical Modeling of Count Data for Infrastructure Systems , 2009 .

[6]  Seth D Guikema,et al.  Prestorm Estimation of Hurricane Damage to Electric Power Distribution Systems , 2010, Risk analysis : an official publication of the Society for Risk Analysis.

[7]  Patricia J. Solomon,et al.  Parameter Orthogonality in Mixed Regression Models for Survival Data , 1997 .

[8]  Kash Barker,et al.  Stochastic Measures of Network Resilience: Applications to Waterway Commodity Flows , 2014, Risk analysis : an official publication of the Society for Risk Analysis.

[9]  Jose Emmanuel Ramirez-Marquez,et al.  Resiliency as a component importance measure in network reliability , 2009, Reliab. Eng. Syst. Saf..

[10]  J. Kalbfleisch,et al.  Marginal likelihoods based on Cox's regression and life model , 1973 .

[11]  Seth D. Guikema,et al.  Hybrid data mining-regression for infrastructure risk assessment based on zero-inflated data , 2012, Reliab. Eng. Syst. Saf..

[12]  Elisa Lee,et al.  Statistical Methods for Survival Data Analysis: Lee/Survival Data Analysis , 2003 .

[13]  Yacov Y Haimes,et al.  Strategic Preparedness for Recovery from Catastrophic Risks to Communities and Infrastructure Systems of Systems , 2012, Risk analysis : an official publication of the Society for Risk Analysis.

[14]  Haibin Liu,et al.  Spatial generalized linear mixed models of electric power outages due to hurricanes and ice storms , 2008, Reliab. Eng. Syst. Saf..

[15]  D.,et al.  Regression Models and Life-Tables , 2022 .

[16]  C. S. Holling Engineering Resilience versus Ecological Resilience , 1996 .

[17]  P. Royston,et al.  Flexible parametric proportional‐hazards and proportional‐odds models for censored survival data, with application to prognostic modelling and estimation of treatment effects , 2002, Statistics in medicine.

[18]  W. M. Evanco,et al.  Using a proportional hazards model to analyze software reliability , 1999, STEP '99. Proceedings Ninth International Workshop Software Technology and Engineering Practice.

[19]  Kash Barker,et al.  Static and dynamic resource allocation models for recovery of interdependent systems: application to the Deepwater Horizon oil spill , 2016, Ann. Oper. Res..

[20]  Seth D Guikema,et al.  Improving the Predictive Accuracy of Hurricane Power Outage Forecasts Using Generalized Additive Models , 2009, Risk analysis : an official publication of the Society for Risk Analysis.

[21]  Stephanie E. Chang,et al.  Fostering resilience to extreme events within infrastructure systems: Characterizing decision contexts for mitigation and adaptation , 2008 .

[22]  S. Love,et al.  Survival Analysis Part II: Multivariate data analysis – an introduction to concepts and methods , 2003, British Journal of Cancer.

[23]  Martin Newby Perspective on Weibull proportional-hazards models , 1994 .

[24]  J. Crowley,et al.  Covariance Analysis of Heart Transplant Survival Data , 1977 .

[25]  John A. Nelder,et al.  Generalized linear models. 2nd ed. , 1993 .

[26]  Tore Markeset,et al.  Application of reliability models with covariates in spare part prediction and optimization - A case study , 2014, Reliab. Eng. Syst. Saf..

[27]  Tore Markeset,et al.  An approach for prediction of petroleum production facility performance considering Arctic influence factors , 2010, Reliab. Eng. Syst. Saf..

[28]  Seth D. Guikema,et al.  Natural disaster risk analysis for critical infrastructure systems: An approach based on statistical learning theory , 2009, Reliab. Eng. Syst. Saf..

[29]  C. J. Dale,et al.  Application of the proportional hazards model in the reliability field , 1985 .

[30]  J. F. Gómez,et al.  Modelling on-line reliability and risk to schedule the preventive maintenance of repairable assets in network utilities , 2013 .

[31]  B. Efron The Efficiency of Cox's Likelihood Function for Censored Data , 1977 .

[32]  Bengt Klefsjö,et al.  Proportional hazards model: a review , 1994 .

[33]  Bijan Sarkar,et al.  Proportional Hazards Modeling of Environmental Impacts on Reliability of Photovoltaic Modules , 2012 .

[34]  Vasiliy V. Krivtsov,et al.  Regression approach to tire reliability analysis , 2002, Reliab. Eng. Syst. Saf..

[35]  K. C. Kapur,et al.  Methodology for Assessing the Resilience of Networked Infrastructure , 2009, IEEE Systems Journal.

[36]  Michel Bruneau,et al.  A Framework to Quantitatively Assess and Enhance the Seismic Resilience of Communities , 2003 .

[37]  Tore Markeset,et al.  Maintainability analysis considering time-dependent and time-independent covariates , 2011, Reliab. Eng. Syst. Saf..

[38]  Jery R. Stedinger,et al.  Negative Binomial Regression of Electric Power Outages in Hurricanes , 2005 .

[39]  A. Rose Economic Resilience to Disasters , 2009 .

[40]  J. I. Ansell,et al.  Practical aspects of modelling of repairable systems data using proportional hazards models , 1997 .

[41]  A. V. Peterson,et al.  On the regression analysis of multivariate failure time data , 1981 .

[42]  Jason Brown,et al.  Reliability: Probabilistic Models and Statistical Methods , 1996 .