Prognostics-Based Identification of the Top-$k$ Units in a Fleet

This paper considers a fleet of identical units where each unit consists of the same critical components. The degradation state of each critical component is assumed to be monitored by an on-board sensor. The paper presents a methodology for identifying the top-k (the k most reliable) units in a fleet using sensor-based prognostic information. Specifically, we develop a prognostics-based ranking (PBR) algorithm that combines stochastic degradation models with computer science database ranking algorithms. The stochastic degradation modeling framework is used to compute and update, in real-time, residual life distributions (RLDs) of the critical components of each unit. Using a base case exponential degradation model, we identify conditions necessary to establish stochastic ordering among the RLDs of similar components. A preference relationship, consistent with the stochastic ordering results, is then used to sort the units of the fleet based on the RLDs of their respective components. A database ranking algorithm, known as the threshold algorithm (TA), is then used to identify the top-k units without necessarily computing all the RLDs. The paper concludes with an illustrative example.

[1]  Seung-won Hwang,et al.  Minimal probing: supporting expensive predicates for top-k queries , 2002, SIGMOD '02.

[2]  D. Bunn.  Stochastic Dominance , 1979 .

[3]  T. A. Harris,et al.  Rolling Bearing Analysis , 1967 .

[4]  K. Doksum,et al.  Models for Variable-Stress Accelerated Life Testing Experiments Based on Wiener Processes and the Inverse Gaussian Distribution , 1992 .

[5]  D. Coit,et al.  Gamma distribution parameter estimation for field reliability data with missing failure times , 2000 .

[6]  V. Roshan Joseph,et al.  Reliability improvement experiments with degradation data , 2006, IEEE Transactions on Reliability.

[7]  D. C. Swanson,et al.  A general prognostic tracking algorithm for predictive maintenance , 2001, 2001 IEEE Aerospace Conference Proceedings (Cat. No.01TH8542).

[8]  Kai Yang,et al.  Degradation Reliability Assessment Using Severe Critical Values , 1998 .

[9]  W. Meeker.  Accelerated Testing: Statistical Models, Test Plans, and Data Analyses , 1991 .

[10]  Haitao Liao,et al.  An extended linear hazard regression model with application to time-dependent dielectric breakdown of thermal oxides , 2006 .

[11]  Munir Ahmad,et al.  Bernstein reliability model: Derivation and estimation of parameters , 1984 .

[12]  G A Whitmore,et al.  Modelling Accelerated Degradation Data Using Wiener Diffusion With A Time Scale Transformation , 1997, Lifetime data analysis.

[13]  B. J. Roylance,et al.  Development of predictive model for monitoring condition of hot strip mill , 1998 .

[14]  Wei Huang,et al.  A generalized SSI reliability model considering stochastic loading and strength aging degradation , 2004, IEEE Transactions on Reliability.

[15]  Nagi Gebraeel,et al.  Sensory-Updated Residual Life Distributions for Components With Exponential Degradation Patterns , 2006, IEEE Transactions on Automation Science and Engineering.

[16]  M. Crowder,et al.  Covariates and Random Effects in a Gamma Process Model with Application to Degradation and Failure , 2004, Lifetime data analysis.

[17]  W. Wang.  A model to determine the optimal critical level and the monitoring intervals in condition-based maintenance , 2000 .

[18]  Rong Li,et al.  Residual-life distributions from component degradation signals: A Bayesian approach , 2005 .

[19]  Piero P. Bonissone,et al.  Predicting the Best Units within a Fleet: Prognostic Capabilities Enabled by Peer Learning, Fuzzy Similarity, and Evolutionary Design Process , 2005, The 14th IEEE International Conference on Fuzzy Systems, 2005. FUZZ '05..

[20]  Kai Yang,et al.  Statistical surface roughness checking procedure based on a cutting tool wear model , 1994 .

[21]  Jye-Chyi Lu,et al.  Statistical inference of a time-to-failure distribution derived from linear degradation , 1997 .

[22]  G. A. Whitmore,et al.  Threshold Regression for Survival Analysis: Modeling Event Times by a Stochastic Process Reaching a Boundary , 2006, 0708.0346.

[23]  Moni Naor,et al.  Optimal aggregation algorithms for middleware , 2001, PODS '01.

[24]  Surya Nepal,et al.  Query processing issues in image (multimedia) databases , 1999, Proceedings 15th International Conference on Data Engineering (Cat. No.99CB36337).

[25]  K. B. Lee,et al.  Internet-based distributed measurement and control applications , 1999 .

[26]  Ewan Macarthur,et al.  Accelerated Testing: Statistical Models, Test Plans, and Data Analysis , 1990 .

[27]  C. Joseph Lu,et al.  Using Degradation Measures to Estimate a Time-to-Failure Distribution , 1993 .

[28]  M E Robinson,et al.  Bayesian Methods for a Growth-Curve Degradation Model with Repeated Measures , 2000, Lifetime data analysis.

[29]  Michael S. Hamada,et al.  Using Degradation Data to Improve Fluorescent Lamp Reliability , 1995 .

[30]  Hsiung Cheng Lin.  Precise Riveting Systems Using Networked PLCs for Remote Monitoring and Control via the Internet , 2006 .

[31]  W. Nelson.  Statistical Methods for Reliability Data , 1998 .

[32]  Jye-Chyi Lu,et al.  A Random Coefficient Degradation Model With Ramdom Sample Size , 1999, Lifetime data analysis.

[33]  Ronald Fagin,et al.  Combining Fuzzy Information from Multiple Systems , 1999, J. Comput. Syst. Sci..

[34]  P. Lall,et al.  Prognostics and health management of electronics , 2006, 2006 11th International Symposium on Advanced Packaging Materials: Processes, Properties and Interface.

[35]  M. Nikulin,et al.  Estimation in Degradation Models with Explanatory Variables , 2001, Lifetime data analysis.

[36]  J. Bert Keats,et al.  Statistical Methods for Reliability Data , 1999 .

[37]  Chanseok Park,et al.  Stochastic degradation models with several accelerating variables , 2006, IEEE Transactions on Reliability.

[38]  M. Boulanger,et al.  Experimental Design for a Class of Accelerated Degradation Tests , 1994 .

[39]  A. H. Christer,et al.  A model of condition monitoring of a production plant , 1992 .

[40]  W. J. Padgett,et al.  Inference from Accelerated Degradation and Failure Data Based on Gaussian Process Models , 2004, Lifetime data analysis.

[41]  G. A. Whitmore,et al.  Failure Inference From a Marker Process Based on a Bivariate Wiener Model , 1998, Lifetime data analysis.

[42]  G A Whitmore,et al.  Estimating degradation by a wiener diffusion process subject to measurement error , 1995, Lifetime data analysis.

[43]  L. Pettit,et al.  Bayesian analysis for inverse gaussian lifetime data with measures of degradation , 1999 .

[44]  Y Shao,et al.  Prognosis of remaining bearing life using neural networks , 2000 .