Prediction of the failure interval with maximum power based on the remaining useful life distribution

Prognosis of the Remaining Useful Life (RUL) of a unit or system plays an important role in system reliability analysis and maintenance decision making. One key aspect of the RUL prognosis is the construction of the best prediction interval for failure occurrence. The interval should have a reasonable length and yield the best prediction power. In current practice, the center-based interval and traditional confidence interval are widely used. Although both are easy to construct, they do not provide the best prediction performance. In this article, we propose a new scheme, the Maximum Power Interval (MPI), for estimating the interval with maximum prediction power. The MPI guarantees the best prediction power under a given interval length. Some technical challenges involved in the MPI method were resolved using the maximum entropy principle and truncation method. A numerical simulation study confirmed that the MPI has better prediction power than other prediction intervals. A case study using a real industry data set was conducted to illustrate the capability of the MPI method.

[1]  Zhigang Tian,et al.  A framework for predicting the remaining useful life of a single unit under time-varying operating conditions , 2013 .

[2]  Rob J Hyndman,et al.  Computing and Graphing Highest Density Regions , 1996 .

[3]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[4]  Qiang Zhou,et al.  Remaining useful life prediction of individual units subject to hard failure , 2014 .

[5]  Anastasios A. Tsiatis,et al.  Joint Modeling of Longitudinal and Time-to-Event Data : An Overview , 2004 .

[6]  Eric Jondeau,et al.  Entropy Densities: With an Application to Autoregressive Conditional Skewness and Kurtosis , 2001 .

[7]  B. B. Bhattacharyya.  One sided chebyshev inequality when the first four moments are known , 1987 .

[8]  Xiao-Sheng Si,et al.  Remaining Useful Life Estimation for Systems with Time-varying Mean and Variance of Degradation Processes , 2014, Qual. Reliab. Eng. Int..

[9]  David W. Coit,et al.  Reliability Analysis for Multi-Component Systems Subject to Multiple Dependent Competing Failure Processes , 2014, IEEE Transactions on Reliability.

[10]  Rafail V. Abramov,et al.  An improved algorithm for the multidimensional moment-constrained maximum entropy problem , 2007, J. Comput. Phys..

[11]  L. Magee,et al.  R 2 Measures Based on Wald and Likelihood Ratio Joint Significance Tests , 1990 .

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

[13]  Towards Determining the Minimum Set of Moments Needed to Accurately Represent Spray Data , 2012 .

[14]  Edward L. Melnick,et al.  Modeling Survival Data , 2011, International Encyclopedia of Statistical Science.

[15]  Kwok-Leung Tsui,et al.  Condition monitoring and remaining useful life prediction using degradation signals: revisited , 2013 .

[16]  A. Tagliani,et al.  Reconstructing heavy-tailed distributions by splicing with maximum entropy in the mean , 2012 .

[17]  Richard A. Highfield,et al.  Calculation of maximum entropy distributions and approximation of marginalposterior distributions , 1988 .

[18]  Tian Pau Chang,et al.  Validity analysis of maximum entropy distribution based on different moment constraints for wind energy assessment , 2011 .

[19]  Menggang Yu,et al.  JOINT LONGITUDINAL-SURVIVAL-CURE MODELS AND THEIR APPLICATION TO PROSTATE CANCER , 2004 .

[20]  M. Rockinger,et al.  Entropy Densities: With an Application to Autoregressive Conditional Skewness and Kurtosis , 2002 .

[21]  K. Goebel,et al.  Prognostic information fusion for constant load systems , 2005, 2005 7th International Conference on Information Fusion.

[22]  M. Crawley.  Mixed‐Effects Models , 2007 .

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

[24]  A. Mohammad-Djafari.  A Matlab Program to Calculate the Maximum Entropy Distributions , 2001, physics/0111126.

[25]  D. Bates,et al.  Mixed-Effects Models in S and S-PLUS , 2001 .

[26]  Donghua Zhou,et al.  Remaining useful life estimation - A review on the statistical data driven approaches , 2011, Eur. J. Oper. Res..

[27]  Nagi Gebraeel,et al.  Stochastic methodology for prognostics under continuously varying environmental profiles , 2013, Stat. Anal. Data Min..

[28]  David W. Coit,et al.  Accelerated burn-in and condition-based maintenance for n-subpopulations subject to stochastic degradation , 2014 .

[29]  P. Buchen,et al.  The Maximum Entropy Distribution of an Asset Inferred from Option Prices , 1996, Journal of Financial and Quantitative Analysis.

[30]  Thomas M. Cover,et al.  Elements of Information Theory , 2005 .

[31]  I. Langner.  Survival Analysis: Techniques for Censored and Truncated Data , 2006 .

[32]  Weiwen Peng,et al.  Inverse Gaussian process models for degradation analysis: A Bayesian perspective , 2014, Reliab. Eng. Syst. Saf..

[33]  M. Gurka.  Selecting the Best Linear Mixed Model Under REML , 2006 .

[34]  Shiyu Zhou,et al.  Evaluation and Comparison of Mixed Effects Model Based Prognosis for Hard Failure , 2013, IEEE Transactions on Reliability.

[35]  Daming Lin,et al.  A review on machinery diagnostics and prognostics implementing condition-based maintenance , 2006 .

[36]  Anil K. Bera,et al.  Maximum entropy autoregressive conditional heteroskedasticity model , 2009 .

[37]  K. Goebel,et al.  Metrics for evaluating performance of prognostic techniques , 2008, 2008 International Conference on Prognostics and Health Management.