Enhanced Kernel Method for Modelling Failure Probability Density Functions

The kernel method is a nonparametric density function estimation method of random processes. This paper proposes some improvements of the characteristics of the method and shows its application to failure data recorded on industrial facilities. The use of this method for building models for maintenance decisions has always been hampered by the data availability and quality. We show how we have improved the accuracy of the estimations and coped with the edge effects. The idea of using nonparametric methods enables to evaluate the behavior of components in their environment and to provide a new decision support tool for assets’ maintenance management.

[1]  D. W. Scott,et al.  Biased and Unbiased Cross-Validation in Density Estimation , 1987 .

[3]  Naomi S. Altman,et al.  Bandwidth selection for kernel distribution function estimation , 1995 .

[4]  Aiwina Soong Yin Heng.  Intelligent prognostics of machinery health utilising suspended condition monitoring data , 2009 .

[5]  Paul Deheuvels,et al.  Estimation automatique de la densité , 1980 .

[6]  B. Silverman.  Density estimation for statistics and data analysis , 1986 .

[7]  V. A. Epanechnikov.  Non-Parametric Estimation of a Multivariate Probability Density , 1969 .

[8]  Peter Hall,et al.  On Pseudodata Methods for Removing Boundary Effects in Kernel Density Estimation , 1996 .

[9]  Pierre Hominal,et al.  Estimation non paramétrique de la densité compte-tenu d'informations sur le support , 1979 .

[10]  M. C. Jones,et al.  Simple boundary correction for kernel density estimation , 1993 .

[11]  M. Rudemo.  Empirical Choice of Histograms and Kernel Density Estimators , 1982 .

[12]  G. Banon.  Sur un estimateur non paramétrique de la densité de probabilité , 1976 .

[13]  Song-xi Chen,et al.  Probability Density Function Estimation Using Gamma Kernels , 2000 .

[14]  L. Breiman,et al.  Variable Kernel Estimates of Multivariate Densities , 1977 .

[15]  M. Rosenblatt.  Remarks on Some Nonparametric Estimates of a Density Function , 1956 .

[16]  Bernard Bobée,et al.  Estimation non paramétrique des quantiles de crue par la méthode des noyaux , 2002 .

[17]  Tadashi Dohi,et al.  Recent Advances in Stochastic Operations Research , 2007 .

[18]  J. Marron,et al.  Transformations to reduce boundary bias in kernel density estimation , 1994 .

[19]  E. Parzen.  On Estimation of a Probability Density Function and Mode , 1962 .

[20]  M. C. Jones,et al.  A SIMPLE NONNEGATIVE BOUNDARY CORRECTION METHOD FOR KERNEL DENSITY ESTIMATION , 1996 .

[21]  David W. Scott,et al.  Multivariate Density Estimation: Theory, Practice, and Visualization , 1992, Wiley Series in Probability and Statistics.

[22]  V. K. Murthy.  Estimation of Jumps, Reliability and Hazard Rate , 1965 .

[23]  M. Pecht,et al.  Prognostics and health management using physics-of-failure , 2008, 2008 Annual Reliability and Maintainability Symposium.