Remaining useful life in theory and practice

Remaining useful life (RUL) is nowadays in fashion, both in theory and applications. Engineers use it mostly when they have to decide whether to do maintenance, or to delay it, due to production requirements. Most often, it is assumed that in later life of an equipment (in wear-out period), the hazard function is increasing, and then the expected RUL, μ(t), is decreasing. We noticed that the standard deviation of RUL, σ(t), is also decreasing, which was expected and known, but that the ratio σ(t)/μ(t) is also increasing, which was a surprise. Initiated by this observation, we have proved that under some general conditions, which include Weibull distribution with shape parameter  > 1, this is indeed the case. Even more, we have proved that the limiting distribution of standardized RUL is exponential, so that the variability of RUL is relatively large. The role of condition monitoring in the evaluation of RUL is discussed. Various models for RUL depending on covariates are considered.

[1]  M. M. Siddiqui,et al.  Residual lifetime distribution and its applications , 1994 .

[2]  David M. Bradley,et al.  Limiting behaviour of the mean residual life , 2003 .

[3]  D. N. Prabhakar Murthy,et al.  Case studies in reliability and maintenance , 2002 .

[4]  N P Jewell,et al.  Semiparametric Estimation of Proportional Mean Residual Life Model in Presence of Censoring , 2005, Biometrics.

[5]  L. Haan,et al.  Residual Life Time at Great Age , 1974 .

[6]  A. Jardine,et al.  Modelling repairable system reliability with explanatory variables and repair and maintenance actions , 2004 .

[7]  Rune Reinertsen,et al.  Residual life of technical systems ; diagnosis, prediction and life extension , 1996 .

[8]  Gangaji Maguluri,et al.  Estimation in the Mean Residual Life Regression Model , 1994 .

[9]  Frank Proschan,et al.  Mean Residual Life: Theory and Applications , 1988 .

[10]  Kaisa Simola,et al.  Application of stochastic filtering for lifetime prediction , 2006, Reliab. Eng. Syst. Saf..

[11]  S. Kalpakam,et al.  On the quasi-stationary distribution of the residual lifetime , 1993 .

[12]  Jens Perch Nielsen,et al.  A framework for consistent prediction rules based on markers , 1993 .

[13]  Ying Zhang,et al.  Time‐Varying Functional Regression for Predicting Remaining Lifetime Distributions from Longitudinal Trajectories , 2005, Biometrics.

[14]  Wei Li,et al.  The limiting distribution of the residual lifetime of a Markov repairable system , 1993 .

[15]  Mikhail Nikulin,et al.  Parametric and semiparametric models with applications to reliability, survival analysis, and quality of life , 2004 .

[16]  P. Sen.  HRQoL and Concomitant Adjusted Mean Residual Life Analysis , 2004 .

[17]  Balkrishan,et al.  Finite range survival model , 1994 .

[18]  Isaac Meilijson.  Limiting Properties of the Mean Residual Lifetime Function , 1972 .

[19]  H. V. Houwelingen.  Dynamic Prediction by Landmarking in Event History Analysis , 2007 .

[20]  Ramesh C. Gupta.  On the monotonic properties of the residual variance and their applications in reliability , 1987 .

[21]  Dragan Banjevic,et al.  Calculation of reliability function and remaining useful life for a Markov failure time process , 2006 .

[22]  Elsayed A. Elsayed.  Mean Residual Life and Optimal Operating Conditions for Industrial Furnace Tubes , 2003 .

[23]  Lixing Zhu,et al.  On the mean residual life regression model , 2003 .