Deterioration and Maintenance Models for Components in Hydropower Plants

In this paper a reliability model is presented which can be used for scheduling and optimization of maintenance and renewal. The deterioration process of technical equipment is modeled by a Markov chain. A framework is proposed how the parameters in the Markov process can be estimated based on a description of the technical condition of components and systems in hydro power plants according to the Norwegian Electricity Industry Association. A time dependent solution of the Markov model is presented. Imperfect periodic inspection can be modeled by the proposed approach. The length of the inspection interval depends on the system condition revealed by the previous inspection. The model can be used to compute performance measures and operational costs over a finite time horizon. Finally, simulation results for a dataset for a Norwegian hydro power plant are presented.

[1]  Kurt E Petersen The EU model evaluation group , 1999 .

[2]  Richard M. Feldman,et al.  A survey of preventive maintenance models for stochastically deteriorating single-unit systems , 1989 .

[3]  George Apostolakis,et al.  The Broadening of Failure Rate Distributions in Risk Analysis: How Good Are the Experts?1 , 1985 .

[4]  Maarten-Jan Kallen,et al.  Statistical inference for Markov deterioration models of bridge conditions in The Netherlands , 2006 .

[5]  Marita Olsson EM Estimation in Phase Type Models , 1995 .

[6]  Terje Aven,et al.  Quantifying uncertainty under a predictive, epistemic approach to risk analysis , 2002, Reliab. Eng. Syst. Saf..

[7]  A. H. Christer,et al.  A prototype cost model of functional check decisions in reliability-centred maintenance , 2002, J. Oper. Res. Soc..

[8]  Robert L. Winkler,et al.  Uncertainty in probabilistic risk assessment , 1996 .

[9]  Rommert Dekker A review of multi-component maintenance models , 2007 .

[10]  K. Chawla,et al.  Mechanical Behavior of Materials , 1998 .

[11]  Christian Genest,et al.  Combining Probability Distributions: A Critique and an Annotated Bibliography , 1986 .

[12]  Rommert Dekker,et al.  Optimal maintenance of multi-component systems: a review , 2008 .

[13]  George J. Anders,et al.  Probabilistic evaluation of the effect of maintenance on reliability. An application [to power systems] , 1998 .

[14]  Hoang Pham,et al.  Availability and maintenance of series systems subject to imperfect repair and correlated failure and repair , 2006, Eur. J. Oper. Res..

[15]  Jan M. van Noortwijk,et al.  A survey of the application of gamma processes in maintenance , 2009, Reliab. Eng. Syst. Saf..

[16]  Anders Wormsen,et al.  A Fatigue Assessment Methodology for Notched Components Containing Defects , 2007 .

[17]  M. J. Kallen,et al.  Markov processes for maintenance optimization of civil infrastructure in the Netherlands , 2007 .

[18]  A. Tversky,et al.  Judgment under Uncertainty: Heuristics and Biases , 1974, Science.

[19]  P. C. Paris,et al.  A Critical Analysis of Crack Propagation Laws , 1963 .

[20]  G. K. Chan,et al.  Optimum maintenance policy with Markov processes , 2006 .

[21]  Rommert Dekker,et al.  Applications of maintenance optimization models : a review and analysis , 1996 .

[22]  Athanasios Papoulis,et al.  Probability, Random Variables and Stochastic Processes , 1965 .

[23]  Maarten-Jan Kallen,et al.  Optimal periodic inspection of a deterioration process with sequential condition states , 2006 .

[24]  T. Aven Foundations of risk analysis , 2003 .

[25]  Antoine Grall,et al.  Continuous-time predictive-maintenance scheduling for a deteriorating system , 2002, IEEE Trans. Reliab..

[26]  G Beazant Good as New , 2004, Science.

[27]  Roger M. Cooke,et al.  Expert judgment in maintenance optimization , 1992 .

[28]  B.H. Bakken,et al.  Hydropower unit start-up costs , 2002, IEEE Power Engineering Society Summer Meeting,.

[29]  George Apostolakis,et al.  Data analysis in risk assessments , 1982 .

[30]  R. Cooke Experts in Uncertainty: Opinion and Subjective Probability in Science , 1991 .

[31]  李幼升,et al.  Ph , 1989 .

[32]  C. van Winden,et al.  Rationalisation of building maintenance by Markov decision models: a pilot case study , 1998, J. Oper. Res. Soc..

[33]  Maarten-Jan Kallen,et al.  Optimal maintenance decisions under imperfect inspection , 2005, Reliab. Eng. Syst. Saf..

[34]  J. Vatn,et al.  Markov State Model for Optimization of Maintenance and Renewal of Hydro Power Components , 2006, 2006 International Conference on Probabilistic Methods Applied to Power Systems.

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

[36]  Marvin Rausand,et al.  System Reliability Theory: Models, Statistical Methods, and Applications , 2003 .

[37]  Harry F. Martz,et al.  On the Correct Use of the Bayesian Method for Reactor Core Melt Frequency , 1980 .

[38]  G. Apostolakis The concept of probability in safety assessments of technological systems. , 1990, Science.

[39]  J. Endrenyi,et al.  The Present Status of Maintenance Strategies and the Impact of Maintenance on Reliability , 2001, IEEE Power Engineering Review.

[40]  G. Theil Parameter evaluation for extended Markov models applied to condition- and reliability-centered maintenance planning strategies , 2006, 2006 International Conference on Probabilistic Methods Applied to Power Systems.

[41]  A. H. Christer,et al.  Developments in delay time analysis for modelling plant maintenance , 1999, J. Oper. Res. Soc..

[42]  Jane M. Booker,et al.  Eliciting and analyzing expert judgement - a practical guide , 2001, ASA-SIAM series on statistics and applied probability.

[43]  Rommert Dekker,et al.  On the impact of optimisation models in maintenance decision making: the state of the art , 1998 .

[44]  Ren Asmussen,et al.  Fitting Phase-type Distributions via the EM Algorithm , 1996 .

[45]  Philip A. Scarf,et al.  On the application of mathematical models in maintenance , 1997 .

[46]  Robert L. Winkler,et al.  Combining Probability Distributions From Experts in Risk Analysis , 1999 .

[47]  J. Doob Stochastic processes , 1953 .

[48]  Hongzhou Wang,et al.  A survey of maintenance policies of deteriorating systems , 2002, Eur. J. Oper. Res..

[49]  Robert G. Easterling Comments on the Bayesian Method for Estimating Reactor Core Melt Frequency , 1980 .

[50]  G. Apostolakis,et al.  The Interpretation of Probability, De Finetti’s Representation Theorem, and their Implications to the Use of Expert Opinions in Safety Assessment , 1993 .

[51]  George Apostolakis,et al.  A taxonomy of issues related to the use of expert judgments in probabilistic safety studies , 1992 .

[52]  R. H. Myers,et al.  Probability and Statistics for Engineers and Scientists , 1978 .