A preventive maintenance policy for a continuously monitored system with correlated wear indicators

A continuously monitored system is considered, that gradually and stochastically deteriorates according to a bivariate non-decreasing Levy process. The system is considered as failed as soon as its bivariate deterioration level enters a failure zone, assumed to be an upper set. A preventive maintenance policy is proposed, which involves a delayed replacement, triggered by the reaching of some preventive zone for the system deterioration level. The preventive maintenance policy is assessed through a cost function on an infinite horizon time. The cost function is provided in full form, and tools are provided for its numerical computation. The influence of different parameters on the cost function is studied, both from a theoretical and/or numerical point of view.

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

[2]  Marvin Zelen,et al.  Mathematical Theory of Reliability , 1965 .

[3]  K. C. Cherian.  A Bi-Variate Correlated Gamma-Type Distribution Function , 1941 .

[4]  佐藤 健一.  Lévy processes and infinitely divisible distributions , 2013 .

[5]  Sophie Mercier,et al.  Bivariate Gamma wear processes for track geometry modelling, with application to intervention scheduling , 2012 .

[6]  S. Taylor,et al.  LÉVY PROCESSES (Cambridge Tracts in Mathematics 121) , 1998 .

[7]  R. Wolpert.  Lévy Processes , 2000 .

[8]  Sophie Mercier,et al.  Comparison of numerical methods for the assessment of production availability of a hybrid system , 2008, Reliab. Eng. Syst. Saf..

[9]  Nozer D. Singpurwalla,et al.  Survival in Dynamic Environments , 1995 .

[10]  P. Sayers,et al.  Time-dependent reliability analysis of flood defences using gamma processes , 2005 .

[11]  S. Asmussen,et al.  Applied Probability and Queues , 1989 .

[12]  Antoine Grall,et al.  MAINTENANCE POLICY FOR A CONTINUOUSLY MONITORED DETERIORATING SYSTEM , 2003 .

[13]  Nader Ebrahimi,et al.  Indirect assessment of the bivariate survival function , 2004 .

[14]  L. Devroye.  Non-Uniform Random Variate Generation , 1986 .

[15]  M. Abdel-Hameed.  A Gamma Wear Process , 1975, IEEE Transactions on Reliability.

[16]  Ken-iti Sato.  Lévy Processes and Infinitely Divisible Distributions , 1999 .