Asymptotic failure rate of a Markov deteriorating system with preventive maintenance

2003 ◽  
Vol 40 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Sophie Mercier ◽  
Michel Roussignol
Keyword(s):  
Failure Rate ◽  
Preventive Maintenance ◽  
Sufficient Conditions ◽  
Maintenance Policy ◽  
System A ◽  
Up States ◽  
Finite State ◽  
Degradation Degree ◽  
Preventive Maintenance Policy ◽  
Finite State Space

We consider a system with a finite state space subject to continuous-time Markovian deterioration while running that leads to failure. Failures are instantaneously detected. This system is submitted to sequential checking and preventive maintenance: up states are divided into ‘good’ and ‘degraded’ ones and the system is sequentially checked through perfect and instantaneous inspections until it is found in a degraded up state and stopped to allow maintenance (or until it fails). Time between inspections is random and is chosen at each inspection according to the current degradation degree of the system. Markov renewal equations fulfilled by the reliability of the maintained system are given and an exponential equivalent is derived for the reliability. We prove the existence of an asymptotic failure rate for the maintained system, which we are able to compute. Sufficient conditions are given for the preventive maintenance policy to improve the reliability and the asymptotic failure rate of the system. A numerical example illustrates our study.

Asymptotic failure rate of a Markov deteriorating system with preventive maintenance

2003 ◽  
Vol 40 (01) ◽  
pp. 1-19 ◽  
Author(s):  
Sophie Mercier ◽  
Michel Roussignol
Keyword(s):  
Failure Rate ◽  
Preventive Maintenance ◽  
Sufficient Conditions ◽  
Maintenance Policy ◽  
System A ◽  
Up States ◽  
Finite State ◽  
Degradation Degree ◽  
Preventive Maintenance Policy ◽  
Finite State Space

We consider a system with a finite state space subject to continuous-time Markovian deterioration while running that leads to failure. Failures are instantaneously detected. This system is submitted to sequential checking and preventive maintenance: up states are divided into ‘good’ and ‘degraded’ ones and the system is sequentially checked through perfect and instantaneous inspections until it is found in a degraded up state and stopped to allow maintenance (or until it fails). Time between inspections is random and is chosen at each inspection according to the current degradation degree of the system. Markov renewal equations fulfilled by the reliability of the maintained system are given and an exponential equivalent is derived for the reliability. We prove the existence of an asymptotic failure rate for the maintained system, which we are able to compute. Sufficient conditions are given for the preventive maintenance policy to improve the reliability and the asymptotic failure rate of the system. A numerical example illustrates our study.

scholarly journals Vulnerability based management of water resources systems

2004 ◽  
Vol 6 (2) ◽  
pp. 133-156 ◽  
Author(s):  
V. K. Kanakoudis
Keyword(s):  
Water Supply ◽  
Preventive Maintenance ◽  
Water System ◽  
Supply System ◽  
Water Supply System ◽  
Maintenance Policy ◽  
Supply Networks ◽  
Water Resources Systems ◽  
Maintenance Schedule ◽  
Preventive Maintenance Policy

Must the water networks be fail-proof or must they remain safe during a failure? What must water system managers try to achieve? The present paper introduces a methodology for the hierarchical analysis (in time and space) of the preventive maintenance policy of water supply networks, using water supply system performance indices. This is being accomplished through a technical–economic analysis that takes into account all kinds of costs referring to the repair or replacement of trouble-causing parts of the water supply network. The optimal preventive maintenance schedule suggested by the methodology is compared with the empirically based maintenance policy applied to the Athens water supply system.

scholarly journals Preventive maintenance policy on leasing by considering the usage rate

2018 ◽  
Vol 204 ◽  
pp. 02016
Author(s):  
Moh. Jufriyanto ◽  
Nani Kurniati ◽  
Ade Supriatna
Keyword(s):  
Preventive Maintenance ◽  
Failure Time ◽  
Equipment Failure ◽  
Maintenance Policy ◽  
Time Duration ◽  
Maintenance Costs ◽  
Operational Conditions ◽  
Penalty Cost ◽  
Usage Rate ◽  
Preventive Maintenance Policy

The needs of the consumers about the functionality of a product and increase maintenance costs of equipment caused the prices of products and treatments to be expensive. Therefore, the company considers the lease rather than buy it. Leasing provides interesting strategy when dealing with expensive equipment. Policy maintenance that is done to the product that has decreased performance. Minimum repair done to fix failed equipment in order to return to operational condition, while imperfect preventive maintenance to improve the operational conditions of the equipment to avoid failure. Time duration for a minimum repair neglected. The lessor will charge a penalty (penalty cost) if the lease equipment failure. Mathematical model built for the minimization cost of maintenance policy. In the final part, the numerical experiment are given to show the maintenance policy taking into account the rate of usage (usage rate) by knowing the minimization the resulting costs.

scholarly journals Lumpings of Markov Chains, Entropy Rate Preservation, and Higher-Order Lumpability

2014 ◽  
Vol 51 (4) ◽  
pp. 1114-1132 ◽  
Author(s):  
Bernhard C. Geiger ◽  
Christoph Temmel
Keyword(s):  
Growth Rate ◽  
Markov Chain ◽  
Sufficient Conditions ◽  
Entropy Rate ◽  
Transition Graph ◽  
Order Markov Chain ◽  
Finite State ◽  
Random Growth ◽  
Irreducible Markov Chain ◽  
Finite State Space

A lumping of a Markov chain is a coordinatewise projection of the chain. We characterise the entropy rate preservation of a lumping of an aperiodic and irreducible Markov chain on a finite state space by the random growth rate of the cardinality of the realisable preimage of a finite-length trajectory of the lumped chain and by the information needed to reconstruct original trajectories from their lumped images. Both are purely combinatorial criteria, depending only on the transition graph of the Markov chain and the lumping function. A lumping is strongly k-lumpable, if and only if the lumped process is a kth-order Markov chain for each starting distribution of the original Markov chain. We characterise strong k-lumpability via tightness of stationary entropic bounds. In the sparse setting, we give sufficient conditions on the lumping to both preserve the entropy rate and be strongly k-lumpable.

Sign in / Sign up

Export Citation Format

Share Document