Research ArticleOpen AccessGoogle Scholar indexed
Semi-Markovian Model of Monotonous System Maintenance with Regard to its Elements’ Deactivation and Age
- 1
- 2
Applied Mathematics·Volume 01 (2010)·Pages 234–243·Published 29 September 2010·DOI10.4236/am.2010.13029
Copy link · social · email
Abstract
An explicit form of reliability and economical stationary performance indexes for monotonous multicomponent system with regard to its elements’ maintenance has been found. The maintenance strategy investigated supposes preventive maintenance execution for elements that has attained certain operating time to failure. Herewith for the time period of elements’ maintenance or restoration operable elements, functionally connected with the failed ones, are deactivated. The problems of maintenance execution frequency optimization have been solved. For the model building the theory of semi-Markovian processes with a common phase field of states is used.
KeywordsMaintenanceSemi-Markovian ProcessSystem Stationary CharacteristicsSystem Performance Indexes Optimization
- C. Valdez-Flores and R. M. Feldman, “A Survey of Preventive Maintenance Models for Stochastically Deteriorating Single-Unit Systems,” Naval Research Logistics, Vol. 36, No. 4, 1989, pp. 419-446.
- D. I. Cho and M. Parlar, “A Survey of Maintenance Models for Multi-Unit Systems,” European Journal of Operational Research, Vol. 51, No. 2, 1991, pp. 1-23.
- R. Dekker and R. A. Wildeman, “A Review of Multi- Component Maintenance Models with Economic Depen- dence,” Mathematical Methods of Operations Research, Vol. 45, No. 3, 1997, pp. 411-435.
- F. Beichelt and P. Franken, “Zuverl?ssigkeit und Instan- phaltung,” Mathematische Methoden, VEB Verlag Tech- nik, Berlin, 1983.
- R. E. Barlow and F. Proschan, “Mathematical Theory of Reliability,” John Wiley and Sons, New York, 1965.
- V. A. Kashtanov and A. I. Medvedev, “The Theory of Complex Systems’ Reliability (Theory and Practice),” European Center for Quality, Moscow, 2002.
- A. I. Peschansky, “Monotonous System Maintenance with Regard to Operating Time to Failure of Each Element,” Industrial Processes Optimization, Vol. 11, 2009, pp. 77-83.
- V. S. Korolyuk and A. F. Turbin, “Markovian Restoration Processes in the Problems of System Reliability,” Nau- kova dumka, Kiev, 1982.
- A. N. Korlat, V. N. Kuznetsov, M. I. Novikov and A. F. Turbin, “Semi-Markovian Models of Restorable and Service Systems,” Shtiintsa, Kishinev, 1991.
- V. M. Shurenkov, “Ergodic Markovian Processes,” Nau- ka, Moscow, 1989.