Semi-Markovian Model of Monotonous System Maintenance with Regard to its Elements’ Deactivation and Age

Yuriy E. Obzherin, Aleksey I. Peschansky
DOI: 10.4236/am.2010.13029                

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.

Keywords

Maintenance, Semi-Markovian Process, System Stationary Characteristics, System Performance Indexes Optimization

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	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.
[2]	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.
[3]	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.
[4]	F. Beichelt and P. Franken, “Zuverl?ssigkeit und Instan- phaltung,” Mathematische Methoden, VEB Verlag Tech- nik, Berlin, 1983.
[5]	R. E. Barlow and F. Proschan, “Mathematical Theory of Reliability,” John Wiley and Sons, New York, 1965.
[6]	V. A. Kashtanov and A. I. Medvedev, “The Theory of Complex Systems’ Reliability (Theory and Practice),” European Center for Quality, Moscow, 2002.
[7]	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.
[8]	V. S. Korolyuk and A. F. Turbin, “Markovian Restoration Processes in the Problems of System Reliability,” Nau- kova dumka, Kiev, 1982.
[9]	A. N. Korlat, V. N. Kuznetsov, M. I. Novikov and A. F. Turbin, “Semi-Markovian Models of Restorable and Service Systems,” Shtiintsa, Kishinev, 1991.
[10]	V. M. Shurenkov, “Ergodic Markovian Processes,” Nau- ka, Moscow, 1989.