Mathematical Model of Corrective Maintenance Based on Operability Checks for Safety Critical Systems
American Journal of Applied Mathematics
Volume 6, Issue 1, February 2018, Pages: 8-14
Received: Jan. 20, 2018; Accepted: Feb. 1, 2018; Published: Mar. 5, 2018
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Ahmed Raza, Department of Electronics, National Aviation University, Kiev, Ukraine
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Maintenance based on equipment operability checks is widely used for technical systems of various physical nature. For commercial and military aircraft such checks are carried-out after a certain amount of time according to specific maintenance programs. Therefore, great attention in the research literature is paid to the mathematical modeling of maintenance on the basis of equipment operability checks. In this study, a mathematical model of corrective maintenance with operability checks at discrete times for the safety critical systems is considered. The criterion of the corrective maintenance effectiveness is proposed to provide a given level of operational reliability with minimum maintenance costs. A finite time interval is considered for modeling the moments of the system operability checks. The graph of decision making is analyzed for imperfect operability checks and the probabilities of possible decisions are determined. Analytical equations for the operational reliability and expected maintenance costs are derived for an arbitrary distribution of time to failure. The criteria of determining optimal policies of sequential checks are formulated. Numerical examples illustrate the developed theory. For the first time it has been shown that conditional probabilities of correct and incorrect decisions when checking system operability are dependent on the time of failure and parameters of the degradation model. Numerical calculations have shown that in the case of mixing deteriorating systems with different initial time points of operation, the interval between operability checks converges to a constant periodicity.
Corrective Maintenance, Imperfect Checks, Operational Reliability, Expected Costs, Sequential Checks
To cite this article
Ahmed Raza, Mathematical Model of Corrective Maintenance Based on Operability Checks for Safety Critical Systems, American Journal of Applied Mathematics. Vol. 6, No. 1, 2018, pp. 8-14. doi: 10.11648/j.ajam.20180601.12
Copyright © 2018 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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