Archive
Special Issues
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
Author
Ahmed Raza, Department of Electronics, National Aviation University, Kiev, Ukraine
Article Tools
Abstract
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.
Keywords
Corrective Maintenance, Imperfect Checks, Operational Reliability, Expected Costs, Sequential Checks
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
References
[1]
R. E. Barlow and F. Proschan, Mathematical Theory of Reliability, New York: John Wiley & Sons, 1965.
[2]
P. R. Tadikamalla, “An inspection policy for the gamma failure distributions,” J. Oper. Res. Soc., vol. 30, pp. 77–80, 1979.
[3]
V. Senna and A. K. Shahani, “A simple inspection policy for the detection of failure”, Eur. J. Oper. Res., vol. 23, pp. 222–227, 1986.
[4]
N. Kaio and S. Osaki, “Comparison of inspection policies,” J. Oper. Res. Soc., vol. 40, pp. 499–503, 1989.
[5]
T. Nakagawa, Maintenance Theory of Reliability, London: Springer, 2005.
[6]
N. Kaio and S. Osaki, “Optimal inspection policy with two types of imperfect inspection probabilities,” Microelectronics Rel., vol. 26, pp. 935–942, 1986.
[7]
M. S. Srivastava and Y. H. Wu, “Estimation & testing in an imperfect-inspection model,” IEEE Trans. Rel., vol. 42, pp. 280–286, 1993.
[8]
K. He, L. M. Maillart, and O. A. Prokopyev, “Scheduling preventive maintenance as a function of an imperfect inspection interval,” IEEE Trans. Rel., vol. 64, № 3, pp. 983 - 997, 2015.
[9]
R. I. Zequeira and C. Bérenguer, “Optimal scheduling of non-perfect inspections,” IMA J. Manag. Math., vol. 17, № 2, pp. 187-207, 2012.
[10]
M. Berrade, A. Cavalcante, and P. Scarf, “Maintenance scheduling of a protection system subject to imperfect inspection and replacement,” Eur. J. Oper. Res., vol. 218, pp. 716-725, 2012.
[11]
F. Badıa and M. D. Berrade, “Optimal inspection and preventive maintenance of units with revealed and unrevealed failures,” Rel. Eng. Syst. Safety, vol. 78, pp. 157-163, 2002.
[12]
Y. Lam, “An inspection-repair-replacement model for a deteriorating system with unobservable state,” J. Applied Prob., vol. 40, № 4, pp. 1031–1042, 2003.
[13]
A. Raza and V. Ulansky, “Modelling of predictive maintenance for a periodically inspected system,” Procedia CIRP, vol. 59, pp. 95-101, 2017.
[14]
C. Ma, Y. Shao, and R. Ma, “Analysis of equipment fault prediction based on metabolism combined model,” J. Machinery Manufac. and Automation, vol. 2(3), pp. 58–62, 2013.
[15]
A. Raza and V. Ulansky “Modelling condition monitoring inspection intervals,” Electronics and electrical engineering book, London: CRC Press, pp. 45-51, 2015.
PUBLICATION SERVICES