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.
Highlights
At present, corrective maintenance based on operability checks is widely used to maintain the operational reliability of various technical systems
Mathematical models of corrective maintenance based on operability checks can be conditionally divided into the two groups: models with perfect checks and models with imperfect checks
If there was no failure on the interval [0, (n + 1) τ] or it was not detected, at the time (n + 1) τ the system is American Journal of Applied Mathematics 2018; 6(1): 8-14 replaced by a new one
Summary
Corrective maintenance based on operability checks is widely used to maintain the operational reliability of various technical systems Evidence of this is a large number of publications on periodic and sequential plans of operability checks. Models with perfect checks were considered in a large number of publications, for example, in [1,2,3,4,5] In these studies, the problems of determining the optimal moments of checks are considered. A new maintenance model is developed for determining optimal moments of operability checks for safety critical systems. The proposed maintenance model takes into account the dependence of the probabilities of correct and incorrect decisions on the time and parameters of the degradation process
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