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An optimal replacement model for gamma deteriorating systems is studied.This methodology uses a gamma distribution to model the material degradation,and the impact of imperfect maintenance actions on the system reliability is investigated.The state of a degrading system immediately after the imperfect maintenance action is assumed as a random variable and the maintenance time follows a geometric process.A maintenance policy (N) is applied by which the system will be repaired whenever it experiences Nth preventive maintenance (PM),and an optimal policy (N*) could be determined numerically or analytically for minimizing the long-run average cost per unit time.Finally,a numerical example is presented to demonstrate the use of this policy.