Bogataj derived estimates for the mangitude of perturbations in values of a quadratic functional, connected with the total (i.e. holding and control) cost of an inventory system, which is governed by a differential-delay equation, especially the realtionship between the perturbed delay b in the control vector u(t) and sup ℝ, where ℝ stands for (the absolute value of) the difference between costs of original and perturbed system. In this paper the results are generalized to the case where the perturbed delay b is a random variable, uniformly distributed on [0,β], where β means the unperturbed delay in control. The authors derive the expression for expected value of sup ℝ. It is shown that its magnitude significantly depends on the whole structure of the system and not only on the magnitude of the delays involved and there is some kind of ‘trade-off’, paid for the desired level of the reliability of the system, on behalf of results in achieving the primary goal, which is minimization of the cost function.
