The well-known formulas for calculating the mean restoration time (as a mathematical expectation of the restoration time of an item–after-failure operational state) assume that the characteristics of the restoration process are set on the entire time axis. This circumstance makes it difficult to use these formulas in solving engineering problems, since, on the one hand, a specific restoration process is limited by the duration of repair works, and, on the other hand, the approximation of the restoration process over an adjacent infinite period of time after the completion of the repair works is not adequate to the process as observed. Then a problem to solve is to calculate the mean restoration time of an item through the characteristics of the restoration process, knowing the ways they work for a limited period of time, the length of which is determined by (i), the duration of repair works, and (ii), their specific conditions. In this paper, such conditions are considered as some specified level of the gamma-percentile restoration time of an item, as well as the restoration rate of an item, which results from the repair works. The selected characteristics of the restoration process have turned out to be sufficient to solve the task. In this paper, the formulas are proved for calculating the indicator “mean restoration time” based on the functional manifestations of the restoration process characteristics (taking into account the specified gamma-percentile restoration level, and the restoration rate) during the repair works to restore the operational state of an item after failure. The proved formulas are valid for any law of the restorative process. The paper also provides two examples of calculating the mean restoration time. In the first example, the uniform law of the restoration process is considered for the time interval of the item being repaired after failure, and in the second example, its exponential law is under study.

Indicator of residual life of technogenic-hazardous objects is determined for the for the hazardous operational life duration. Calculation formulas, estimates, and limit values are proved for the determined indicator.

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The widespread use of cutting-edge components in the composition of non-restorable items has made it difficult to assess their reliability at the stages of designing and production. Therefore, items with underestimated values of the assigned (warranted) operating life are put into operation. By now, the service life of such items has reached the assigned limits, the items still maintaining a fairly high dependability rate. Thus, there has been a problem of extending the service life beyond the originally assigned rates. As originally assigned rates are determined by such measures as the mean operating life and gamma-percentile operating life, the non-restorable item’s life margin is determined as related to these rates by means of measures of the residual operating life, namely the mean residual operating life and gamma-percentile residual operating life. The mean residual operating life and gamma-percentile residual operating life are determined in this paper, to calculate the extendable service life. For these measures, we have derived calculation formulas and assessments which make it possible to determine the extended service life. In addition, for these measures, calculation formulas and assessments are obtained for non-restorable items whose margin allocation is distributed exponentially and uniformly. The paper examines the issues of attainability of the obtained assessments and the conditions of their attainability; also, the influence of failure rate monotonic change on the assessments is analyzed.