In the direct methods for evaluating reliability of industrial machinery, performance indicators are ascertained from statistical analyses of the randomly fluctuating response variable using pre-established threshold levels of acceptable performance. The accuracy of the results depends directly on the rigor of the probabilistic procedure employed. In this paper, a new approach for calculating the probability measures of the randomly enveloped areas of the response excursions about any given threshold level is presented. The area excursions contain important information on both the time durations of the excursions as well as their intensity levels above the critical value and thus give a direct reliability estimate of the system performance. The mathematical development of the method, derivation of reliability indices, sample calculations, and life estimates are included.

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