Insufficiency of Instantaneous Strength Determinations for Failure Rate Prediction

The failure of an element subjected to a steady applied stress is associated with the time-wise deterioration of the element's strength. At the instant of failure, the element can no longer perform to specifications. The strength of the element can be obtained at a specified point in time by abruptly modifying the applied stress to a level which causes the element to fail. The instantaneous strengths determined by this procedure are investigated for the possibility of reducing the test time necessary in obtaining the failure rate associated with exponentially distributed failure times. A simple, physically plausible class of strength deterioration functions is considered and the distributional character of the instantaneous strengths at any time instant is determined. It is found that when the underlying distribution of time to failure is exponential, the instantaneous strengths have distributions which are invariant with time. This result indicates that no clue to the form of strength deterioration can be obtained by testing for the instantaneous strengths. Thus the conclusion is reached, in the case of the exponential failure distribution, that instantaneous destruction tests for strength determination are ineffective for assessing the underlying failure rate.