Some Statistical Aspects of the Determination of a Safe Life from Fatigue Data

摘要

The probability that within a future large second sample no failures will occur before the expiration of a safe service life estimated from a small first sample and the probability that the proportion of all future observations failing before the estimated safe service life is smaller than a given proportion, are the two measures of safety that we adopt here. Assuming the logarithm of the fatigue life is normal with known variance, we derive formulae for these measures of safety. Setting the safe life as some fraction of the mean estimated by the first sample, we then compare the influence of other parameters on these measures of safety. From this assumption it is shown that one has virtually as high an assurance of safety, measured by the first criterion, when using only the minimum of the first sample, as one does by using all the observations in the first sample. If one uses the standard second criterion, namely, the confidence level of a lower tolerance bound, as a measure such an advantage is not retained. (Author)