Determination of Optimum Sample Size in Reliability-Based Fatigue-Proof Design

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The fatigue strength or life of a structural component is of indeterministic nature, and the parameter estimation of its distribution is usually performed on the basis of only a limited number of experimental data which would, of course, vary from sample to sample. Therefore the failure probability during a given service period of a structural component under service loading which is evaluated by use of such parameter estimates has first been modelled as a statistics based upon the assumption that fatigue life under constant stress amplitude follows a log-normal distribution. Then, a simple but important reliability-based fatigue-proof design principle is introduced which requires that a value samller than a proscribed allowable value for the failure probability be correct with a prescribed reliability. Further, the relationship among allowable faiure probability, confidence or reliability level and sample size is considered in detail. Finally, the procedure has been established of how to determine the optimum sample size of the fatigue experiment in order to meet the design requirement where reliability plays an important role. In referance to wide applicability of a Weibull distribution as a statistical life model, the parameter-free statistics of the estimators of its shape and scale parameters have been discussed and their statistical properties have been clarified with the aid of Monte-Carlo simulation techniques.