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

结构部件的疲劳强度或寿命是不确定的，其分布的参数估计通常仅基于有限数量的实验数据，当然，这些数据会因样本而异。因此，基于恒应力幅值下疲劳寿命服从对数正态分布的假设，首先将使用载荷下结构构件在给定服役周期内的失效概率建模为统计量。然后，介绍了一种简单而重要的基于可靠性的疲劳抗设计原则，该原则要求失效概率的取值比所禁止的许用值在规定的可靠度下是正确的。此外，还详细讨论了容许失效概率、置信度或可靠性水平与样本量之间的关系。最后，建立了如何确定疲劳试验的最佳样本量以满足可靠性起重要作用的设计要求的程序。针对威布尔分布作为统计寿命模型的广泛适用性，讨论了其形状参数和尺度参数估计量的无参数统计量，并借助于蒙特卡罗模拟技术阐明了它们的统计性质。

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.