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

结构部件的疲劳强度或寿命具有不确定性，其分布的参数估计通常仅根据有限数量的实验数据进行，当然，这些数据会因样本而异。因此，在给定的服务期内的结构部件在服务负载下，这是通过使用这样的参数估计值进行评估的失效概率已首先被建模为基于恒定应力幅下的疲劳寿命遵循对数正态分布的假设的统计。然后，介绍了一个简单但重要的基于可靠性的抗疲劳设计原则，该原则要求在规定的可靠度下，失效概率的值小于规定的允许值。进一步，详细考虑了容许失效概率、置信度或可靠度水平与样本容量之间的关系。最后，建立了在可靠性起重要作用的情况下，如何确定疲劳试验的最佳样本量以满足设计要求的方法。为了适应威布尔分布作为统计寿命模型的广泛适用性，本文讨论了威布尔分布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.