1.1 本规程涵盖了石墨单轴强度数据的报告以及截尾和非截尾数据的概率分布参数估计。石墨材料的破坏强度被视为连续随机变量。通常，许多试样不符合以下标准:试验方法 C565型 , C651型 , C695 , C749 实践 C781 或指南 D7775 . 记录每个试样失效时的载荷。由此产生的失效应力用于获得与潜在总体分布相关的参数估计。这种做法仅限于可由双参数威布尔分布表征的失效强度。此外，本规程仅限于主要承受单轴应力状态的试样（主要是拉伸和弯曲试样）。 1.2 出于各种原因对失效时的强度进行测量:比较两种材料的相对质量，预测相关结构的失效概率，或确定应用中的极限载荷。本规程提供了一种估算分布参数的程序，这些参数是估算特定失效概率水平的载荷极限所需的。 1.3 本国际标准是根据世界贸易组织技术性贸易壁垒（TBT）委员会发布的《关于制定国际标准、指南和建议的原则的决定》中确立的国际公认标准化原则制定的。 ====意义和用途====== 5.1 威布尔分布存在两个和三个参数公式。 这种做法仅限于双参数公式。本实践的目的是通过使用包含故障数据的定义良好的函数来获得未知威布尔分布参数的点估计。这些函数称为估计量。期望估计量是一致且有效的。此外，估计器应产生分布参数的唯一、无偏估计 ( 6. ) . 存在不同类型的估计量，例如矩估计量、最小二乘估计量和最大似然估计量。本实践详细介绍了最大似然估计量的使用。 5.2 拉伸和弯曲试样是石墨最常用的测试配置。观察到的强度值取决于试样尺寸和试验几何形状。近似各向同性石墨的拉伸和弯曲试样失效数据 ( 7. ) 如所示 图1 . 由于石墨材料的失效数据可能取决于试样几何形状，因此威布尔分布参数估计( m , S c )应针对给定的试样几何形状进行计算。 图1 几乎各向同性石墨的拉伸试样（左）和弯曲试样（右）的破坏强度 ( 7. ) 5.3 威布尔参数的偏差和不确定性取决于试样总数。随着采集更多样本，参数估计的可变性呈指数下降。然而，在进行额外强度试验的成本可能不合理的情况下，达到了回报递减的点。这建议限制用于确定威布尔参数的试样数量，以获得与参数估计相关的期望置信水平。所需的样本数量取决于结果参数估计或结果置信边界中所需的精度。 有关置信边界计算的详细信息（与估计精度直接相关）如所示 8.3 和 8.4 .

1.1 This practice covers the reporting of uniaxial strength data for graphite and the estimation of probability distribution parameters for both censored and uncensored data. The failure strength of graphite materials is treated as a continuous random variable. Typically, a number of test specimens are failed in accordance with the following standards: Test Methods C565 , C651 , C695 , C749 , Practice C781 or Guide D7775 . The load at which each specimen fails is recorded. The resulting failure stresses are used to obtain parameter estimates associated with the underlying population distribution. This practice is limited to failure strengths that can be characterized by the two-parameter Weibull distribution. Furthermore, this practice is restricted to test specimens (primarily tensile and flexural) that are primarily subjected to uniaxial stress states. 1.2 Measurements of the strength at failure are taken for various reasons: a comparison of the relative quality of two materials, the prediction of the probability of failure for a structure of interest, or to establish limit loads in an application. This practice provides a procedure for estimating the distribution parameters that are needed for estimating load limits for a particular level of probability of failure. 1.3 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee. ====== Significance And Use ====== 5.1 Two- and three-parameter formulations exist for the Weibull distribution. This practice is restricted to the two-parameter formulation. An objective of this practice is to obtain point estimates of the unknown Weibull distribution parameters by using well-defined functions that incorporate the failure data. These functions are referred to as estimators. It is desirable that an estimator be consistent and efficient. In addition, the estimator should produce unique, unbiased estimates of the distribution parameters ( 6 ) . Different types of estimators exist, such as moment estimators, least-squares estimators, and maximum likelihood estimators. This practice details the use of maximum likelihood estimators. 5.2 Tensile and flexural specimens are the most commonly used test configurations for graphite. The observed strength values depend on specimen size and test geometry. Tensile and flexural test specimen failure data for a nearly isotropic graphite ( 7 ) is depicted in Fig. 1 . Since the failure data for a graphite material can be dependent on the test specimen geometry, Weibull distribution parameter estimates ( m , S c ) shall be computed for a given specimen geometry. FIG. 1 Failure Strengths for Tensile Test Specimens (left) and Flexural Test Specimens (right) for a Nearly Isotropic Graphite ( 7 ) 5.3 The bias and uncertainty of Weibull parameters depend on the total number of test specimens. Variability in parameter estimates decreases exponentially as more specimens are collected. However, a point of diminishing returns is reached where the cost of performing additional strength tests may not be justified. This suggests a limit to the number of test specimens for determining Weibull parameters to obtain a desired level of confidence associated with a parameter estimate. The number of specimens needed depends on the precision required in the resulting parameter estimate or in the resulting confidence bounds. Details relating to the computation of confidence bounds (directly related to the precision of the estimate) are presented in 8.3 and 8.4 .