The railroad industry has historically used the 2-Parameter Weibull equation to determine the rate of rail fatigue defect occurrences and to forecast the fatigue life of railroad rail. However, the 2-Parameter Weibull equation has significant limitations to include inability to analyze segments of track with limited number of rail defects. These limitations are addressed through modification of the traditional 2-Parameter Weibull equation with a novel approach developed from Parametric Bootstrapping. The result is a Parametric Bootstrapping modified Weibull (PBW) forecasting approach. This methodology is applied to rail segments with insufficient numbers of defects to allow for appropriate defect forecasting analysis. Thus, the PBW method provides reasonable estimates of the rate of defects for track segments that have little or no prior defect history. This approach allows for more track to be analyzed and forecasts the probability of rail defect occurrence as a function of key parameters such as cumulative traffic over the rail. A validation of the proposed methodology was performed. Comparison of the output results of over 300,000 track segments with over 200,000 rail defects showed a major improvement in percentage of segments with reasonable Weibull parameters (alpha and beta). This percentage increased from 11% of segments using traditional Weibull analysis to 77% of segments using Parametric Bootstrap modified Weibull approach. These results show that the PBW Analysis approach introduced here offers a more accurate and effective approach to determining the probability of developing future rail defects. This provides a benefit to railroads in planning maintenance of their expensive rail assets.

铁路行业历来使用 2 参数威布尔方程来确定钢轨疲劳缺陷的发生率并预测铁路钢轨的疲劳寿命。然而，2 参数 Weibull 方程有很大的局限性，包括无法分析轨道缺陷数量有限的轨道段。这些限制是通过使用从参数自举开发的新方法修改传统的 2 参数威布尔方程来解决的。结果是参数自举修正威布尔 (PBW) 预测方法。这种方法适用于缺陷数量不足的铁路段，以便进行适当的缺陷预测分析。因此，PBW 方法提供了对具有很少或没有先前缺陷历史的轨道段的缺陷率的合理估计。这种方法允许分析更多的轨道，并根据关键参数（例如铁路上的累计交通量）预测铁路缺陷发生的概率。对提议的方法进行了验证。将超过 300,000 个轨道段的输出结果与超过 200,000 个轨道缺陷的输出结果进行比较，表明具有合理 Weibull 参数（alpha 和 beta）的段的百分比有了重大改进。这个百分比从使用传统威布尔分析的 11% 的段增加到使用参数引导修改威布尔方法的段的 77%。这些结果表明，此处介绍的 PBW 分析方法提供了一种更准确、更有效的方法来确定未来出现铁路缺陷的可能性。这为铁路计划维护其昂贵的铁路资产提供了好处。