Warp breakage data is a critical metric for assessing the durability of warp yarns, which typically follows a Weibull distribution. The three-parameter Weibull distribution is a prevalent distribution in which scale, position, and shape parameters influence the statistical information of the distribution. The confidence interval is the degree to which the true value has a certain probability of falling around the measurement result, and it is important statistical information. In instances where the calculation of the confidence interval of a Weibull distribution is performed in the presence of missing data, employing solely complete data estimation can lead to the introduction of bias. However, in the context of missing data, the utilization of bootstrap interpolation has been demonstrated to yield outcomes that are often superior to those obtained through unprocessed data. The specific process entails the simulation of the Weibull dataset, incorporating random missing values of 5%, 20%, 50%, and 75%, and the subsequent comparison of the results of calculating confidence intervals using not missing and Bootstrap interpolation. The experimental results demonstrate that the presence of missing data exerts a negligible influence on the extent of confidence intervals, and the Bootstrap interpolation method yields values that approximate the median. This phenomenon results in an overall scarcity of discrete data. The experiment was verified using real warp fracture data, and the results were essentially consistent with the simulation experiment.