概率论与数理统计课程教学问题与汽车检测专业应用融合探究——基于贝叶斯公式深度案例的教学改革实践

Exploring the Integration of Probability Theory and Mathematical Statistics Course Teaching with the Application in Automotive Inspection Specialty—A Teaching Reform Practice Based on the In-Depth Case of Bayes’ Formula

摘要: 概率论与数理统计是汽车检测与维修技术专业的重要基础课程，但长期存在理论教学与专业实践脱节、学生学习兴趣不足等问题。本文以授课计划中“条件概率与贝叶斯公式”为切入点，选取“汽车发动机抖动故障诊断”作为典型应用场景，详细展示了从历史维修数据获取先验概率、设计检测指标确定条件概率、首次贝叶斯更新到引入第二项证据进行迭代更新的完整过程。通过数据表格和概率对比，定量呈现了点火系统故障的确信度由50%提升至71.4%、最终达96.6%的诊断优势。在此基础上，本文讨论了案例模型在故障互斥性假设、数据获取及多重故障场景下的局限性。研究表明，深度嵌入专业案例并辅以可视化手段，有望降低抽象概念的理解门槛，激发学生学习内驱力。本文为概率统计课程面向汽车类应用型人才培养的教学改革提供了一个具有参考价值的案例范式。

Abstract: Probability theory and mathematical statistics are foundational courses for automotive inspection and maintenance majors, yet a persistent disconnect between theoretical instruction and professional practice, along with low student engagement, has long been observed. This paper focuses on “conditional probability and Bayes’ formula” in the teaching plan and selects “automobile engine shaking fault diagnosis” as a typical application scenario. It systematically demonstrates the entire Bayesian reasoning process—from obtaining prior probabilities from historical maintenance records, designing diagnostic indicators to determine conditional probabilities, conducting the first Bayesian update, to introducing a second piece of evidence for iterative refinement. Quantitative results, presented via data tables and probability comparisons, show that the posterior confidence in ignition system failure increases from 50% to 71.4% and finally to 96.6%. Based on this case, this paper discusses the limitations of the case model under the assumptions of fault mutual exclusivity, data acquisition challenges, and complex multiple-fault scenarios. Findings indicate that deeply embedding professional cases with visualization tools is expected to lower the cognitive threshold for abstract concepts and enhance students’ intrinsic motivation. This paper provides a valuable reference paradigm for the teaching reform of probability and statistics courses oriented toward applied talent cultivation in the automotive industry.