基于Copula理论的竞争失效相关场合加速试验方法研究

Predicting the equipment’s life accurately and efficiently has great importance to guarantee the equipments to make maintenance plans and serve reliably and safely. The products may suffer many different failure modes, which may react with each other. When the product fails because of one of many possible failure modes, and the lifetime of the product is the latent failure time of the first failure mode, then we call this competing failure. Therefore, the study of theories of life prediction of products with competing failures is of great significance. Aiming at the problems that the competing failures are dependent, and efficiency of traditional life test is too low to gain valid and sufficient test data, this project propose a new idea from introduction of accelerated testing and copula theory: copula model is applied to combine the marginal distribution of the competing failure models with the time to failure distribution of the products, and based on this, the studies of a general statistical inference model and optimal design for accelerated testing with dependent competing failures are carried out to realize the accurate and efficient life prediction. In this project, the theory and methodology including statistical inference, optimal design method and copula construction & selection method for accelerated testing with dependent competing failures are studied systematically, and the experimental validation in combination with engineering application is implemented, and it will consequently provide theoretic and methodological support to life prediction of products with competing failures.

准确高效预测重大装备及其关键部件的寿命和可靠性水平是提高其运行可靠性、安全性、可维护性的基础。本项目针对重大装备及其关键部件寿命预测和可靠性评估需求及其竞争失效相关的事实，瞄准竞争失效相关场合加速试验统计分析方法和优化设计方法这两个制约装备寿命预测与可靠性评估准确性和效率的关键科学问题，基于Copula理论，以多维Copula模型为工具建立各竞争失效模式潜在寿命分布与产品寿命联合分布之间的关系，系统研究基于Copula理论的竞争失效相关性建模、加速试验统计分析和试验优化设计等理论问题，建立一套基于Copula理论的竞争失效相关场合加速试验理论与方法，有效指导产品竞争失效相关场合加速试验方案优化设计和数据统计分析，提高加速试验效率和可靠性评估准确性，为准确高效预评估产品可靠性水平、预测产品寿命提供理论方法支撑，同时为重大装备及其关键部件的可靠、安全运行提供理论和工程保障。

本项目针对重大装备及其关键部件寿命预测和可靠性评估需求及其竞争失效相关的事实，研究了竞争失效相关场合加速试验统计分析方法和优化设计方法这两个制约装备寿命预测与可靠性评估准确性和效率的关键科学问题，主要研究内容包括：（1）基于Copula理论的竞争失效相关性分析与建模；（2）竞争失效相关场合加速试验统计分析方法；（3）竞争失效相关场合加速试验优化设计方法基于Copula理论；（4）基于Copula理论的滚动轴承竞争失效相关场合加速试验应用验证。本项目的特色与创新之处包括：①率先提出了系统研究基于Copula理论的竞争失效相关场合加速试验统计分析方法的思路。通过引入Copula 连接函数描述各竞争失效模型边缘分布和产品失联合分布之间的相关关系，建立各竞争失效模式之间的相关性模型，在相关性模型的基础上，系统研究竞争失效相关场合加速试验统计分析方法。②提出基于Copula理论的竞争失效相关场合加速试验仿真优化设计方法。当前的加速试验优化设计方法都基于单一失效和竞争失效独立的情形，本项目提出了基于Copula理论，研究竞争失效相关场合加速试验仿真优化设计方法。③提出针对竞争失效相关场合加速试验的多维Copula模型构造和选择方法，系统研究和完善Copula理论在加速试验中的应用问题。项目主要取得的成果包括：①理论成果：建立了基于Copula理论的竞争失效相关场合加速试验统计分析模型和仿真优化设计方法，为竞争失效产品加速试验数据分析和方案设计提供了理论依据，形成了系统的基于加速试验和Copula理论的竞争失效产品寿命预测理论与方法。②技术方法：形成了一套滚动轴承加速寿命试验方法。本项目的研究成果可有效指导产品竞争失效相关场合加速试验方案优化设计和数据统计分析，提高加速试验效率和可靠性评估准确性，为准确高效预评估产品可靠性水平、预测产品寿命提供了理论方法支撑，同时为重大装备及其关键部件的可靠、安全运行提供理论和工程保障。