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Fatigue life assessment is an integral part of the durability and reliability evaluation process of vehicle exhaust components and systems. The probabilistic life assessment approaches, including analytical, experimental, and simulation, CAE implementation in particular, are attracting significant attentions in recent years. In this paper, the state-of-the-art probabilistic life assessment methods for vehicle exhausts under combined thermal and mechanical loadings are reviewed and investigated. The loading cases as experienced by the vehicle exhausts are first categorized into isothermal fatigue, anisothermal fatigue, and high-temperature thermomechanical fatigue (TMF) based on the failure mechanisms. Subsequently, the probabilistic life assessment procedures for each category are delineated, with emphasis on product validation.

Fatigue testing and related fatigue life assessment are essential parts of the design and validation processes of vehicle components and systems. Fatigue bench test is one of the most important testing methods for durability and reliability assessment, and its primary function is to construct design curves based on a certain amount of repeated tests, with which recommendations on product design can be advised. How to increase the accuracy of predictions from test results, the associated life assessment, and to reduce the cost through reducing test sample size is an active and continuous effort. In this paper the current engineering practices on constructing design curves for fatigue test data are reviewed first.

Engineering components and systems are usually subjected to mixed-mode and multiaxial fatigue loadings, and these conditions should be considered in product durability and reliability design and the maintenance of aging equipment, especially mission-critical components and systems. However, modeling the damage and degradation processes under these complex loading conditions is difficult and challenging task because not only the concepts, such as range, mean, peak, valley etc., developed for uniaxial loading usually cannot be directly transferred to mixed-mode and multiaxial loadings, but also some very unique phenomena related to these complex loading conditions. One such a phenomenon is the loading path effect that can be simply described as: out-of-phase loading is more damaging than in-phase loading for some ductile materials.

A modern definition of quality control and improvement is the reduction of variability in processes and products. The reduced variability can be directly translated into lower costs, better functions and fewer repairs. However, the final quality of processes and products is sometimes derived from other measured variables through some implicit or explicit functional relationships. Sometimes, a tiny uncertainty in a variable can produce a huge uncertainty in a derived quantity. Therefore, the propagation of uncertainty needs to be understood and the individual variables need to be well controlled. More importantly, the critical factors that affect quality the most should be identified and thoroughly investigated. Design of experiments and statistical control plays central roles in finding root cause of failure, reduction of variability and quality improvement.

In product design and development stage, validation assessment methods that can provide very high reliability and confidence levels are becoming highly demanded. High reliability and confidence can generally be achieved and demonstrated by conducting a large number of tests with the traditional approaches. However, budget constraints, test timing, and many other factors significantly limit test sample sizes. How to achieve high reliability and confidence levels with limited sample sizes is of significant importance in engineering applications. In this paper, such approaches are developed for two fundamental and widely used methods, i.e. the test-to-failure method and the Binomial test method. The concept of RxxCyy (e.g. R90C90 indicates 90% in reliability and 90% in confidence) is used as a criterion to measure the reliability and confidence in both the test-to-failure and the Binomial test methods.