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Durability/reliability design of products, such as auto exhaust systems, is essentially based on the observation of test data and the accurate interpretation of these data. Therefore, test planning and related data analysis are critical to successful engineering designs. To facilitate engineering applications, testing and data analysis methods have been standardized over the last decades by several standard bodies such as the American Society for Testing and Materials (ASTM). However, over the last few years, several effective testing and data analysis methods have been developed, and the existing standard procedures need to be updated to incorporate the new observations, knowledge, and consensus. In this paper, the common practices and the standard test planning and data analysis procedures are reviewed first. Subsequently, the recent development in accelerated testing, equilibrium based data fitting, design curve construction, and Bayesian statistical data analysis is presented.

This paper reviews the correlation concepts and tools available, with the emphasis on their historical origins, mathematical properties and applications. Two of the most commonly used statistical correlation indicators, i.e., modal assurance criterion (MAC) for structural deformation pattern identification/correlation and the coefficient of determination (R2) for data correlation are investigated. The mathematical structure of R2 is critically examined, and the physical meanings and their implications are discussed. Based on the insights gained from these analyses, a data scatter measure and a dependency measure are proposed. The applications of the measures for both linear and nonlinear data are also discussed. Finally, several worked examples in vehicle dynamics analysis and statistical data analyses are provided to demonstrate the effectiveness of these concepts.

Vehicle exhaust components and systems under fatigue loading often show multiple failure modes, which should be treated, at least theoretically, with rigorous advanced bi-modal and multi-modal statistical theories and approaches. These advanced methods are usually applied to mission-critical engineering applications such as nuclear and aerospace, in which large amounts of test data are often available. In the automotive industry, however, the sample size adopted in the product validation is usually small, thus the bi-modal and multi-modal phenomena cannot be distinguished with certainty.

Structural stress methods are now widely used in fatigue life assessment of welded structures and structures with stress concentrations. The structural stress concept is based on the assumption of a global stress distribution at critical locations such as weld toes or weld throats, and there are several variants of structural stress approaches available. In this paper, the linear traction stress approach, a nodal force based structural stress approach, is reviewed first. The linear traction stress approach offers a robust procedure for extracting linear traction stress components by post-processing the finite element analysis results at any given hypothetical crack location of interest. Pertinent concepts such as mesh-insensitivity, master S-N curve, fatigue crack initiation and growth mechanisms are also discussed.

Durability and reliability performance is one of the most important concerns of a recently developed Thermal Regeneration Unit for Exhaust (T.R.U.E-Clean®) for exhaust emission control. Like other ground vehicle systems, the T.R.U.E-Clean® system experiences cyclic loadings due to road vibrations leading to fatigue failure over time. Creep and oxidation cause damage at high temperature conditions which further shortens the life of the system and makes fatigue life assessment even more complex. Great efforts have been made to develop the ability to accurately and quickly assess the durability/reliability of the system in the early development stage. However, reliable and validated simplified engineering methods with rigorous mathematical and physical bases are still urgently needed to accurately manage the margin of safety and decrease the cost, whereas iterative testing is expensive and time consuming.

The approaches of obtaining both fatigue strength distribution and fatigue life distribution for a given set of fatigue S-N data are reviewed in this paper. A new fatigue S-N curve transformation technique, which is based on the fundamental statistics definition and some reasonable assumptions, is specifically developed in this paper to transform a fatigue life distribution to a fatigue strength distribution. The procedures of applying the technique to multiple-stress level, two-stress level, and one-stress level fatigue S-N data are presented.

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.

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.