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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.

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.

In the Big Data era, the capability in statistical and probabilistic data characterization, data pattern identification, data modeling and analysis is critical to understand the data, to find the trends in the data, and to make better use of the data. In this paper the fundamental probability concepts and several commonly used probabilistic distribution functions, such as the Weibull for spectrum events and the Pareto for extreme/rare events, are described first. An event quadrant is subsequently established based on the commonality/rarity and impact/effect of the probabilistic events. Level of measurement, which is the key for quantitative measurement of the data, is also discussed based on the framework of probability. The damage density function, which is a measure of the relative damage contribution of each constituent is proposed. The new measure demonstrates its capability in distinguishing between the extreme/rare events and the spectrum events.

A probabilistic distribution function roughly consists of two parts: the middle part and the tails. The fatigue life distribution at a stress/load level is often described with two-parameter lognormal or Weibull distribution functions, which are more suitable for modeling the mean (middle) behaviors. The domains of the conventional probabilistic distribution functions are often unbounded, either infinite small (0 for the two-parameter Weibull) or infinite large or both. For most materials in low- and medium-cycle fatigue regimes, the domains of fatigue lives are usually bounded, and the inclusion of the bounds in a probabilistic model is often critical in some applications, such as product validation and life management. In this paper, four- and five-parameter Weibull distribution functions for the probabilistic distributions with bounds are developed. Finally, the applications of these new models in fatigue data analysis and damage assessment are provided and discussed.

Recent stringent government regulations on emission control and fuel economy drive the vehicles and their associated components and systems to the direction of lighter weight. However, the achieved lightweight must not be obtained by sacrificing other important performance requirements such as manufacturability, strength, durability, reliability, safety, noise, vibration and harshness (NVH). Additionally, cost is always a dominating factor in the lightweight design of automotive products. Therefore, a successful lightweight design can only be accomplished by better understanding the performance requirements, the potentials and limitations of the designed products, and by balancing many conflicting design parameters. The combined knowledge-based design optimization procedures and, inevitably, some trial-and-error design iterations are the practical approaches that should be adopted in the lightweight design for the automotive applications.

It is important to quantitatively characterize the automotive events in order to not only accurately interpret their past but also to reliably predict and forecast their short-term, medium-term, and even long-term future. In this paper, several automotive industry related events, i.e. vehicle safety, vehicle weight/HP ratio, the emissions of CO2, HC, CO, and NOx, are analyzed to find their general trends. Exponential and power law functions are used to empirically fit and quantitatively characterize these data with an emphasis on the two functions’ effectiveness in predictability. Finally, three empirical emission laws based on the historical HC, CO, and NOx data are proposed and the impact of these laws on emission control is discussed.

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.

Driven by diesel engine emission regulation, more emission aftertretment products have been under development by Tenneco to address the Particular Matter (PM) and NOx reduction needs. The T.R.U.E. (Thermal Regeneration Unit for Exhaust) Clean active thermal management system is one of the examples to reduce PM. The system is designed to increase exhaust temperatures for DPF (Diesel Particulate Filter) regeneration. This product is exposed to high temperature and high oxidation. Therefore, thermal fatigue, creep, oxidation and the interaction become critical mechanism to be considered for its durability. One of the key challenges to validate this product is to find a way of accelerated testing for thermal, creep, and oxidation as well as for vibration. In this paper, accelerated durability test strategy for high temperature device like T.R.U.E Clean is addressed.

Corrosion-fatigue (CF) and stress corrosion cracking (SCC) have long been recognized as the major degradation and failure mechanisms of engineering materials under combined mechanical loading and corrosive environments. How to model and characterize these failure phenomena and how to screen, rank, and select materials in corrosion-fatigue and stress corrosion cracking resistance is a significant challenge in the automotive industry and many engineering applications. In this paper, the mathematical structure of a superposition-theory based corrosion-fatigue model is investigated and possible closed-form and approximate solutions are sought. Based on the model and the associated solutions and test results, screening and ranking of the materials in fatigue, corrosion-fatigue are discussed.

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.