Engineers in the manufacturing industries have used accelerated test (AT) experiments for many decades. The purpose of AT experiments is to acquire reliability information quickly. Test units of a material, component, subsystem or entire systems are subjected to higher-than-usual levels of one or more accelerating variables such as temperature or stress. Then the AT results are used to predict life of the units at use conditions. The extrapolation is typically justified (correctly or incorrectly) on the basis of physically motivated models or a combination of empirical model fitting with a sufficient amount of previous experience in testing similar units. The need to extrapolate in both time and the accelerating variables generally necessitates the use of fully parametric models. Statisticians have made important contributions in the development of appropriate stochastic models for AT data [typically a distribution for the response and regression relationships between the parameters of this distribution and the accelerating variable(s)], statistical methods for AT planning (choice of accelerating variable levels and allocation of available test units to those levels) and methods of estimation of suitable reliability metrics. This paper provides a review of many of the AT models that have been used successfully in this area.Comment: Published at http://dx.doi.org/10.1214/088342306000000321 in the Statistical Science (http://www.imstat.org/sts/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Maximum likelihood (ML) provides a powerful and extremely general method for making inferences over a wide range of data/model combinations. The likelihood function and likelihood ratios have clear intuitive meanings that make it easy for students to grasp the important concepts. Modern computing technology has made it possible to use these methods over a wide range of practical applications. However, many mathematical statistics textbooks, particularly those at the Senior/Masters level, do not give this important topic coverage commensurate with its place in the world of modern applications. Similarly, in nonlinear estimation problems, standard practice (as reflected by procedures available in the popular commercial statistical packages) has been slow to recognize the advantages of likelihood-based confidence regions/intervals over the commonly use "normal-theory" regions/intervals based on the asymptotic distribution of the "Wald statistic." In this note we outline our approach for presenting, to students, confidence regions/intervals based on ML estimation.

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