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

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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The molecular basis of general anesthetic action on membrane proteins that control ion transport is not yet understood. In a previous report (Covarrubias, M., and Rubin, E. (1993) Proc. Natl. Acad. Sci. 90, 6957-6960), we found that low concentrations of ethanol (17-170mM) selectively inhibited a noninactivating cloned K+ channel encoded by Drosophila Shaw2. Here, we have conducted equilibrium dos-inhibition experiments, single channel recording, and mutagenesis in vitro to study the mechanism underlying the inhibition of Shaw2K+ channels by a homologous series of n-alkanols (ethanol to 1-hexanol). The results showed that: (i) these alcohols inhibited Shaw2 whole-cell currents, the equilibrium dose-inhibition relations were hyperbolic, and competition experiments revealed the presence of a discrete site of action, possibly a hydrophobic pocket; (ii) this pocket may be part of the protein because n-alkanol sensitivity can be transferred to novel hybrid K+ channels composed of Shaw2 subunits and homologous ethanol-insensitive subunits: (iii) moreover, a hydrophobic point mutation within a cytoplasmic loop of an ethanol-insensitive K+ channel (human Kv3.4) was sufficient to allow significant inhibition by n-alkanols, with a dose-inhibition relation that closely resembled that of wildtype Shaw2 channels; and (iv) 1-butanol selectively inhibited long duration single channel openings in a manner consistent with a direct effect on channel gating. These results strongly suggest that a discrete site within the ion channel protein is the primary locus of alcohol and general anesthetic action.

High reliability systems generally require individual system components having extremely high reliability over long periods of time. Short product development times require reliability tests to be conducted with severe time constraints. Frequently few or no failures occur during such tests, even with acceleration. Thus, it is difficult to assess reliability with traditional life tests that record only failure times. For some components, degradation measures can be taken over time. A relationship between component failure and amount of degradation makes it possible to use degradation models and data to make inferences and predictions about a failure-time distribution. This article describes degradation reliability models that correspond to physicalfailure mechanisms. We explain the connection between degradation reliability models and failure-time reliability models. Acceleration is modeled by having an acceleration model that describes the effect that temperature (or another accelerating variable) has on the rate of a failure-causing chemical reaction. Approximate maximum likelihood estimation is used to estimate model parameters from the underlying mixed-effects nonlinear regression model. Simulation-based methods are used to compute confidence intervals for quantities of interest (e. g., failure probabilities). Finally we use a numerical example to compare the results of accelerated degradation analysis and traditional accelerated life-test failure-time analysis. Statistics and Probability CommentsThis preprint has been published in Technometrics 40 (1998): 89-99. AbstractHigh reliability systems generally require individual system components having extremely high reliability o ver long periods of time. Short product development times require reliability tests to be conducted with severe time constraints. Frequently few or no failures occur during such tests, even with acceleration. Thus, it is di cult to assess reliability w i t h traditional life tests that record only failure times. For some components, degradation measures can be taken over time. A relationship between component failure and amount o f degradation makes it possible to use degradation models and data to make inferences and predictions about a failure-time distribution.This paper describes degradation reliability models that correspond to physical-failure mechanisms. We explain the connection between degradation reliability models and failuretime reliability m o d e l s . Acceleration is modeled by h a ving an acceleration model that describes the e ect that temperature (or another accelerating variable) has on the rate of a failure-causing chemical reaction. Approximate maximum likelihood estimation is used to estimate model parameters from the underlying mixed-e ects nonlinear regression model. Simulation-based methods are used to compute con dence intervals for quantities of interest (e.g., failure probabilities). Finally we u s e a n umerical example to compare the results of accelerated degradation analysis and traditional accelerated lif...