Many products & systems age, wear, or degrade over time before they fail or break down. Thus, in many engineering reliability experiments, measures of degradation or wear toward failure can often be observed over a period of time before failure occurs. Because the degradation values provide additional information beyond that provided by the failure observations, both sets of observations need to be considered when doing inference on the statistical parameters of the product or system lifetime distributions. For highly-reliable modern products, it often takes much more time to obtain lifetime & degradation data under usual use conditions, and this requires one to use accelerated tests. Accelerated tests expose the products to greater environmental stress levels so that we can obtain lifetime & degradation measurements in a more timely fashion. In addition, many products are exposed to several environmental variables in some manufacturing processes, or under some operating conditions. This motivates the need for developing general accelerated test models with several accelerating variables for inference based on both observed failure values, and degradation measurements. In this paper, new accelerated test models are developed based on a generalized cumulative damage approach with a stochastic process characterizing a degradation phenomenon.

Based on a generalized cumulative damage approach with a stochastic process describing initial damage for a material specimen, a broad class of statistical models for material strength is developed. Plausible choices of stochastic processes for the initial damage include Brownian motion, geometric Brownian motion, and the gamma process; and additive & multiplicative cumulative damage functions are considered. The resulting general statistical model gives an accelerated test form of the inverse Gaussian distribution, special cases of which include some existing models in addition to several new models. Model parameterizations & estimation by maximum likelihood from accelerated test data are discussed, and the applicability of the general model is illustrated for three sets of strength data. The proposed models are compared with the power-law Weibull model, and the inverse Gaussian generalized linear models.