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There are many circumstances in reliability and in biostatistics where it is of interest to design experiments that yield rapid results in a setting where observing the desired outcome under ordinary use conditions takes a long time. One way to achieve this is by introducing an accelerating agent, called an acceleration variable, to the experimental environment which expedites the process leading to the desired outcome. In the reliability literature, such methods are known as accelerated testing and are commonly used. Similar approaches are also employed in pre-clinical testing as well as in toxicology where subjects may be exposed to higher doses, or extreme conditions e.g. heat, light etc. in order to speed up the failure process. The data obtained from such accelerated environments are then transformed to the ordinary use conditions via acceleration models, which capture the relationship between the acceleration variable and the response.
In these experiments, determining the levels of the acceleration variable where the actual observations will be collected as well as appropriately allocating sample sizes to each level are important issues. In practice, these values are typically chosen based on experience and without regard to statistical optimality. In this paper, a very general approach is proposed which can be used with a wide variety of failure distributions and acceleration models. Our method introduces a “locally penalized” D-optimal (LPD-optimal) design criterion for determining “nearly optimal” levels of the acceleration variable to use in testing. The approach avoids the usual recommendation of D-optimality, namely choosing the extreme levels, by penalizing such choices. The goal is to obtain a function of the information matrix, which has a local maximum in terms of the values of the acceleration variable in an acceptable (practical) range. The LPD-optimality is appealing due to its generality and the fact that it minimizes the overall variation of the parameter estimators (or maximizes information).
This article appears in the Journal of Statistical Planning and Inference 2003. The co-author is William Padgett (University of South Carolina).