Robust design with application and implementation

我的工作重点是构建回归问题的实验设计。当拟合的模型不正确时，好的设计应该在估计中导致小的偏差，当拟合的模型实际上是正确的时，好的设计也应该在估计中有效(即，导致小的方差)。我打算用一个非常一般的设置来研究回归问题的设计构造。回归响应被认为是线性函数的函数。我们关注这样一种情况，即拟合的模型可能不能准确地代表真相。其他可能偏离通常假设的因素也被考虑在内。例如，误差可能与它们假设的不同。本文还探讨了加速寿命试验(ALT)的应用。ALT是在相对较短的时间内确定具有较长寿命的产品或材料的寿命的过程。为了获得故障，必须加快电压、温度、压力和利用率等正常使用条件的恢复。将在加速水平上对数据进行ALT模型拟合，并将估计外推到正常使用水平。正如我在过去的工作中所展示的那样，上面讨论的设计的推导在数学上往往是复杂的。我打算研究如何以相对较小的效率折衷来简化设计构造。

My work focuses on constructing the experimental designs for regression problems. Good designs should lead to small biases in the estimates when the fitted model is incorrect, and should also be efficient (i.e., lead to small variances) in the estimates when the fitted model is in fact correct. I intend to work on the design constructions for the regression problem with a very general setup. The regression responses are considered to be a function of a linear function. We watch for the situation where the fitted model may not exactly represent the truth. Other possible departures from the usual assumptions are also taken into account. Errors may not equally vary as they are assumed, for instance.Applications to accelerated life testing (ALT) are explored as well. ALT is the process of determining the lifetime of a product or material with a long lifespan in a relatively short period of time. In order to obtain the failures, the normal use conditions such as voltage, temperature, pressure, and use rate have to be accelerated. An ALT model will be fitted to the data at accelerated levels and the estimates are extrapolated to the normal use levels. The designs constructed are also expected to incorporate censoring schemes and/or stress loading plans for ALT in a good manner.The derivation of the designs discussed above tends to be complicated mathematically, as I have demonstrated in my past work. I intend to investigate how to simplify design construction with a relatively small tradeoff in efficiency.