Design & Analysis of Experiments, and Inference in Reliability Studies

建议的第一部分（第1-6节）涉及实验设计和分析的几个重要方面。在第1节中，我们研究了正交表可以容纳的因子的最大数目的基本问题。在第二节中，我们研究了设计选择的三个问题：（i）具有最小像差的混合2-和4-水平设计的确定和构造，（ii）新设计准则的研究，（iii）为完全和部分析因设计选择“最优”区组方案的理论。在第3节中，我们提出了一些最优设计算法来构造有效的过饱和设计。在第4节中，我们研究分析策略，使我们能够接受和估计复杂的别名设计的相互作用。在第五节中，我们研究了析因实验中M-估计的性质。第六节讨论了稳健参数设计中位置和色散效应的联合建模和有效估计。建议的第二部分涉及一些可靠性研究中出现的估计问题。第7.1节考虑了在“发现”或观测数据的分析中存在固有的大小偏差的情况。第7.2节讨论了时间和协变量删失的回归模型中的推断。最后，在第7.3节中，我们考虑在加速变换模型下的可靠性推断，允许研究非线性变换。 科学探究的一个重要方法是通过有目的地改变感兴趣的变量的条件来进行实验。它已成功地应用于许多工业和农业调查。 实验研究中的两个主要问题是如何正确选择实验条件（即，设计），并分析实验数据（即，分析）。 我们提出的研究努力寻找新的设计，实现更高的效率和经济性，更广泛的应用，并开发新的分析策略，可以从数据中提取更多的信息，以更好的决策。 第二部分是关于产品的可靠性。我们建议开发更广泛的一类模型，可以更好地描述工业和商业产品的实际可靠性的统计推断方法。这些统计方法也可以用于研究其他有趣的问题，如医疗随访，软件可靠性和石油储量的消耗。

The first part of the proposal (sections 1-6) is concerned with several important aspects of the design and analysis of experiments. In section 1 we study a fundamental problem on the maximum number of factors an orthogonal array can accommodate. In section 2 we examine three problems of design selection: (i) determination and construction of mixed 2- and 4-level designs with minimum aberration, (ii) study of a new design criterion, (iii) a theory for choosing ``optimum'' blocking schemes for full and fractional factorial designs. In section 3 we propose some optimal design algorithms for constructing efficient supersaturated designs. In section 4 we study analysis strategies that allow us to entertain and estimate interactions from designs with complex aliasing. In section 5, we study the properties of M-estimators in the context of factorial experiments. Section 6 deals with joint modeling and efficient estimation of location and dispersion effects in robust parameter design. The second part of the proposal is concerned with estimation problems that arise in some reliability studies. Section 7.1 considers situations where there are size-biases inherent in the analysis of ``discovery'' or observational data. Section 7.2 deals with inference in regression models with both time and covariate censoring. Finally, in Section 7.3 we consider reliability inference under an acceleration transform model, allowing the study of non-linear transformations. An important method of scientific inquiry is to run experiments by purposely changing the conditions of the variables of interest. It has been successfully employed in many industrial,and agricultural investigation. Two major issues in experimental investigation are how to properly choose the experimental conditions(i.e., design), and to analyze the experimental data(i.e., analysis). Our proposed research strives to find novel designs that achieve higher efficiencies and economy, and wider applications, and to develop novel analysis strategies that can extract more information from the data for better decision making. The second part of the proposal is on product reliability. We propose to develop methods of statistical inference for a wider class of models that can better describe the actual reliability of industrial and commercial products. These statistical methods can also be used to study other interesting problems like medical follow-up, software reliability and depletion of petroleum reserves.