Design & Analysis of Experiments, and Inference in Reliability Studies

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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.