The use of historical data in statistical selection and robust product design
Abstract
Historical data is routinely collected in many industrial situations and can be critical in accurately representing the current state of the processes under study. In turn, the robustness of many statistical procedures depend upon accurate representation of parameters associated with the current state of the process. The purpose of the present study was to investigate the use of historical data in two such statistical procedures. Modifications which incorporate historical data sets into the procedures are proposed in order to provide for more robust statistical applications. The first part of this thesis studies classical and Bayesian procedures for estimating normal tail probabilities. A particular situation is considered which demonstrates that the Bayes procedure is not robust to mis-specification of prior parameter values. Therefore, an empirical Bayes approach is investigated which utilizes historical data with the goal of properly specifying the prior parameter values. The second part of this thesis examines response surface methodology alternatives to Taguchi methods. It is shown that the response surface alternatives have a calibration problem and are not robust to mis-specification of the noise factor distribution (i.e. the distribution of factors which are not controllable). A solution to the robustness problem is given by deriving a response surface model which allows for greater flexibility in statistical modeling and more general distributional assumptions. In order to deal with the calibration problem, a parametric bootstrap procedure is proposed. The given solutions to both the robustness and the calibration problem depend upon the availability of historical data to accurately specify the noise factor distribution.
Degree
Ph.D.
Advisors
Kuczek, Purdue University.
Subject Area
Statistics
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