Topics in engineering statistics

In statistics, any procedure P is based on certain assumptions A. Box and Luceno in 1997 conceptually represent the robustness of the procedure as the product of: the size of the departure Delta A from the assumption; and the sensitivity dP/ dA of the procedure to such a departure. Box (1999) called the later the robustness factor. In this thesis we study three main topics linked together by different interpretations of the robustness factor.; Most of the work on robustness is concerned with the violation of the normality assumption. We discuss this issue and show how procedures commonly used might be affected by departures from the independence and homoscedasticity of observations. These properties are usually assumed and consequences of their violation ignored. We use the robustness factor to assess the sensitivity of various procedures and show how the robustness of different procedures may be compared. We show for example, that the t-test is more robust to correlated data than Bartlett's M-test to normality.; Secondly, using a different interpretation of the robustness factor, the problem of parameter design in industry is presented. We define the modulus of this factor is a measure of the robustness of a product to environmental variation. This setup leads naturally to the problem of constrained optimization. Appropriate analysis is presented for split-plot arrangements of different kinds depending in particular on the way in which the design factors and the environmental factors are allocated to the strata. We also consider the construction of confidence regions for robust products.; Finally, we developed further the Bayesian approach to factor screening used by Box and Meyer (1986, 1993) and study the robustness of the consequent procedures by direct interpretation of the derivatives as the robustness factor. MD-optimal follow-up designs of Meyer, Steinberg and Box (1996) are developed and applied to a one-run-at-a time experimentation. The BsMD R-package for Bayesian screening and model discrimination was developed mid used for the computations in this chapter.; Although the examples presented in this thesis are motivated by engineering or industrial examples the procedures are quite general and are not restricted to these fields.