Performance evaluation of CT measurements made on step gauges using statistical methodologies

Abstract

In this paper, a study is presented in which statistical methodologies were applied to evaluate the measurement of step gauges on an X-ray computed tomography (CT) system. In particular, the effects of step gauge material density and orientation were investigated. The step gauges consist of uni- and bidirectional lengths. By confirming the repeatability of measurements made on the test system, the number of required scans in the design of experiment (DOE) was reduced. The statistical model was checked using model adequacy principles; model adequacy checking is an important step in validating the applicability of a model to fitting experimental results. If the residuals after fitting the model are normally distributed (normality test), then the residuals represent random errors in the data. If the normality test is not satisfied, the model is said to fit the data poorly. If the model fit to the data were correct, the residuals would approximate the random errors (also called normality). The most common significance level is α=0.05; for normality to be satisfied, the P value for the residuals must not be smaller than 0.05. The initial results show that the residuals failed the normality test due to a small P value (P<0.005). Some remedies in achieving a larger P value include (1) fitting a different model, (2) evaluating the data differently and (3) excluding outliers. The authors determined that there were too few data to delete outliers. Instead, discussions and conclusions were carried out based on main effect and interaction plots. It means that the conclusions were not based on the analysis of variance (ANOVA). The following conclusions can be drawn: X-ray scattering is more problematic for dense metal parts. Thus, the statement of “influence of orientation” should be constrained by the material type. But it is important to have in mention that probably the repeatability of the vertical case is much worse. This can be documented experimentally, by tracing back to the fitting quality of the planes. The fitting point deviation of these planes are typically larger when dense metal step gauges are scanned vertically; this can also be done with simulation, as it is “assumed” that the large errors related to “vertical direction” might be caused by X-ray scattering noise, this theory can be tested by simulating CT scans of metal and plastic step gauge without X-ray scattering and see whether “vertical direction” is still worse for aluminium step gauge.