On the dynamics of topological patterns in statistical imputation

Accompanying heavy costs in sampling processes, many a time there are missing items in the collected data, whether the population may come from a great variety of sources: social, economical, or engineering. In semiconductor manufacturing, due to the inherent reentrant flows of product-mixes and tool-constraints, uneven distributions of populations give the norm of missing data [1,2] in all the samples. This brings about many severe problems to applications of advanced process controls, fault detection and classifications, virtual metrologies, yield analyses, etc. In this paper, we present an explorative study on the dynamics of topological patterns behind the algorithm of a common statistical method in missing data imputation [3,4]. Without much loss of generality, we exemplify our results through an in-depth analysis of a 2D-table with certain patterns of missing values. For the first time, the results shed many insights into a shop floor practice whose inherent characteristics and limitations have so far evaded close scrutiny. Detail computation steps are exemplified to illustrate the underlying techniques employed for analyses of other cases encountered in more widespread operational applications.