Physical Sciences and Mathematics Commons^™

Determining Sample Size For A Control Chart, Shu-Yang Catherine Jean

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The essential tool in statistical quality control is the control chart. In spite of the apparent simplicity of the control chart, most engineers, production men, and inspectors find that its use calls for an entirely new point of view. The power of this technique lies in its ability to separate out assignable causes of quality variation. This makes possible the diagnosis and correction of many production troubles and often brings substantial improvements in product quality and reduction of spoilage and rework. The control chart tells when to leave a process alone and thus prevents unnecessarily frequent adjustments that tend to …

Principal Component Factor Analysis, Kuang-Ming Chu

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

The principal-factor solution is probably the most widely used technique in factor analysis and a relatively straight forward method to determine the minimum number of independent dimensions needed to account for most of the variance in the original set of variables.

The principal components approach to parsimony was first proposed by Karl Pearson (1901) who studied the problem for the case of nonstochastic variables, and in a different context. Hotelling provided the full development of the method (1933) and Thomson (1947) was the first to apply it to the principal factor analysis.

This method was first developed to deal with …

Matrix Norms, I-Hui C. Cheng

All Graduate Plan B and other Reports, Spring 1920 to Spring 2023

In many situations it is very useful to have a single nonnegative real number to be, in some sense, the measure of the size of a vector or a matrix. As a matter of fact we do a similiar thing with scalars, we let jÀj represent the familiar absolute value or modulus of À. Fora vector x e: C , one way n of assigning magnitude is the usual definition of length, Il I 1/2 2 1/2 xl= = {jxij } , which is called the euclidean norm of x. In this case, length gives an overall estimate of the …