Contributed Session: Process Characterization

Session Chair: Jack Wang, NIST

Statistical Geometrical Methods in Paper Formation

Min Deng
Dept. of Mathematics, Univ. of Wisconsin - Stevens Point

C. T. J. Dodson
Dept. of Mathematics, Univ. of Toronto

The two-dimensional variability of areal density is of interest in the characterization of flat fibrous networls such as paper and non-woven textiles. this article gives an analytical description of the spatial variability of random networks made from uniform star patterns. This is based on the derivation of the point autocorrelation function for stars with different numbers of arms. It is found that the coefficient of variation of local basis weight for commercial newsprint is typically double that for random paper made from the same furnish. We show that such a formation arises from the deposition of stars having four arms.

[Min Deng Dept. of Mathematics,, Univ. of Wisconsin-Stevens Point, Stevens Point, WI 54481, USA; mdeng@uwspmail.uwsp.edu ]

Statistical Characterization of Light Point Defects on Silicon Wafers

Peter C. Pankratz
Technology Dept., MEMC Electronic Materials, Inc.

Particles on wafers constitute one of the largest challenges to electronic device makers today. Instruments for detecting particles on silicon wafers all depend upon the measurement of scattered light giving rise to the practice of referring to such measurements as light point defects or LPD counts.

The lognormal probability distribution provides a good model for LPD's except that, in recent years, the number of LPD's on wafers has dropped to the point where a significant fraction of wafers tested show no LPD's detected. This paper describes how the lognormal model provides a good representation for LPD counts when the zero counts are treated as missing values. Using example data of LPD measurements, alternative probability models will be shown to be inferior. Precedent for this approach will be provided as coming from analogous problems in the biological sciences.

[Peter C. Pankratz, 501 Pearl Drive, MD33, St Peters, MO 63376 USA; ppankratz@memc.com]

Multivariate Process Capability Analysis

Vani H. Sundaraiyer
Dept. of Mathematics, Univ. of Northern Iowa

Some approaches to defining and estimating process capability in multivariate situations will be discussed. Bootstrap is among the tools explored.

[Vani H. Sundaraiyer, Dept. of Mathematics, Univ. of Northern Iowa, Cedar Falls, IA 50614-0506 USA; sundaraiyer@uni.edu ]

Analyzing Temporally Dependent Ordered Categorical Data

Vijayan N. Nair
Chuanguo Wang
Dept. of Statistics, Univ. of Michigan

This paper deals with a model for analyzing temporally dependent ordered categorical data. In many applications, one is interested in the nature and extent of temporal dependence and also in detecting any changes in the process based on dependent ordered categorical data. To study this, we model the ordered categorical data as indicator variables obtained from latent continuous variables which are temporally dependent. Specifically, we consider an AR(1) model for the latent variables X_t. The ordinal data Y_t are generated from X_t as follows: Y_t= j if theta_j-1< X_tle theta_j, where theta_j are unknown cut points. Inference about temporal dependence and about process changes can be made by estimating the relevant parameters based on Y_t. Maximum likelihood estimation is computationally intractable in this problem, we describe two alternative estimation procedures: a) pseudo-likelihood estimators and b) Bayesian inference using data augmentation methods.