Paper 1:
TITLE: Multivariate Zero-Inflated Poisson Regression and Its Applications to Equipment Fault Detection
AUTHORS: Jinho Park, Jye-Chyi Lu, Di Chen, Sujit Ghosh, Paul A. Brinkley and John F. Peterson
Paper 2:
TITLE: Statistical Procedures for Detecting Semiconductor Equipment Problems
AUTHORS: M.M. Gardner, J.C. Lu, J.C. Davis, C.T. Wu, D. Chen, R.S. Gyurcsik, J.J. Wortman
Paper 3:
TITLE: Statistical Methods on Improving Antenna Manufacturing Quality
AUTHORS: W. Zhou, J.C. Lu, S. Ghosh, R. Gentry, S. Tourkodimitrics, A. Hartford, P.A. Brinkley
Paper 4:
TITLE: Statistical Inferences Based on Mixed Bivariate Censored Data
AUTHORS: S. Tourkodimitris, J.C. Lu and D. Chen
Paper 5:
TITLE: Wavelet Analysis of Mass Spectrometry Signals for Transient Event Detection and Run-to-Run Process Control
AUTHORS: E.A. Rying, R.S. Gyurcsik, J.C. Lu, G. Bilbro, G. Parsons and F.Y. Sorrell
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An abstract submitted to 1997 Joint Statistical Meetings for a Special Contributed Paper Session
TITLE: Multivariate Zero-Inflated Poisson Regression and Its Applications to Equipment Fault Detection
AUTHORS: Jinho Park, Jye-Chyi Lu, Di Chen, Sujit Ghosh, Paul A. Brinkley and John F. Peterson
ADDRESS: Department of Statistics, North Carolina State University, Campus Box 8203, Raleigh, NC 27695-8203
Presenter: Sujit Ghosh
Organizer: Jye-Chyi Lu
KEY WORDS: Maximum Likelihood, Mixture Distribution, Multivariate Bernoulli, Multivariate Poisson, Quality Improvement, Spatial Modeling
Abstract: When a manufacturing process is properly conditioned and at its perfect state, near zero defect will be observed; when the process is at an imperfect state, Poisson-type of defects will be observed. The zero-inflated Poisson (ZIP) distribution is commonly used to model this type of data, especially in printed circuit boards (PCB) manufacturing studies. When there are several types of defects, multivariate ZIP models are useful to integrate information from different sources together for process monitoring and control and for equipment fault detection. This presentation proposes a multivariate ZIP model and investigate its distributional properties. Simulation studies show that compared to the method of moment, the maximum likelihood method has smaller bias and variance in estimating model parameters, zero-inflated probability and conditional expectations. Our model is applied to a real-life example from Nortel, where there are 36 PCBs located at three levels of 12 spatial-sites. By using spatial signatures constructed from multivariate ZIP probabilities and expectations, equipment problems can be detected automatically to improve machine utilization and production quality. Several case studies illustrate the potential of the ZIP model in process improvement.
An abstract submitted to 1997 Joint Statistical Meetings for a Special Contributed Paper Session
TITLE: Statistical Procedures for Detecting Semiconductor Equipment Problems
AUTHORS: M.M. Gardner, J.C. Lu, J.C. Davis, C.T. Wu, D. Chen, R.S. Gyurcsik, J.J. Wortman
ADDRESS: Department of Statistics, North Carolina State University, Campus Box 8203, Raleigh, NC 27695-8203
Presenter: Martha M. Gardner
Organizer: Jye-Chyi Lu
KEY WORDS: Bootstrap, Spatial Sampling, Semiconductor manufacturing, Simulation, Spatial Signatures, Spline,
Abstract: Equipment faults are often the cause of major variations in semiconductor processes. As wafer sizes increase and device characteristics shrink, the use of spatial information will have a greater impact during wafer processing. This paper describes new results of using a recently developed equipment fault detection methodology that incorporates spatial information. The method utilizes thin-plate splines to fit a virtual wafer surface to data sampled from semiconductor wafers fabricated using equipment with and without faults. Physically motivated spatial signature metrics are constructed based on visual differences between the baseline process surface and surfaces that may have potential faults. Bootstrap simulations provide the null distribution of the signature metrics which is used to determine the significance of the spatial signature. The methodology has been modified where a randomization procedure is implemented in the bootstrap for including wafer to wafer variation in the decision rule. The methodology is also used to evaluate the performance of different sampling schemes, with respect to their robustness in handling different types of equipment faults, through simulation studies. Real-life examples from deposition processes at North Carolina State University and Texas instruments, Inc. show the potential and impact of this methodology in identifying sources of equipment problems.
An abstract submitted to 1997 Joint Statistical Meetings for a Special Contributed Paper Session
TITLE: Statistical Methods on Improving Antenna Manufacturing Quality
AUTHORS: W. Zhou, J.C. Lu, S. Ghosh, R. Gentry, S. Tourkodimitrics, A. Hartford, P.A. Brinkley
ADDRESS: Department of Statistics, North Carolina State University, Campus Box 8203, Raleigh, NC 27695-8203
Presenter: Weixin Zhou
Organizer: Jye-Chyi Lu
KEY WORDS: Bootstrap, Regression, Quality Improvement, Spline, Statistical Process Control, Variance Modeling, Wireless Communication.
Abstract: Wireless communication becomes very popular recently, and the demand of antenna equipment for sending and for receiving communication signals is growing. Antenna manufacturing quality is usually checked at signal transmission chambers, where near-field signals are collected and transformed to far-field signals, which match the information collected at regular usage-distances. The far-field data are three-dimensional and consist of numerous edge-connected lobes with a single peak in each lobe. The lobes near the center have higher values than the lobes far away from the center. Anntena specification limits are placed on the peak, the "drop" between the peak and the valley of the three main lobes near the center, and the horizontal distance between the peak and the valley. The objective of this paper is to show how antenna data can be used to monitor production quality and possibly to detect manufacturing problems. A spline procedure is first used to smooth disturbances in data collection routines. Then, the peaks, the drops and the peak-valley horizontal distances of the three main lobes can be identified and checked against the specifications to qualify the antenna. For monitoring the production quality, the average of signals from 30 randomly selected antennas is treated as the target. A spatially correlated random coefficients model is applied to the variances of data at different signal locations. Smoothed three-sigma bounds are constructed for checking if signals from individual antenna are inside the bounds. A few performance measures such as sum of squares of the differences between signals from the target and the individual antenna are established. Applications of the bootstrap procedure provide the control limits of these measures. The confidence and the control limits are displayed at Nortel's quality tracking system in real-time for monitoring their antenna manufacturing quality. Performance measures are also used to create production-fault detection signatures. Several real-life examples show that our method can identify manufacturing problems and improve machine utilization efficiency and production quality significantly.
An abstract submitted to 1997 Joint Statistical Meetings for a Special Contributed Paper Session
TITLE: Statistical Inferences Based on Mixed Bivariate Censored Data
AUTHORS: S. Tourkodimitris, J.C. Lu and D. Chen
ADDRESS: Department of Statistics, North Carolina State University, Campus Box 8203, Raleigh, NC 27695-8203
Presenter: S. Tourkodimitris
Organizer: Jye-Chyi Lu
KEY WORDS: Asymptotics, Bivariate Normal, Concomitant order statistics, Maximum likelihood, Modified maximum likelihood, Reliability, Simulation.
Abstract: A new plan of life-testing two-component (A and B) parallel system is proposed. This plan terminates experiments at the rth smallest order statistics X(r) of component A. The data type consists of type-II censored data X(i), i = 1, 2, ..., n from component A and their concomitants Y[i] randomly censored at X(r) from component B. Because the likelihood function is very complicated, the maximum likelihood (ML) estimation is impractical. Our method estimates the mean and variance parameters in the bivariate normal distribution based on marginal information X(i)'s and Y[i]'s separately. Then, the bivariate normal is transformed to the standard bivariate normal with a single correlation parameter rho, and a modified ML method based on this standard model is developed to estimate rho. The large sample theory of the simple estimators is difficult due to the censoring structure. The finite sample and large sample distributions of parameter estimates are obtained from the simulation and normal approximation procedures. Define W(n) as the maximum of Wi = max(Xi, Yi), i = 1, 2, ..., n. Compared to the plan with complete samples, where the experiment is terminated until observing the cost of the loss of estimation quality due to the early termination of experimentation can be compensated from the gain of shortening the test duration and of saving unfailed components.
An abstract submitted to 1997 Joint Statistical Meetings for a Special Contributed Paper Session
TITLE: Wavelet Analysis of Mass Spectrometry Signals for Transient Event Detection and Run-to-Run Process Control
AUTHORS: E.A. Rying, R.S. Gyurcsik, J.C. Lu, G. Bilbro, G. Parsons and F.Y. Sorrell
ADDRESS: Department of Electrical and Computer Engineering, North Carolina State University, Campus Box 7911, Raleigh, NC 27695-7911
Presenter: E.A. Rying
Organizer: Jye-Chyi Lu
KEY WORDS: Quality Improvement, Semiconductor Manufacturing, Sensors, Signal Processing, Statistical Process Control.
Abstract: The wavelet transform has been useful in speech, radar and event/fault detection with turbine blades. This paper provides applications of using the wavelet analysis technique to model mass spectrometry signals for detection and control of run-to-run variability in a semiconductor process. Mass spectroscopy has shown to be a non-intrusive process-state sensor of gas phase reactant and of product species during plasma deposition. Mass spectrometric signals obtained from an RTCVD on Si process are analyzed using the wavelet transform to detect transient events. Since the signals are decomposed on a multiresolution basis, the wavelet transform is shown to extract both high-frequency events, such as spiking, and low-frequency events such as system shifts or drifts and equipment faults, from the mass spectrometry signals. For comparison purposes, the signals are analyzed using Fisher's discriminant analysis to detect transient events. By decorrelating different transient events on a time-frequency basis, the authors show the direct implication of wavelets for process modeling and run-to-run control. Our study shows the potential of wavelet modeling for process quality improvement and for equipment fault detection in semiconductor manufacturing.