Yield prediction via spatial modeling of clustered defect counts across a wafer map

Bae, Seung Yong; Hwang, Jung Yoon; Kuo, Way

doi:10.1080/07408170701275335

Cited by 27 publications

(12 citation statements)

References 25 publications

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“…Nevertheless, one must be aware that sometimes a shift in one parameter can result in a shorter signal time for the CUSUM chart designed to detect shifts in the other parameter.The ZIP model has applications in manufacturing processes, see, e.g. Bae et al 9 . In addition, it can be used with accident data for which accidents are recorded, but the numbers of fatalities are being monitored.…”

mentioning

confidence: 99%

CUSUM charts for monitoring a zero‐inflated poisson process

Huang

Woodall

2011

Quality & Reliability Eng

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A zero‐inflated Poisson (ZIP) process is different from a standard Poisson process in that it results in a greater number of zeros. It can be used to model defect counts in manufacturing processes with occasional occurrences of non‐conforming products. ZIP models have been developed assuming that random shocks occur independently with probability p, and the number of non‐conformities in a product subject to a random shock follows a Poisson distribution with parameter λ. In our paper, a control charting procedure using a combination of two cumulative sum (CUSUM) charts is proposed for monitoring increases in the two parameters of the ZIP process. Furthermore, we consider a single CUSUM chart for detecting simultaneous increases in the two parameters. Simulation results show that a ZIP‐Shewhart chart is insensitive to shifts in p and smaller shifts in λ in terms of the average number of observations to signal. Comparisons between the combined CUSUM method and the single CUSUM chart show that the latter's performance is worse when there are only increases in p, but better when there are only increases in λ or when both parameters increase. The combined CUSUM method, however, is much better than the single CUSUM chart when one parameter increases while the other decreases. Finally, we present a case study from the light‐emitting diode packaging industry. Copyright © 2011 John Wiley & Sons, Ltd.

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confidence: 99%

CUSUM charts for monitoring a zero‐inflated poisson process

Huang

Woodall

2011

Quality & Reliability Eng

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“…Like in scenario I,p 0 is substituted for p 0 in Equations (6), (10), (12), and (17) for constructing the phase II charts. 10 Finally, under scenario III where both ZIP parameters shift from its IC values, none of them can be accurately estimated and the MMEp 0 and̂0 are given by Equations (4). The results are shown in Figures 3 and 4.…”

Section: The Steady-state Performancementioning

confidence: 96%

Monitoring of zero‐inflated Poisson processes with EWMA and DEWMA control charts

Alevizakos

Koukouvinos

2019

Quality & Reliability Eng

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The zero‐inflated Poisson (ZIP) distribution is an extension of the ordinary Poisson distribution and is used to model count data with an excessive number of zeros. In ZIP models, it is assumed that random shocks occur with probability p, and upon the occurrence of random shock, the number of nonconformities in a product follows the Poisson distribution with parameter λ. In this article, we study in more detail the exponentially weighted moving average control chart based on the ZIP distribution (regarded as ZIP‐EWMA) and we also propose a double EWMA chart with an upper time‐varying control limit to monitor ZIP processes (regarded as ZIP‐DEWMA chart). The two charts are studied to detect upward shifts not only in each parameter individually but also in both parameters simultaneously. The steady‐state performance and the performance with estimated parameters are also investigated. The performance of the two charts has been evaluated in terms of the average and standard deviation of the run length, and compared with Shewhart‐type and CUSUM schemes for ZIP distribution, it is shown that the proposed chart is very effective especially in detecting shifts in p when λ remains in control (IC) and in both parameters simultaneously. Finally, one real example is given to display the application of the ZIP charts on practitioners.

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“…The distribution of global defects can be modelled by the spatial homogeneous Poisson process (HPP) (Bae et al 2007). The properties of the spatial HPP are described by its intensity function, which governs the likelihood of an observation occurring at a location x 2 < d .…”

Section: Appendix a Homogeneous Poisson Process (Hpp)mentioning

confidence: 99%

Multi-step ART1 algorithm for recognition of defect patterns on semiconductor wafers

Choi

Kim

et al. 2011

International Journal of Production Research

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The integrated circuits (ICs) on wafers are highly vulnerable to defects generated during the semiconductor manufacturing process. The spatial patterns of locally clustered defects are likely to contain information related to the defect generating mechanism. For the purpose of yield management, we propose a multi-step adaptive resonance theory (ART1) algorithm in order to accurately recognise the defect patterns scattered over a wafer. The proposed algorithm consists of a new similarity measure, based on the p-norm ratio and run-length encoding technique and pre-processing procedure: the variable resolution array and zooming strategy. The performance of the algorithm is evaluated based on the statistical models for four types of simulated defect patterns, each of which typically occurs during fabrication of ICs: random patterns by a spatial homogeneous Poisson process, ellipsoid patterns by a multivariate normal, curvilinear patterns by a principal curve, and ring patterns by a spherical shell. Computational testing results show that the proposed algorithm provides high accuracy and robustness in detecting IC defects, regardless of the types of defect patterns residing on the wafer.

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Yield prediction via spatial modeling of clustered defect counts across a wafer map

Cited by 27 publications

References 25 publications

CUSUM charts for monitoring a zero‐inflated poisson process

CUSUM charts for monitoring a zero‐inflated poisson process

Monitoring of zero‐inflated Poisson processes with EWMA and DEWMA control charts

Multi-step ART1 algorithm for recognition of defect patterns on semiconductor wafers

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