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TECHNICAL PAPERS

Finite Mixture Models for Nonidentical Multiple Tooled Manufacturing

[+] Author and Article Information
Allen T. Bracken

 General Atomics—Systems Integration, 1343 Flint Meadows Drive, Kaysville, UT 84037allen.bracken@ga-utah.com

J. Manuf. Sci. Eng 128(4), 996-1005 (Mar 07, 2006) (10 pages) doi:10.1115/1.2280635 History: Received April 05, 2005; Revised March 07, 2006

This paper presents a novel method to assess nonidentical multiple tooled (NIMT) manufacturing processes (like multiple cavity injection molding) using finite mixture distribution (FMD) models. A stepwise methodology is presented, including supporting mathematics and statistics. The methodology is illustrated and supported by its application to two sets of real multicavity injection molding data. The method is commercially relevant and is significant in that it allows enhanced examination of the fraction of the parts nonconforming or better setting of the specification level. Included are discussions of FMD models versus normal models and novel tail probability comparison methods (ratio of tail probabilities and log PDF comparisons). The methodology is recommended for NIMT processes, and is thought to better address the adequacy evaluation of processes where there are multiple nonidentical distributions mixing in production.

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Copyright © 2006 by American Society of Mechanical Engineers
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Figures

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Figure 1

Flow chart of methodology

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Figure 2

Probability density functions (PDF) for the normal and FMD models for the two example data sets. Top—Fig. 2, four cavity example with FMD model as solid line and the normal model as dotted line. Bottom—Fig. 2, sixteen cavity example with FMD model as solid line, normal model as dotted line, and scaled histogram of the data as bars.

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Figure 3

Log PDF for the normal and FMD models for the two example data sets. Top—Fig. 3, four cavity example with FMD model as solid line and the normal model as dotted line. Bottom—Fig. 3, sixteen cavity example with FMD model as solid line and normal model as dotted line.

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Figure 4

RTP for the two example data sets. Left—Fig. 4, four cavity example. Right—Fig. 4, sixteen cavity example.

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Figure 5

Plots showing the fraction nonconforming for various levels of the specification for the two example data sets. Top—Fig. 5, four cavity example. Bottom—Fig. 5, sixteen cavity example.

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