A Note on "Capability Assessment for Processes with Multiple Characteristics: A Generalization of the Popular Index Cpk". (8th February 2012)

• Record Type: Journal Article
• Authors: Pearn, W. L.; Wu, C. H.; Tsai, M. C.
• Is Part Of: Quality and reliability engineering international. Volume 29:Number 2(2013:Mar.)
• Page Start: 159
• Page End: 163
• Publication Date: 2012-02-08
• Subjects: Reliability (Engineering) -- Periodicals; Quality control -- Periodicals; High technology -- Periodicals; 620.00452
• DOI: 10.1002/qre.1295
• Languages: English
• ISSNs: 0748-8017

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>The generalized yield index <inline-graphic mimetype="image" xlink:href="ark:/27927/pgg1tv9nw33" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="urn:x-wiley:07488017:media:qre1295:qre1295-math-0001" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>C</mml:mi><mml:mtext>pk</mml:mtext><mml:mi>T</mml:mi></mml:msubsup></mml:math> establishes the relationship between the manufacturing specifications and the actual process performance, which provides a lower bound on process yield for two‐sided processes with multiple characteristics. The results attended are very practical for industrial application. In this article, we extended the results in cases with one‐sided specification and multiple characteristics. The generalized index <inline-graphic mimetype="image" xlink:href="ark:/27927/pgg1tv9nvzc" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="urn:x-wiley:07488017:media:qre1295:qre1295-math-0002" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>C</mml:mi><mml:mtext>PU</mml:mtext><mml:mi>T</mml:mi></mml:msubsup></mml:math> was considered, and the asymptotic distribution of the natural estimator <inline-graphic mimetype="image" xlink:href="ark:/27927/pgg1tv9nw2j" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="urn:x-wiley:07488017:media:qre1295:qre1295-math-0003" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mover accent="true"><mml:mi>C</mml:mi><mml:mo>^</mml:mo></mml:mover><mml:mtext>PU</mml:mtext><mml:mi>T</mml:mi></mml:msubsup></mml:math> was developed. Then, we derived the lower confidence bounds as well as the critical values of index <inline-graphic mimetype="image" xlink:href="ark:/27927/pgg1tv9nvt5" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math altimg="urn:x-wiley:07488017:media:qre1295:qre1295-math-0004" overflow="scroll" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>C</mml:mi><mml:mtext>PU</mml:mtext><mml:mi>T</mml:mi></mml:msubsup></mml:math>. We not only provided some tables but also presented an application example. Copyright © 2012 John Wiley & Sons, Ltd.</p> </abstract>