Out‐of‐Control Signals in Three‐Part Compositional T2 Control Chart. (24th October 2013)

• Record Type: Journal Article
• Authors: Vives‐Mestres, Marina; Daunis‐i‐Estadella, Josep; Martín‐Fernández, Josep‐Antoni; Goos, Peter; De Ketelaere, Bart
• Is Part Of: Quality and reliability engineering international. Volume 30:Number 3(2014:Apr.)
• Page Start: 337
• Page End: 346
• Publication Date: 2013-10-24
• Subjects: Reliability (Engineering) -- Periodicals; Quality control -- Periodicals; High technology -- Periodicals; 620.00452
• DOI: 10.1002/qre.1583
• Languages: English
• ISSNs: 0748-8017

Abstract

<abstract abstract-type="main"> <title> <x xml:space="preserve">Abstract</x> </title> <p>Interpretation of out‐of‐control signals in multivariate control charts is a persistent problem. Identifying the variables contributing to the signal is of crucial importance for process control. Both procedures turn out to be more complicated when observations are compositions (variables adding to a constant sum). Compositional <italic>T</italic><sup>2</sup> control chart (<alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4sxzkg4g" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" overflow="scroll" altimg="urn:x-wiley:07488017:media:qre1583:qre1583-math-0001" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi mathvariant="bold-italic">T</mml:mi><mml:mi mathvariant="bold-italic">C</mml:mi><mml:mn mathvariant="bold">2</mml:mn></mml:msubsup></mml:math></alternatives>) is suitable for monitoring compositions because it is based on a transformation of the data, which moves it from restricted to real space. This paper proposes a method for interpreting the out‐of‐control signals of the <alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgg4sxzkg3x" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" overflow="scroll" altimg="urn:x-wiley:07488017:media:qre1583:qre1583-math-0002" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi mathvariant="bold-italic">T</mml:mi><mml:mi mathvariant="bold-italic">C</mml:mi><mml:mn mathvariant="bold">2</mml:mn></mml:msubsup></mml:math></alternatives> control chart for three‐part compositions on the basis of an appropriate selection of the transformation. An example of industrial application illustrates the introduced techniques. Copyright © 2013 John Wiley & Sons, Ltd.</p> </abstract>