18-run nonisomorphic three level orthogonal arrays

Evangelaras, H.; Koukouvinos, Christos; Lappas, E.

doi:10.1007/s00184-006-0085-4

“…The GWLP results were obtained earlier by Evangelaras et al 9 . Note, however, that the GWLPs of these authors are a factor of 2 smaller than our GWLPs.…”

Section: Table VII Gives the Gwlp And The A (3)supporting

confidence: 67%

“…Owing to complete enumeration, Evangelaras et al 9 were able to confirm that there are exactly three isomorphism classes. In addition, in the present paper we establish three classes of 3 7 2 1 arrays.…”

Section: Enumerationmentioning

confidence: 92%

“…Therefore, it is of practical as well as of theoretical interest to collect the combinatorially inequivalent arrays and to classify these in a way meaningful for qualitative factors. In particular, Evangelaras et al 9 obtained all such arrays for three up to seven factors. The arrays were classified with the generalized aberration (GA) criterion proposed by Ma and Fang 18 and Xu and Wu 19 .…”

Section: Literature Reviewmentioning

confidence: 96%

“…Pure three-level 18-run arrays have been studied extensively before, however. In particular, Evangelaras et al 9 obtained all such arrays for three up to seven factors and classified these arrays. Our reasons to reconsider the pure arrays will be made clear later in this paper.…”

Section: Introductionmentioning

confidence: 98%

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All orthogonal arrays with 18 runs

Schoen

¹

2008

Quality & Reliability Eng

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All combinatorially inequivalent orthogonal arrays with 18 runs and eight or less factors are generated. Their potential as practical experimental designs is evaluated by a classification using generalized word-length patterns of the original arrays and those of their projections into less factors. Arrays of special interest are given explicitly. This paper includes the statistical analysis of results from a real-life experiment based on one of the arrays.

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“…Moreover, Lam and Tonchev [22,23] found 68 nonisomorphic OA (27,13,3, 2)'s. Recently, Evangelaras et al [17,18] enumerated and classified all orthogonal arrays with q three-level columns and n = 18 and 27 runs. Their results are depicted in Table 22.…”

Section: Factors With More Than Two Levelsmentioning

confidence: 99%

Advances in Robust Parameter Design: From Taguchi's Inner‐Outer Arrays to Combined Arrays

Evangelaras

¹

,

Koukouvinos

²

,

Koutras

³

2005

Encyclopedia of Statistical Sciences

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Robust parameter design, originally proposed by Taguchi, is an off‐line technique for maintaining variance reduction and improving quality. According to Taguchi, product variation from the desirable target is affected by two types of factors: control factors and noise factors. The basic idea in robust parameter design is to identify the levels of the control factors so that the product's quality characteristic becomes insensitive to changes in the levels of the noise factors. As a consequence, the effect of uncontrollable variations on the response will be reduced. Taguchi suggested the use of inner‐outer arrays with the control factors being assigned to an inner array and the noise factors assigned to an outer array. After the collection of the data, a performance measure called signal‐to‐noise ratio is calculated and analyzed in order to identify the optimal levels of the control factors. After the introduction of Taguchi's philosophy in the field of experimental design and data analysis, several new designs and techniques have been explored and adopted in this field. This chapter overviews well established approaches and analysis techniques that have been exploited to the robust parameter design field.

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Advances in Robust Parameter Design: From Taguchi's Inner‐Outer Arrays to Combined Arrays

Evangelaras¹,

Koukouvinos²,

Koutras³

2014

Wiley StatsRef: Statistics Reference Online

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Robust parameter design, originally proposed by Taguchi, is an off‐line technique for maintaining variance reduction and improving quality. According to Taguchi, product variation from the desirable target is affected by two types of factors: control factors and noise factors. The basic idea in robust parameter design is to identify the levels of the control factors so that the product's quality characteristic becomes insensitive to changes in the levels of the noise factors. As a consequence, the effect of uncontrollable variations on the response will be reduced. Taguchi suggested the use of inner‐outer arrays with the control factors being assigned to an inner array and the noise factors assigned to an outer array. After the collection of the data, a performance measure called signal‐to‐noise ratio is calculated and analyzed in order to identify the optimal levels of the control factors. After the introduction of Taguchi's philosophy in the field of experimental design and data analysis, several new designs and techniques have been explored and adopted in this field. This chapter overviews well established approaches and analysis techniques that have been exploited to the robust parameter design field.

show abstract

18-run nonisomorphic three level orthogonal arrays

Abstract: Orthogonal arrays, Isomorphism, Construction algorithm, Projection properties, Primary 62K15, Secondary 05B20,

Cited by 24 publications

References 13 publications

All orthogonal arrays with 18 runs

All orthogonal arrays with 18 runs

Advances in Robust Parameter Design: From Taguchi's Inner‐Outer Arrays to Combined Arrays

Advances in Robust Parameter Design: From Taguchi's Inner‐Outer Arrays to Combined Arrays

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