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  • 1.
    Almimi, Ashraf A.
    et al.
    NASA Langley Research Center, Hampton.
    Kulahci, Murat
    Informatics and Mathematical Modeling, Technical University of Denmark, Lyngby.
    Montgomery, Douglas C.
    Division of Mathematical and Natural Sciences, Arizona State University, Department of Industrial, Systems and Operations Engineering Arizona State University.
    Checking the adequacy of fit of models from split-plot designs2009Ingår i: Journal of QualityTechnology, ISSN 0022-4065, Vol. 41, nr 3, s. 272-284Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    One of the main features that distinguish split-plot experiments from other experiments is that they involve two types of experimental errors: the whole-plot (WP) error and the subplot (SP) error. Taking this into consideration is very important when computing measures of adequacy of fit for split-plot models. In this article, we propose the computation of two R2, R 2-adjusted, prediction error sums of squares (PRESS), and R 2 -prediction statistics to measure the adequacy of fit for the WP and the SP submodels in a split-plot design. This is complemented with the graphical analysis of the two types of errors to check for any violation of the underlying assumptions and the adequacy of fit of split-plot models. Using examples, we show how computing two measures of model adequacy of fit for each split-plot design model is appropriate and useful as they reveal whether the correct WP and SP effects have been included in the model and describe the predictive performance of each group of effects.

  • 2.
    Almimi, Ashraf A.
    et al.
    NASA Langley Research Center, Hampton.
    Kulahci, Murat
    Arizona State University, Tempe.
    Montgomery, Douglas C.
    Division of Mathematical and Natural Sciences, Arizona State University, Arizona State University, Tempe.
    Follow-up designs to resolve confounding in split-plot experiments2008Ingår i: Journal of QualityTechnology, ISSN 0022-4065, Vol. 40, nr 2, s. 154-166Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Split-plot designs are effective in industry due to time and/or cost constraints, restriction on randomization of the treatment combinations of the hard-to-change factors, and different sizes of experimental units. Some of the results of fractional factorial split-plot experiments can be ambiguous and a need may arise to conduct follow-up experiments to separate effects of potential interest by breaking their alias links with others. For completely randomized fractional factorial experiments, methods have been developed to construct follow-up experiments. In this article, we extend the foldover technique to break the alias chains of split-plot experiments. Because it is impractical or not economically possible to foldover the whole-plot factors, as their levels are often hard or expensive to change, the focus of this article is on folding over only one or more subplot factors in order to de-alias certain effects. Six rules are provided to develop foldovers for minimum aberration resolution III and resolution IV fractional factorial split-plot designs.

  • 3.
    Hubele, Norma Faris
    et al.
    Arizona State University.
    Vännman, Kerstin
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    The effect of pooled and un-pooled variance estimators on Cpm when using subsamples2004Ingår i: Journal of QualityTechnology, ISSN 0022-4065, Vol. 36, nr 2, s. 207-222Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    The vast majority of research on capability indices has assumed that the data consists of one large, representative sample. In practice, and in much of the quality control literature, process data are collected over time in subsamples representing rational subgroups. In this paper we examine the statistical behavior of two Cpm estimators based on this more realistic data structure. The estimators correspond to pooled and un-pooled variance estimators. The theoretical findings are applied to hypothesis testing and power calculations.The power functions of the tests based on the two estimators are used to determine the minimum number of subsamples needed to meet a threshold requirement that power exceeds 0.80. Extensive tables of the recommended number of subsamples are provided with comments on their usage

  • 4.
    Kulahci, Murat
    et al.
    Arizona State University, Tempe.
    Ramirez, José
    W. L. Gore & Associates, Inc.
    Tobias, Randy
    SAS Institute Inc.
    Split-plot fractional designs: Is minimum aberration enough?2006Ingår i: Journal of QualityTechnology, ISSN 0022-4065, Vol. 38, nr 1, s. 56-64Artikel i tidskrift (Refereegranskat)
    Abstract [en]

    Split-plot experiments are commonly used in industry for product and process improvement. Recent articles on designing split-plot experiments concentrate on minimum aberration as the design criterion. Minimum aberration has been criticized as a design criterion for completely randomized fractional factorial design and alternative criteria, such as the maximum number of clear two-factor interactions, are suggested (Wu and Hamada (2000)). The need for alternatives to minimum aberration is even more acute for split-plot designs. In a standard split-plot design, there are several types of two-factor interactions, not all of them equally interesting. However, minimum aberration is not designed to distinguish among the different types of two-factor interactions. It should be noted that this criticism is valid not only for the minimum aberration but also for any other design criteria originally proposed for completely randomized designs. Consequently, we provide a modified version of the maximum number of clear two-factor interactions design criterion to be used for split-plot designs

  • 5.
    Vännman, Kerstin
    Luleå tekniska universitet, Institutionen för teknikvetenskap och matematik, Matematiska vetenskaper.
    Discussion. In Process capability indices, a review, 1992-20002002Ingår i: Journal of QualityTechnology, ISSN 0022-4065, Vol. 34, nr 1, s. 40-42Artikel i tidskrift (Övrigt vetenskapligt)
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