Construction of Two-Level Split-Lot Fractional Factorial Designs for Multistage Processes

Butler, Neil A.

doi:10.1198/004017004000000446

Cited by 16 publications

(18 citation statements)

References 15 publications

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“…Butler 12 focuses on two-level designs, and presents minimum aberration strip-plot designs for two-stage processes and minimum aberration split-lot designs (which are generalizations of strip-plot designs) for three-and four-stage processes. The minimum aberration property of the designs guarantees minimal confounding between main effects and two-factor interaction effects.…”

Section: Combinatorial Construction Methodsmentioning

confidence: 99%

Design and analysis of industrial strip‐plot experiments

Arnouts

Goos

Jones

2009

Quality & Reliability Eng

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The cost of experimentation can often be reduced by forgoing complete randomization. A well-known design with restricted randomization is a split-plot design, which is commonly used in industry when some experimental factors are harder to change than others or when a two-stage production process is studied. Split-plot designs are also often used in robust product design to develop products that are insensitive to environmental or noise factors. Another, lesser known, type of experimental design plan that can be used in such situations is the strip-plot experimental design. Strip-plot designs are economically attractive in situations where the factors are hard to change and the process under investigation consists of two distinct stages, and where it is possible to apply the second stage to groups of semi-finished products from the first stage. They have a correlation structure similar to row-column designs and can be seen as special cases of split-lot designs. In this paper, we show how optimal design of experiments allows for the creation of a broad range of strip-plot designs.

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Section: Combinatorial Construction Methodsmentioning

confidence: 99%

Design and analysis of industrial strip‐plot experiments

Arnouts

Goos

Jones

2009

Quality & Reliability Eng

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“…This has the same implication as the multi-way split-unit design proposed by Taguchi [17]. Butler [2] also mentioned that a split-lot design with two stages is equivalent to a strip-plot design as described by Miller [11] and provided guidelines for constructing two-level split-lot fractional factorial designs for multistage processes. However, these studies only focused on the design of experiments for multistage processes; they did not emphasize the analysis of the experiments.…”

Section: Introductionmentioning

confidence: 94%

“…Compared to the process in Figure 1(a), the process in Figure 1(b) has two distinct features: first, there is a distinct difference in terms of the time or location of the factors. In Figure 1(b), factor 1 x functions first at stage 1, while the second factor, 2 x , functions at a later stage, after the effect of 1 x on ' y , which is unobservable in practice. Second, a new interaction structure is presented in the process.…”

Section: Introductionmentioning

confidence: 97%

“…Second, a new interaction structure is presented in the process. With the variation propagating from upstream stages to downstream stages, the error term from stage 1, '  , enters stage 2 and may interact with 2 x , while it is physically impossible for the disturbance at stage 2,  , to move backward to interact with 1…”

Section: Introductionmentioning

confidence: 99%

“…Butler [2] suggested that split-lot designs are potentially useful for multistage processes. In such a design, each stage has a split-plot structure.…”

Section: Introductionmentioning

confidence: 99%

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A Mixed-Effect Model for Analyzing Experiments with Multistage Processes

Wang

Dai

2014

Quality Technology & Quantitative Management

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______________________________________________________________________Abstract: In industrial practice, most products are produced by processes that involve multiple stages.In studying multistage processes via designed experiments, some practitioners treat them as single-stage processes and follow the usual factorial designs or split-plot designs. In this paper, through an analysis of the error transmission mechanism, we propose a mixed-effect model for analyzing experiments with multistage processes. Based on an analysis of simulated and real experimental data, we find that different conclusions about factor significance may be drawn if the data are analyzed differently. In addition, the mixed-effect model can help separate errors at different stages and hence provide more information on process improvement.

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Bibliography

2011

Optimal Design of Experiments

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Construction of Two-Level Split-Lot Fractional Factorial Designs for Multistage Processes

Cited by 16 publications

References 15 publications

Design and analysis of industrial strip‐plot experiments

Design and analysis of industrial strip‐plot experiments

A Mixed-Effect Model for Analyzing Experiments with Multistage Processes

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