Explore the vast range of titles available.

Fractional factorial (FF) designs are commonly used for factorial experiments in many fields. When some prior knowledge has shown that some factors are more likely to be significant than others, Li, et al. (2015) proposed a new pattern, called the individual word length pattern (IWLP), which, defined on a column of the design matrix, measures the aliasing of the effect assigned to this column and effects involving other factors. In this paper, the authors first investigate the relationships between the IWLP and other popular criteria for regular FF designs. As we know, fractional factorial split-plot (FFSP) designs are important both in theory and practice. So another contribution of this paper is extending the IWLP criterion from FF designs to FFSP designs. The authors propose the IWLP of a factor from the whole-plot (WP), or sub-plot (SP), denoted by the I w WLP and I s WLP respectively, in the FFSP design. The authors further propose combined word length patterns C w WLP and C s WLP, in order to select good designs for different cases. The new criteria C w WLP and C s WLP apply to the situations that the potential important factors are in WP or SP, respectively. Some examples are presented to illustrate the selected designs based on the criteria established here.

Purpose The purpose of this paper is to show how to properly use the method of replacement to construct mixed two- and four-level minimum setup split-plot type designs to accommodate the presence of hard-to-assemble parts. Design/methodology/approach Split-plot type designs are economical approaches in industrial experimentation. These types of designs are particularly useful for situations involving interchangeable parts with different degrees of assembly difficulties. Methodologies for designing and analyzing such experiments have advanced lately, especially for two-level designs. Practical needs may require the inclusion of factors with more than two levels. Here, the authors consider an experiment to improve the performance of a Baja car including two- and four-level factors. Findings The authors find that the direct use of the existing minimum setup maximum aberration (MSMA) catalogs for two-level split-plot type designs may lead to inappropriate designs (e.g. low resolution). The existing method of replacement for searching exclusive sets of the form (α, β, αβ) available in the literature is suitable for completely randomized designs, but it may not provide efficient plans for designs with restricted randomization. Originality/value The authors provide a general framework for the practitioners and have extended the algorithm to find out the number of generators and the number of base factor at each stratum, which guide the selection of mixed two-level and four-level MSMA split-plot type designs.

This article introduces a new class of experimental designs, called split factorials, which allow for the estimation of both response surface effects (fixed effects of crossed factors) and variance components arising from nested random effects. With an economical run size, split factorials provide flexibility in dividing the degrees of freedom among the different estimations. For a split factorial design, it is shown that the OLS estimators for the fixed effects are BLUE and that the variance component estimators from the mean squared errors on the ANOVA table are minimum variance among unbiased quadratic estimators. An application involving concrete mixing demonstrates the use of a split factorial experiment.

A promising technology for integration of top-down nanomanufacturing is equal channel angular pressing, a process transforming metallic materials into nanostructured or ultra-fine grained materials with significantly enhanced performance characteristics. To bridge the gap between process potential and actual manufacturing output a novel prototype system identified as indexing equal channel angular pressing (IX-ECAP) was developed to capitalize on sustainable engineering opportunities of transforming spent or scrap engineering elements into key engineering commodities by recycling 4043 aluminium alloy welding rod residuals. A resolution III fractional factorial split-plot experiment assessed significance of predictors on the response, microhardness, with multiple linear regression used for model development. Five process parameters involving pressing temperature, number of passes, pressing speed, back pressure, and vibration were studied. Microhardness conversions allowed theoretical determination of grain sizes employing Hall-Petch relationships. IX-ECAP offered a viable solution whereby processing of discrete variable length work pieces proved very successful.

Considerable effort has been put over the last few decades into clarifying the correct design and analysis of split-plot factorial experiments. However, the information found in the literature is scattered and sometimes still not easy to grasp for non-experts. Because of the importance of split-plots for the industry and the fact that any experimenter may need to use them at some point, a detailed and step-by-step guide collecting all the available information on the fundamental methodology in one place was deemed necessary. More specifically, this paper discusses the simple case of an unreplicated split-plot factorial experiment with more than one whole-plot (WP) factors and all factors set at two levels each. Explanations on how to properly design the experiment, analyze the data, and assess the proposed model are provided. Special attention is given to clarifications on the calculations of contrasts, effects, sum of squares (SS), parameters, WP and sub-plot (SP) residuals, as well as the proper division of the proposed model into its sub-designs and sub-models for calculating measures of adequacy correctly. The application of the discussed theory is showcased by a case study on the recycling of molybdenum (Mo) from CIGS solar cells. Factors expected to affect Mo recovery were investigated and the analysis showed that all of them are significant, while the way they affect the response variable was also revealed. After reading this guide, the reader is expected to acquire a good understanding of how to work with split-plots smoothly and handle with confidence more complex split-plot types.

Many industrial experiments involve factors with levels more difficult to change or control than others, which leads to the development of two-level fractional factorial split-plot (FFSP) designs. Recently, mixed-level FFSP designs were proposed due to the requirement of different-level factors. In this paper, we generalize the Bayesian optimal criterion for mixed two- and four-level FFSP designs, and then provide Bayesian minimum aberration (MA) criterion to rank FFSP designs. Bayesian MA criterion can give a natural ordering for the effects involving two-level factors and three components of a four-level factor. We also discuss the relationship between the Bayesian optimal and Bayesian MA criteria. Furthermore, we consider the designs with both qualitative and quantitative factors.

The past decade has seen rapid advances in the development of new methods for the design and analysis of split-plot experiments. Unfortunately, the value of these designs for industrial experimentation has not been fully appreciated. In this paper, we review recent developments and provide guidelines for the use of split-plot designs in industrial applications.

Minimum aberration is a popular method of selecting fractional factorial designs. Numerous extensions to the original methods have benefited fields of experimental design such as multi-stratum designs, multi-group designs, and multi-platform designs. However, most of these extensions are ad hoc, developed on case-by-case bases without strong statistical justifications or a unified rationale. As such, we provide a new perspective on minimum aberration using a Bayesian approach. Our theory includes a unified framework for minimum aberration and is easily applied to many situations. Furthermore, it enables experimenters to derive their own aberration criteria. Several theoretical results and three numerical illustrations are provided.

Under the potential outcomes framework, we propose a randomization based estimation procedure for causal inference from split-plot designs, with special emphasis on 2² designs that naturally arise in many social, behavioral and biomedical experiments. Point estimators of factorial effects are obtained and their sampling variances are derived in closed form as linear combinations of the between- and within-group covariances of the potential outcomes. Results are compared to those under complete randomization as measures of design efficiency. Conservative estimators of these sampling variances are proposed. Connection of the randomization-based approach to inference based on the linear mixed effects model is explored. Results on sampling variances of point estimators and their estimators are extended to general split-plot designs. The superiority over existing model-based alternatives in frequency coverage properties is reported under a variety of simulation settings for both binary and continuous outcomes.

Fractional factorial split-plot designs are widely used when it is impractical to perform fractional factorial experiments in a completely random order. When there are too many subplots per whole plot, or too few whole plots, fractional factorial split-plot designs with replicated settings of the whole plot factors are preferred. However, such an important study is undeveloped in the literature. This paper considers fractional factorial split-plot designs with replicated settings of the WP factors from the viewpoint of clear effects. We investigate the sufficient and necessary conditions for this class of designs to have clear effects. An algorithm is proposed to generate the desirable designs which have the most clear effects of interest. The fractional factorial split-plot design with replicated settings of the WP factors is analysed and the results are discussed.