Screening Procedures to Identify Robust Product or Process Designs Using Fractional Factorial Experiments

In many quality improvement experiments, there are one or more ``control'' factors that can be modified to determine a final product design or manufacturing process, and one or more ``environmental'' (or `` noise'') factors that vary under field or manufacturing conditions. In many applications, the product design or process design is considered seriously flawed if its performance is poor for any level of the environmental factor. For example, if a particular prosthetic heart valve design has poor fluid flow characteristics for certain flow rates, then a manufacturer will not want to put this design into production. Thus this paper considers cases when it is appropriate to measure a product's quality to be its {\em worst} performance over the levels of the environmental factor. We consider the frequently occurring case of combined-array experiments and extend the subset selection methodology of Gupta (1956, 1965) to provide statistical screening procedures to identify product designs that maximize the worst case performance of the design over the environmental conditions for such experiments. A case study is provided to illustrate the proposed procedures

Selection and Screening Procedures to Determine Optimal Product Designs. (REVISED, April 1997)

To compare several promising product designs, manufacturers must measure their performance under multiple environmental conditions. In many applications, a product design is considered to be seriously flawed if its performance is poor under any level of the environmental factor. For example, if a particular automobile battery design does not function well under some temperature conditions, then a manufacturer may not want to put this design into production. Thus, in this paper we consider the overall measure of a given product's quality to be its worst performance over the environmental levels. We develop statistical procedures to identify (a near) the optimal product design among a given set of product designs, i.e., the manufacturing design associated with the greatest overall measure of performance. We accomplish this for intuitive procedures based on the split-plot experimental design (and the randomized complete block design as a special case); split-plot designs have the essential structure of a product array and the practical convenience of local randomization. Two classes of statistical procedures are provided. In the first, the delta-best formulation of selection problems, we determine the number of replications of the basic split-plot design that are needed to guarantee, with a given confidence level, the selection of a product design whose minimum performance is within a specified amount, delta, of the performance of the optimal product design. In particular, if the difference between the quality of the best and 2nd best manufacturing designs is delta or more, then the procedure guarantees that the best design will be selected with specified probability. For applications where a split-plot experiment involving several product designs has been completed without the planning required of the delta-best formulation, we provide procedures to construct a "confidence subset" of the manufacturing designs; the selected subset contains the optimal product design with a prespecified confidence level. The latter is called the subset selection formulation of selection problems. Examples are provided to illustrate the procedures

A Note on Teaching Binomial Confidence Intervals

For constructing confidence intervals for a binomial proportion $p$, Simon (1996, Teaching Statistics) advocates teaching one of two large-sample alternatives to the usual $z$-intervals $\hat{p} \pm 1.96 \times S.E(\hat{p})$ where $S.E.(\hat{p}) = \sqrt{ \hat{p} \times (1 - \hat{p})/n}$. His recommendation is based on the comparison of the closeness of the achieved coverage of each system of intervals to their nominal level. This teaching note shows that a different alternative to $z$-intervals, called $q$-intervals, are strongly preferred to either method recommended by Simon. First, $q$-intervals are more easily motivated than even $z$-intervals because they require only a straightforward application of the Central Limit Theorem (without the need to estimate the variance of $\hat{p}$ and to justify that this perturbation does not affect the normal limiting distribution). Second, $q$-intervals do not involve ad-hoc continuity corrections as do the proposals in Simon. Third, $q$-intervals have substantially superior achieved coverage than either system recommended by Simon

From here, from there, and from beyond: endogenous and exogenous factors triggering change along the cluster life cycle in a multi-scalar environment

While explaining cluster internal impacts on cluster development, cluster life cycle theory fails to explain the influence of cluster external factors. Based on a multiscalar approach, this study investigates factors causing change within an agritech cluster applying a qualitative approach. Main shifts in cluster development and their inducing factors from multiple scalar and thematic contexts are investigated. Concluding, incremental changes are mainly induced by knowledge dynamics within the same industry, especially from the local level. Radical change is the result of an exogenous shock from the national institutional environment. In total, specific changes are induced by specific factors from specific scales

The Use of Subset Selection in Combined Array Experiments to Determine Optimal Product or Process Designs. (REVISED, June 1997)

A number of authors in the quality control literature have advocated the use of combined-arrays in screening experiments to identify robust product or process designs [Shoemaker, Tsui, and Wu (1991); Nair et al. (1992); Myers, Khuri, and Vining (1992), for example]. This paper considers a product manufacturing or process design setting in which there are several factors under the control of the manufacturer, called control settings, and other environmental (noise) factors that that vary under field or manufacturing conditions. We show how Gupta's subset selection philosophy can be used in such a quality improvement setting to identify combinations of the levels of the control factors that correspond either to products that are robust to environmental variations during their use or to processes that fabricate items whose quality is independent of the variations in the raw materials used in their manufacture. [Gupta (1956, 1965)]

Pointwise consistency of the kriging predictor with known mean and covariance functions

This paper deals with several issues related to the pointwise consistency of the kriging predictor when the mean and the covariance functions are known. These questions are of general importance in the context of computer experiments. The analysis is based on the properties of approximations in reproducing kernel Hilbert spaces. We fix an erroneous claim of Yakowitz and Szidarovszky (J. Multivariate Analysis, 1985) that the kriging predictor is pointwise consistent for all continuous sample paths under some assumptions.Comment: Submitted to mODa9 (the Model-Oriented Data Analysis and Optimum Design Conference), 14th-19th June 2010, Bertinoro, Ital

09181 Abstracts Collection -- Sampling-based Optimization in the Presence of Uncertainty

This Dagstuhl seminar brought together researchers from statistical ranking and selection; experimental design and response-surface modeling; stochastic programming; approximate dynamic programming; optimal learning; and the design and analysis of computer experiments with the goal of attaining a much better mutual understanding of the commonalities and differences of the various approaches to sampling-based optimization, and to take first steps toward an overarching theory, encompassing many of the topics above

Semi-rational engineering of cellobiose dehydrogenase for improved hydrogen peroxide production

Abstract Background The ability of fungal cellobiose dehydrogenase (CDH) to generate H2O2 in-situ is highly interesting for biotechnological applications like cotton bleaching, laundry detergents or antimicrobial functionalization of medical devices. CDH’s ability to directly use polysaccharide derived mono- and oligosaccharides as substrates is a considerable advantage compared to other oxidases such as glucose oxidase which are limited to monosaccharides. However CDH’s low activity with oxygen as electron acceptor hampers its industrial use for H2O2 production. A CDH variant with increased oxygen reactivity is therefore of high importance for biotechnological application. Uniform expression levels and an easy to use screening assay is a necessity to facilitate screening for CDH variants with increased oxygen turnover. Results A uniform production and secretion of active Myriococcum thermophilum CDH was obtained by using Saccharomyces cerevisiae as expression host. It was found that the native secretory leader sequence of the cdh gene gives a 3 times higher expression than the prepro leader of the yeast α-mating factor. The homogeneity of the expression in 96-well deep-well plates was good (variation coefficient <15%). A high-throughput screening assay was developed to explore saturation mutagenesis libraries of cdh for improved H2O2 production. A 4.5-fold increase for variant N700S over the parent enzyme was found. For production, N700S was expressed in P. pastoris and purified to homogeneity. Characterization revealed that not only the kcat for oxygen turnover was increased in N700S (4.5-fold), but also substrate turnover. A 3-fold increase of the kcat for cellobiose with alternative electron acceptors indicates that mutation N700S influences the oxidative- and reductive FAD half-reaction. Conclusions Site-directed mutagenesis and directed evolution of CDH is simplified by the use of S. cerevisiae instead of the high-yield-host P. pastoris due to easier handling and higher transformation efficiencies with autonomous plasmids. Twelve clones which exhibited an increased H2O2 production in the subsequent screening were all found to carry the same amino acid exchange in the cdh gene (N700S). The sensitive location of the five targeted amino acid positions in the active site of CDH explains the high rate of variants with decreased or entirely abolished activity. The discovery of only one beneficial exchange indicates that a dehydrogenase’s oxygen turnover is a complex phenomenon and the increase therefore not an easy target for protein engineering.The authors thank the European Commission (FP7 243529-2-COTTONBLEACH) for financial support. CKP thanks the Austrian Science Fund (FWF) for financial support (grant P22094). IK is a member of the doctoral program BioToP (Biomolecular Technology of Proteins) of the Austrian Science Fund (FWF; W1224). MA thanks the Spanish Government for financial support (BIO2010-19697).Peer Reviewe