Two-level Fractional Factorial Research Articles

Pilot-Scale Protease Production by Bacillus sp. C4 for Silk Degumming Processes

ABSTRACT The serine protease of Bacillus sp. C-4 has been reported as candidate proteases in the degumming process of the silk industry. The optimization of protease production by Bacillus sp. C4 was carried out using two-level fractional factorial and central composite designs. The investigation was followed by laboratory and pilot-scale protease production using molasses in batch and fed-batch bioreactors to reduce the production cost. The highest protease activity observed (1546.5 U/mL, equivalent to 34.4 U/mL/h) in a 5-L bioreactor was obtained under fed-batch fermentation compared with batch process. The production of protease was subsequently scaled up to a pilot-scale 300-L fed-batch bioreactor, and a maximum protease activity of 1260 U/mL (28 U/mL/h) was observed. The degumming efficiencies of the protease produced by Bacillus sp. C4 in the CCD and bioreactors were 88.3% and 81.6%, respectively, relative to the alkaline degumming method. Furthermore, the stability test of the protease showed that the addition of CaCl2 prolonged the stability of the protease activity from 4 to 8 weeks at room temperature. Furthermore, the protease can be conveniently preserved at room temperature for 1 month and at 4°C for more than 2 months without the addition of any chemicals/cryoprotectants.

The use of factorial design in screening of factors influencing hexavalent chromium extraction by continuous green emulsion liquid membrane

Recently, increasing concerns on hexavalent chromium as an environmental pollutant can be observed due to its build-up to toxic levels in the environment, resulting from various industrial and agricultural activities such as electroplating, stainless steel production, leather tanning and textile manufacturing. This work screens the significant factors that largely affect the efficiency of hexavalent chromium (Cr(VI)) removal from electroplating wastewater in continuous green emulsion liquid membrane using fractional factorial design. There are six factors investigated for affecting the removal of chromium which are residence time (t), TOMAC concentration (M), stripping agent concentration (M), rotational speed (rpm), treat ratio, and modifier concentration (w/v). The response variable of the chromium removal was identified using the two-level fractional factorial (two level) design and the results were analyzed statistically. Five factors were identified to have significant influence on chromium removal which are retention time, rotational speed, treat ratio, modifier concentration and carrier concentration. Regression models for chromium extraction were developed and the adequacy of the model was examined. The results of this study indicate that fractional factorial design is capable to predict the significant factors affecting hexavalent chromium extraction by using continuous green emulsion liquid membrane.

Development of a New Microextraction Fiber Combined to On-Line Sample Stacking Capillary Electrophoresis UV Detection for Acidic Drugs Determination in Real Water Samples.

A new analytical method coupling a (off-line) solid-phase microextraction with an on-line capillary electrophoresis (CE) sample enrichment technique was developed for the analysis of ketoprofen, naproxen and clofibric acid from water samples, which are known as contaminants of emerging concern in aquatic environments. New solid-phase microextraction fibers based on physical coupling of chromatographic supports onto epoxy glue coated needle were studied for the off-line preconcentration of these micropollutants. Identification and quantification of such acidic drugs were done by capillary zone electrophoresis (CZE) using ultraviolet diode array detection (DAD). Further enhancement of concentration sensitivity detection was achieved by on-line CE “acetonitrile stacking” preconcentration technique. Among the eight chromatographic supports investigated, Porapak Q sorbent showed higher extraction and preconcentration capacities. The screening of parameters that influence the microextraction process was carried out using a two-level fractional factorial. Optimization of the most relevant parameters was then done through a surface response three-factor Box-Behnken design. The limits of detection and limits of quantification for the three drugs ranged between 0.96 and 1.27 µg∙L−1 and 2.91 and 3.86 µg∙L−1, respectively. Recovery yields of approximately 95 to 104% were measured. The developed method is simple, precise, accurate, and allows quantification of residues of these micropollutants in Genil River water samples using inexpensive fibers.

Application of multivariate designs in the development of a method for vanadium determination in natural waters by HR-CS GF AAS after cloud-point extraction

A method for trace vanadium determination in natural waters was developed using multivariate approaches (two-level fractional factorial, Doehlert and constrained mixture designs). The preconcentration method was based on the cloud point extraction of vanadium after its complexation with 2-(5-bromo-2-pyridylazo)-5-(diethylamino)-phenol (5-Br-PADAP), separation of a micellar phase on the cloud point of the non-ionic surfactant polyethylene glycol tert-octylphenyl ether (Triton X-114) and subsequent determination using high resolution continuous source graphite furnace atomic absorption spectrometry (HR-CS GF AAS). The developed method presented limits of detection and quantification of 0.13 and 0.42μgL−1 respectively, an enrichment factor of 13.3-fold and precision expressed as a repeatability (% RSD, n=10, 2μgL−1) of 2.5%. Analysis of a certified reference material (Trace elements water, NIST 1643e) and spike tests with recoveries between 84% and 123% showed that the proposed method presents adequate accuracy. The proposed method was applied in the analysis of natural waters collected in an area with naturally occurring vanadium (Maracás, Bahia, Brazil) and groundwater collected from artesian wells located at gas stations.

Copper nanoparticles applied to the preconcentration and electrochemical determination of β-adrenergic agonist: An efficient tool for the control of meat production

A novel method for preconcentration and electrochemical detection of zinterol in bovine urine samples was developed. In order to improve the limit of detection, the surface of a screen-printed carbon electrode was modified with electrodeposited metal copper nanoparticles. The experimental electrodeposition optimization was performed using a central composite design (CCD), involving the variables: precursor concentration, potential and time applied. Copper nanoparticles were characterized by transmission electron microscopy, scanning electron microscopy, cyclic voltammetry, and energy dispersive X-ray spectroscopy. Mesoporous shuttle-like copper oxide nanoparticles were used for the preconcentration step to avoid interferences with many compounds present in the sample matrix. The optimal working conditions for the preconcentration approach were found by means of both two-level fractional factorial and CCD designs. The obtained enhancement factor for a sample volume of 30mL was 35 fold. The calibration curve showed linearity between 0.5 and 45ngmL−1 and the limit of detection was 0.16ngmL−1. The intra and inter assay coefficients of variability were below 4% and 5%; respectively.

Partially replicated two-level fractional factorial designs via semifoldover

Most fractional factorial designs have no replicated points and thus do not provide a reliable estimate for experimental error. The objective of this paper is to study the issue of partially replicated two-level fractional factorial (FF) designs, thereby allowing for the unbiased estimation of the experimental error while maintaining the orthogonality of the main effects. Through the tool of indicator function and the idea of semifoldover, we propose two simple and effective techniques to produce designs with partially replicated points in general two-level FF designs, whether they are regular or not. The related properties of constructed partially replicated designs are investigated. Our results indicate that partially replicated FF are competitive in practice.

Creating clear designs: a graph-based algorithm and a catalog of clear compromise plans

A graph-based algorithm is proposed for creating regular fractional factorial designs with two-level factors such that a pre-specified set of two-factor interactions is clear of aliasing with any main effects or two-factor interactions (clear design). The Clear Interactions Graph (CIG) used in the algorithm is unique for each design and different in nature from the well-known Taguchi linear graph. Based on published catalogs of two-level fractional factorials, enhanced by the CIG, a search algorithm finds an appropriate clear design or declares its non-existence. The approach is applied to the creation of a catalog of minimum aberration clear compromise plans, which is also of interest in its own right. [Supplementary materials are available for this article. Go to the publisher’s online edition of IIE Transactions for additional discussions on run times and implementation of the algorithm for larger designs.]

Application of Modified Organo-Nanoclay as the Sorbent for Zinc Determination by FAAS: An Optimization Study of an Online Pre-concentration System

An online column pre-concentration technique, coupled with flame atomic absorption spectrometry, was developed using a column filled with nanoclay modified with morin. For this purpose, zinc was determined in the water and biological samples. The sample solution was passed through the modified nanoclay column. The adsorbed zinc was subsequently eluted from the column with nitric acid solution. The optimization step was performed using two-level fractional factorial (2(5-2)) and Box-Behnken designs. Firstly, the fractional factorial design was performed for preliminary evaluation of the significant factors. The results showed that pH, amount of morin, and concentration of eluent were significant. The Box-Behnken experimental design was carried out in order to determine the optimum conditions. The optimum conditions were found to be at pH 5.8, 1.8 mg L(-1) of morin and 3.0 mol L(-1) of eluent concentration. Under these optimum conditions, the limit of detection was found to be 0.11 μg L(-1). Furthermore, the relative standard deviation of the ten replicate determinations was <2.8.0%. The method was validated by analyzing the zinc using a certified reference material that is NRCC-SLRS-4 riverine water. The developed procedure was applied to the extraction and determination of zinc in the water and biological samples.

Thermogravimetric analysis and the optimisation of bio-oil yield from fixed-bed pyrolysis of rice husk using response surface methodology (RSM)

The effects of pyrolysis temperature, heating rate, particle size, holding time, and gas flow rate were investigated to optimize bio-oil yield from rice husk pyrolysis. Thermogravimetric analysis showed thermal degradation of hemicellulose, cellulose and lignin, indicating faster decomposition of cellulose compared to lignin. The optimisation process was analysed by employing central composite design (CCD) in response surface methodology (RSM) using Design Expert Version 7.5.1 (StatEase, USA). A two-level fractional factorial was initially carried out and followed by RSM. The statistical analysis showed that pyrolysis temperature, heating rate, particle size and holding time significantly affected the bio-oil yield. By utilising response surface method, these four factors were investigated, analysed and optimal conditions were obtained at pyrolysis temperature of 473.37°C, heating rate of 100°C/min, particle size of 0.6mm and holding time of 1min. Confirmation runs gave 48.30% and 47.80% of bio-oil yield compared to 48.10% of predicted value. Furthermore, the pyrolytic bio-oils obtained from fixed-bed pyrolysis were examined using gas chromatographic/mass spectroscopy (GC/MS), Fourier transform infrared (FTIR) methods, elemental analyzer, pH probe and bomb calorimeter.

Minimum Aberration Two-Level Fractional Factorial Split-Plot Designs with Hard to Change Factors

In this article we will consider industrial experiments in which some experimental factors have hard to change levels and others have levels which are easy to change. In such situations, fractional factorial split plot designs are often used where the hard to change factors are included as a subset of the whole plot factors and the easy to change factors make up the subplot factors. Here we consider the problem of finding two-level split plot designs which have minimum aberration among those designs which also minimize the number of level changes for the hard to change factors.

Computer experiments: application to the case of a recovery boiler

Computer experiments are increasingly used to generate useful information about process and product, which could hardly be possible otherwise. This article explores the applicability of two-level fractional factorials for computer experiments with the aim at identifying the operating parameters of a black liquor recovery boiler, which have the strongest effect on the mass of carryover particles by flue gases. Six analysis methods, which can be easily used by practitioners for factor screening are reviewed and illustrated. The results show that scree plot is a practical and effective tool for screening by using deterministic computer models. Regarding the results, this study allows reducing the mass of carryover particles.

Applications of design of experiments in engineering

Applications of design of experiments in engineering

Optimal Foldover Plans for Two-Level Fractional Factorial Split-Plot Designs

We consider the construction of foldovers of two-level fractional factorial split-plot designs. As a follow-up strategy, the foldover technique is useful when the objective is to systematically de-alias effects of interest after the initial fractional factorial split-plot design has been run. Due to the sequential nature in which the runs of the initial and foldover designs are conducted, the resulting combined design (the design consisting of both the initial design and its foldover) is a blocked fractional factorial split-plot design. Using the minimum aberration criterion for blocked fractional factorial split-plot designs, in conjunction with other optimality criteria, we provide a catalog of optimal foldover plans for initial minimum aberration fractional factorial split-plot designs consisting of 16 and 32 runs.

Optimization of thaumatin extraction by aqueous two-phase system (ATPS) using response surface methodology (RSM)

The work attempts to study and optimize aqueous two-phase system (ATPS) made of polyethylene glycol (PEG)/sodium sulfate and PEG/potassium phosphate. Five factors (PEG's molecular weight, PEG's concentration, pH, concentration of sodium chloride and phase-forming salt) affecting the thaumatin partitioning were studied. A two-level fractional factorial was initially carried out. The statistical analysis showed that for both the systems, the phase-forming salt concentration and the concentration of sodium chloride significantly affects the K value for thaumatin partitioning. However, the performance of PEG/sodium sulfate system was generally better than the PEG/potassium phosphate system. Hence a detail study was carried out on the PEG/sodium sulfate system using central composite rotatable design (CCRD) in response surface methodology (RSM). It was observed that high salt concentration increased the K value by sevenfold and the PEG molecular weight was not a significant factor. The optimal condition gave a K value for thaumatin partitioning of 24.15 with a yield of 96.02%.

A generalization of the alias matrix

The investigation of aliases or biases is important for the interpretation of the results from factorial experiments. For two-level fractional factorials this can be facilitated through their group structure. For more general arrays the alias matrix can be used. This tool is traditionally based on the assumption that the error structure is that associated with ordinary least squares. For situations where that is not the case, we provide in this article a generalization of the alias matrix applicable under the generalized least squares assumptions. We also show that for the special case of split plot error structure, the generalized alias matrix simplifies to the ordinary alias matrix.

Irregular Four-level Response Surface Designs

Four-level response surface designs based on regular two-level fractional factorial designs were introduced by Edmondson (1991). Here, the methods are extended to include designs based on irregular two-level fractional factorials. These designs allow orthogonal blocking and require fewer experimental units than the regular designs.

Two-Level Factorial and Fractional Factorial Designs in Blocks of Size Two

It is sometimes necessary to perform two-level factorial designs in blocks of size two. We investigate what combinations of designs in different pairing arrangements permit estimation of all main effects and two-factor interactions. The confounding patterns of selected combination designs which combine several 2k designs in different pairings are presented for k = 2, 3, 4, and 5. We seek “best” combination designs which provide the most pure (within block) estimates of main effects and two-factor interactions under each confounding pattern given. Some “best” sequential combinations of 2k designs with various choices of initial arrangements are also given. The popular mirror-image pairing design is not the best initial arrangement, but is valuable for providing pure estimates of all the main effects. Extensions to 2k−p fractional factorial designs are illustrated. An example illustrates the use of a follow-up inter-block analysis.

Optimal Foldover Plans for Two-Level Fractional Factorial Designs

A commonly used follow-up experiment strategy involves the use of a foldover design by reversing the signs of one or more columns of the initial design. Defining a foldover plan as the collection of columns whose signs are to be reversed in the foldover design, this article answers the following question: Given a 2k−p design with k factors and p generators, what is its optimal foldover plan? We obtain optimal foldover plans for 16 and 32 runs and tabulate the results for practical use. Most of these plans differ from traditional foldover plans that involve reversing the signs of one or all columns. There are several equivalent ways to generate a particular foldover design. We demonstrate that any foldover plan of a 2k−p fractional factorial design is equivalent to a core foldover plan consisting only of the p out of k factors. Furthermore, we prove that there are exactly 2k−p foldover plans that are equivalent to any core foldover plan of a 2k−p design and demonstrate how these foldover plans can be constructed. A new class of designs called combined-optimal designs is introduced. An n-run combined-optimal 2k−p design is the one such that the combined 2k−p+1 design consisting of the initial design and its optimal foldover has the minimum aberration among all 2k−p designs.

Deconfounding Two-Factor Interactions with a Minimum Number of Extra Runs

In two-level fractional factorial (2 k−p ) designs, resolution is a concept that describes the type of confounding present for the design in use. A resolution IV fractional factorial experimental d...

Latin Squares and Two-Level Fractional Factorial Designs

In an industrial setting one is often challenged to find minimum run designs that will result in maximal information and can be readily understood by all involved. The following discussion considers an example where the design was constructed such that it was both a Latin square and a fractional factorial in order to optimize analysis options as well as presentation options. For an M × M Latin square if M = 2k, then the three factors (rows, columns, and treatments) can also be studied using the same number of runs and a 23k–k fractional factorial design. The advantage to this is that the results can be easily analyzed using Yates' algorithm and the confounding pattern is readily available. While every Latin square corresponds to a subset of the points in a complete 23k design, only one standard square corresponds to a 23k–k fractional factorial design, and all the others correspond to designs where the contrasts are not all orthogonal. Thus, it may not always be desirable to choose a Latin square at random. An example using a Latin square/fractional factorial design to study a fermentation process is discussed.