Three-level Design Research Articles

Direct construction of three-level designs with less β-aberration

The β-wordlength pattern has been justified as an appropriate criterion for measuring designs with quantitative factors. However, construction methods of designs with less β-aberration have not been fully investigated. In this paper, some properties of β-wordlength pattern for three-level designs will be firstly provided, and then a direct construction method is proposed to generate three-level designs with using 2-level orthogonal arrays. Subsequently, two methods of level rearrangement are discussed to reduce the β 3 and β 4 of the resultant designs. Moreover, the advantages of these two methods are also compared. Finally, numerical examples are presented to illustrate the effectiveness of the proposed methods.

Best Linear Unbiased Prediction of Latent Means in Three-Level Data

Decomposing variables into between and within components are often required in multilevel analysis. This method of decomposition should not ignore possible unreliability of an observed group mean (i.e., arithmetic mean) that is due to small cluster sizes and can lead to substantially biased estimates. Adjustment procedures that allow unbiased estimation have been defined and implemented in software for a two-level model. This study shows how to implement a two-stage adjustment procedure in a three-level design. A simulation study showed that the adjustment procedure provides unbiased estimates. To demonstrate how the adjustment procedure can change results in a real data context, an illustration is provided using a set up in which 355 Level-1 units are nested in 93 Level-2 and 19 Level-3 units.

Wordlength enumerator for fractional factorial designs

While the minimum aberration criterion is popular for selecting good designs with qualitative factors under an ANOVA model, the minimum $\beta$-aberration criterion is more suitable for selecting designs with quantitative factors under a polynomial model. In this paper, we propose the concept of wordlength enumerator to unify these two criteria. The wordlength enumerator is defined as an average similarity of contrasts among all possible pairs of runs. The wordlength enumerator is easy and fast to compute, and can be used to compare and rank designs efficiently. Based on the wordlength enumerator, we develop simple and fast methods for calculating both the generalized wordlength pattern and the $\beta$-wordlength pattern. We further obtain a lower bound of the wordlength enumerator for three-level designs and characterize the combinatorial structure of designs achieving the lower bound. Finally, we propose two methods for constructing supersaturated designs that have both generalized minimum aberration and minimum $\beta$-aberration.

Microwave-Assisted Extraction of Andrographolide, 14-Deoxy-11,12- didehydroandrographolide and Neoandrographolide from Andrographis paniculata: An Optimisation Study

Background: Andrographis paniculata is often used as functional foods owing to its broad range of pharmaceutical activities due to the presence of main terpene compounds such as andrographolide, 14-deoxy-11,12-didehydroandrographolide and neoandrographolide. The aforementioned compounds must be extracted from the plant material before it can be routinely used as a functional food ingredient. Objective: This work presents an optimisation study of microwave-assisted extraction (MAE) of terpene from Andrographis paniculata. In this study, two factors at three-level central composite face centred design was employed to optimise the process variables, including the effect of microwave power (75-175 W) and ethanol concentration (20-85%) on extraction of terpene from Andrographis paniculata. Methods: The experimental design was set based on initial screening on the effect of mesh size and solid solvent ratio. The present work was performed at fixed mesh size and solid solvent ratio, which corresponds to the highest yield established experimentally. Two most significant factors, i.e. microwave power and ethanol concentration was chosen and further studied for optimisation using a response surface methodology. The three-level, two-factor central composite design (CCD) has been employed to determine the effect of microwave power (15, 25 and 35 W/mL) and ethanol concentration (20, 52.5 and 85%) on the yield of terpene extraction. Identification and quantification of the terpene were performed via Ultra-Performance Liquid Chromatography- Photodiode Array (UPLCPDA). Results: The regression analysis showed good fit of the experimental data to the quadratic equation with coefficient of determination (R2) value of 0.997. The optimum condition was found at microwave power of 140 W with 85% ethanol concentration, produced the highest yield of andrographolide (10.926 ± 0.053 mg/g DW), 14-deoxy-11,12-didehydroandrographolide (4.336 ± 0.215 mg/g DW) and neoandrographolide (5.698 ± 0.252 mg/g DW). The model developed through response surface modelling has a desirability of 97.5% and the error between the experiment and the model predictions ranged from 2.4 to 5.2%. Conclusion: A successful optimisation of terpene extraction from A. paniculata via MAE was achieved at microwave power of 140 W and 85% ethanol. The model developed from the regression analysis is sufficiently accurate and can be used to predict the yield of terpene extraction from A. paniculata.

Microencapsulation of betacyanin from red dragon fruit (Hylocereus polyrhizus) peels using pectin by simple coacervation to enhance stability.

Betacyanin is a red natural dye pigment widely used in food products. However, the pigment is also unstable and easily degraded by temperature during storage and food processing. This research aims to increase the stability of betacyanin obtained from dragon fruit peels using pectin as a wall medium via the coacervation method. Due to the efficiency and shell integrity, the coacervation method was selected instead of spray drying to enhance betacyanin's stability. Coacervation was conducted in a three-necked round-bottomed flask fitted with a mercury-sealed stirrer and reflux condenser. An accelerated stability test was conducted at 80°C and 100°C for 30min and considered completed after obtaining a stable absorbance. Two full factorials, three-level design, for 80°C and 100°C, were analyzed by Response Surface Methodology using Minitab® 19. The core/wall ratio, agitation speed, and pH were the continuous variables, with temperature as the categorical variables. The models were yielded high R-square and low coefficient of variance on the validation process. Simple coacervation is selected because of a superior method such as simplicity, low-cost, high efficiency, and high shell integrity.

Design, assembly, and pre-commissioning of cryostat for 3W1 superconducting wiggler magnet

One of the most important devices for the High Energy Photon Source Test Facility project, the 2.6 T 32-pole 3W1 superconducting wiggler, was designed by the Institute of High Energy Physics (IHEP); its magnetic gap is 68 mm, and its storage energy is 286 kJ. It will be installed at the storage ring of the Beijing Electron Positron Collider Upgrade Project at the IHEP to replace the old permanent wiggler. The primary purpose of the cryostat is to create a safe and reliable system and realize long-term operation with zero liquid helium consumption. To maintain liquid helium temperature, four identical two-stage cryocoolers are placed symmetrically at the wiggler ends. The cryostat has only one 60 K thermal shield, which is used to reduce the heat load to the liquid helium vessel. The cryostat has several novel features, including a suspension system with little heat leakage that is self-centered during cooling of the cryostat, a special copper liner and high-efficiency condensers, three pairs of binary current leads, and three-level safety design. The cryogenic system has been cooled three times, and the residual cooling capacity is approximately 0.41 W at 4.2 K without current.

Multistage work hardening assisted by multi-type twinning in ultrafine-grained heterostructural eutectic high-entropy alloys

High strength of materials usually comes with low ductility due to the lost or short-lived strain hardening. Here, we uncover a sequentially-activated multistage strain hardening (SMSH) that allows for sustained and effective strain-hardening capability in strong ultrafine-grained eutectic high-entropy alloy (EHEA). Consequently, exceptional ductility is realized in an ultrafine-grained EHEA, accompanied with high ultimate strength. We demonstrate that the SMSH is derived from a coordinated three-level design on structural heterogeneity, grain-size control, and intragranular composition modification, which enables the sequential activation of stress-dependent multiple hardening mechanisms. Furthermore, despite the well-known low twinning propensity due to ultrafine grains and medium-to-high stacking fault energies of prototype EHEAs, our coordinated design sequentially activates three types of deformation twinning to assist this SMSH. This work sheds light on the SMSH effect assisted by multi-type twinning previously unexpected in ultrafine-grained EHEAs, and thereby represents a promising route for improving ductility of high-strength materials.

Multi-response optimization of AA 8011 and 12 wt.-% fly ash composites

Abstract The present research work is focused on the production of aluminum alloy 8011 with 12 wt.-% fly ash composite by using the stir casting method. A three-level central composite design experiment is developed using response surface methodology (RSM) with various parameters. Load, time and sliding velocity are varied in the range of (5-15 N), (5-15 min) and (1.5-4.5 m × s-1), respectively. Dry sliding wear tests are performed as per the experimental design using a pin-on-disc at room temperature. This paper describes how optimization studies were carried out on a dry sliding wear process with multi-response characteristics based on MCDM using the TOPSIS approach. The process parameters, load, time and sliding velocity are optimized with multi-response characteristics, including the wear rate (WR), and the coefficient of friction (COF). A sensitivity analysis is also carried out and compared with the relative impact of input parameters on wear behavior in order to verify the measurement errors on the values of the uncertainty in estimated parameters. The experimental results indicate that the multi-response characteristics of aluminum alloy 8011 with 12 wt.-% fly ash composite used during the wear behavior process can be enhanced through the TOPSIS method.

An appealing technique for designing optimal large experiments with three-level factors

Experimental design is arguably the most commonly used and effective methodology in scientific investigations and industrial applications. Real-world experiments may have hundreds or even thousands of input variables (factors) and thus a large number of observations (experimental runs) is needed to gain a better understanding of the phenomena under the investigation and estimate the most important parameters without bias and with minimum variance. Constructing optimal designs for these large experiments is a significant NP-hard problem investigators may face. This paper gives a new simple efficient technique, called multiple tripling technique, for constructing optimal (in view of distance, aberration, power moments, orthogonality, uniformity) designs for large experiments with three-level factors by multiple tripling of small and simple three-level initial designs. Some logical questions are now arising, such as how to effectively select initial designs to get optimal resulting multiple triple designs, how to measure the optimality of a resulting multiple triple design relative to all the possible designs with the same size, and what is the efficiency of the multiple tripling technique relative to the existing widely used techniques for constructing large three-level designs? Through theoretical and computational justifications, this paper tries to answer these significant questions. Without computational time (no computer search), the multiple tripling technique is used to construct new recommended optimal designs which are better than the existing recommended designs or cannot be constructed by the existing techniques due to their large sizes.

A new foldover strategy and optimal foldover plans for three-level design

The foldover is a useful technique in construction of factorial designs. It is also a standard follow-up strategy discussed in many textbooks by adding a second fraction called a foldover design. In this paper uniformity criterion measured by the wrap-around $$L_2$$ -discrepancy is used to further distinguish the optimal foldover plan for three-level designs. For three-level fractional factorials as the original designs, a new foldover strategy is provided based on level permutation of each factor, which vastly enlarge the full foldover space. Some theoretical properties of the defined foldover plans are obtained, a tighter lower bound of the wrap-around $$L_2$$ -discrepancy of combined designs is also provided, which can be used as a benchmark for searching optimal foldover plans. For illustration of our theoretical results and comparison with the existing results, a catalog of optimal foldover plans of the new strategy for uniform initial designs with s three-level factors is tabulated, where $$2\le s \le 11$$ .

Validated Stability Indicating and Assay Method Development of Linagliptin in Formulation by RP-HPLC Using Quality by Design

Quality by Design (QbD) approach was used to facilitate stability indicating HPLC method development of linagliptin (LIN) in tablet dosage form. The method was developed using the PrimesilC18, 250 mm x 4.6 mm, 5µ column using the mobile phase consisting of 0.3% TEA: methanol. (60:40 v/v) pH 4.5 adjusted with o-phosphoric acid. Design of experiment tools was used for optimization of the chromatographic conditions. A three-level Box-Behnken design was employed and statistical analysis of the experimental data showed the significant influential factor of chromatographic conditions. The design space suggested that the current center point parameters could be further modified results with better acceptability for the response parameters. The performance of the optimized method was validated according to ICH guidelines. Linagliptin was exposed to different stress conditions (acid, base, neutral, oxidative, thermal and photolytic) and chromatograms recorded at 292 nm. The degradation of linagliptin followed zero order kinetics for acidic, oxidative and neutral hydrolysis whereas for basic hydrolysis first-order kinetics under experimental conditions. Peak purity plots were evaluated for the degraded sample. The results obtained suggest that the method can be adopted for its analysis and is stability indicating as well. The three-level design helps in understanding the interaction among factors rather than one time one variation as carried out in routine method development. DOI: http://dx.doi.org/10.17807/orbital.v12i2.1194

Investigation of Stability of CO2 Microbubbles—Colloidal Gas Aphrons for Enhanced Oil Recovery Using Definitive Screening Design

CO2 microbubbles have recently been used in enhanced oil recovery for blocking the high permeability zone in heterogeneous reservoirs. Microbubbles are colloidal gas aphrons stabilized by thick shells of polymer and surfactant. The stability of CO2 microbubbles plays an important role in improving the performance of enhanced oil recovery. In this study, a new class of design of experiment (DOE)—definitive screening design (DSD) was employed to investigate the effect of five quantitative parameters: xanthan gum polymer concentration, sodium dodecyl sulfate surfactant concentration, salinity, stirring time, and stirring rate. This is a three-level design that required only 11 experimental runs. The results suggest that DSD successfully evaluated how various parameters contribute to CO2 microbubble stability. The definitive screening design revealed a polynomial regression model has ability to estimate the main effect factor, two-factor interactions and pure-quadratic effect of factors with high determination coefficients for its smaller number of experiments compared to traditional design of experiment approach. The experimental results showed that the stability depend primarily on xanthan gum polymer concentration. It was also found that the stability of CO2 microbubbles increases at a higher sodium dodecyl sulfate surfactant concentration and stirring rate, but decreases with increasing salinity. In addition, several interactions are presented to be significant including the polymer–salinity interaction, surfactant–salinity interaction and stirring rate–salinity interaction.

DESIGN, FORMULATION, AND CHARACTERIZATION OF APREMILAST-SACCHARIN COCRYSTALS LOADED WITH TOPICAL GEL

Objective: Most of the drugs are relevant to BSC class II and class IV having solubility problems. Cocrystallization of drug with conformer is an immense approach used to explore the physicochemical properties of drug. The objective of the present work was to design formulate and evaluate the drug cocrystals of poorly soluble drug apremilast (APR) with saccharin.
 Methods: Cocrystals of APR were prepared using the solvent evaporation technique. The saturated solubility study and in vitro dissolution study of cocrystals were carried out. The prepared cocrystals were characterized by differential scanning calorimetry (DSC), X-ray diffraction (XRD), and Fourier-transform infrared (FTIR) spectroscopy. The topical gel of APR cocrystals was formulated optimized and evaluated using three-level factorial design.
 Results: The cocrystals of APR were prepared in 1:1 molar ratio with saccharin. APR cocrystals showed the improvement in solubility and dissolution as compared to pure APR. The formation of cocrystals was confirmed from change in endothermic peak of DSC and from shifting of FTIR spectra of cocrystals. Crystallinity of cocrystal was confirmed from XRD pattern and noteworthy change in 2θ values of the intense peak. The topical gel of APR cocrystals was formulated and optimized using three-level factorial design using Carbapol-940 and hydroxypropyl methylcellulose (HPMC) as a gelling agent.
 Conclusion: The cocrystals with altered physicochemical properties of APR were prepared with saccharin and formulated as a topical gel to overcome the problems related to oral administration.

Power and Sample Size Determination for Multilevel Mediation in Three-Level Cluster-Randomized Trials

Mediation analyses supply a principal lens to probe the pathways through which a treatment acts upon an outcome because they can dismantle and test the core components of treatments and test how these components function as a coordinated system or theory of action. Experimental evaluation of mediation effects in addition to total effects has become increasingly common but literature has developed only limited guidance on how to plan mediation studies with multi-tiered hierarchical or clustered structures. In this study, we provide methods for computing the power to detect mediation effects in three-level cluster-randomized designs that examine individual- (level one), intermediate- (level two) or cluster-level (level three) mediators. We assess the methods using a simulation and provide examples of a three-level clinic-randomized study (individuals nested within therapists nested within clinics) probing an individual-, intermediate- or cluster-level mediator using the R package PowerUpR and its Shiny application.

Supervisory Performance Control of Concurrent Mobile Apps for Energy Efficiency

Two critical quality factors for mobile devices (e.g., smartphones, tablets) are battery life and user-perceived performance of User Interface (UI) events, e.g., responsiveness of user action events and frame rate of video playback events. Unfortunately, state-of-the-art solutions have at least one of the following three limitations: 1) they cannot efficiently handle concurrent UI events of multiple apps (either foreground or background) and so may lead to performance imbalance and high energy consumption, 2) they try to regulate UI event performance periodically and thus may not efficiently handle the aperiodicity of user action events, which can result in poor responsiveness or high overheads, and 3) they rely mainly on CPU frequency/voltage scaling and so may have limited energy savings. In this paper, we present SURF, Supervisory control of User-perceived peRFormance, which is designed to overcome the three limitations. First, it dynamically allocates resources to concurrent UI events for balanced performance. Second, SURF uses supervisory control theory to handle the aperiodicity of user action events. Third, it optimizes the allocation of UI events to CPU cores for additional energy savings. SURF features a three-level architecture design that performs the three tasks at different time scales, according to their different overheads and timing requirements. We test SURF on several mobile device models with real-world open-source apps and show that, without causing perceivable performance degradation, it can reduce the CPU energy consumption by 28-98 percent compared to state-of-the-art solutions. In particular, by optimizing the allocation of UI events to the CPU cores, SURF achieves, 28-76 percent more CPU energy savings compared to other solutions.

Statistical evaluation of growth parameters in biofuel waste as a culture medium for improved production of single cell protein and amino acids by Yarrowia lipolytica

Yarrowia lipolytica is an oleaginous yeast species with the ability to grow on a number of substrates types, especially industrial wastes. This paper concerns the statistical optimization of fermentation parameters and media to ensure consistent and improved Y. lipolytica protein production. A strain of Y. lipolytica A-101 was observed to be proficient in producing single cell protein, amino acids, and vitamin B12 while utilizing biofuel waste instead of a complete YPD medium for yeast growth. A fractional fractal design experiment was then applied, and the two fermentation parameters of temperature and pH were recognized to have a significant effect on the protein and amino acid production. Subsequently, the response surface methodology with a three-level complete factorial design was employed to optimize these influential parameters. Therefore, five different measuring systems were utilized to construct a quadratic model and a second-order polynomial equation. Optimal levels of parameters were then obtained by analysis of the model and the numerical optimization method. When the Y. lipolytica A-101 was cultivated at optimized pH (5.0) using biofuel waste as a medium, the protein concentration was increased to 8.28—a 44% enhancement as compared to the original (3.65). This study has thus demonstrated a beneficial way to cultivate Y. lipolytica A-101 on biofuel waste for enhanced production of single cell protein and amino acids for use in human diet and in animal feed.

Statistical power in partially nested designs probing multilevel mediation

Objective: Analysis of the intermediate behaviors and mechanisms through which innovative therapies come to shape outcomes is a critical objective in many areas of psychotherapy research because it supports the iterative exploration, development and refinement of theories and therapies. Despite widespread interest in the intermediate behaviors and mechanisms that convey treatment effects, there is limited guidance on how to effectively and efficiently design studies to detect such mediated effects in the types of partially nested designs that commonly arise in psychotherapy research. In this study, we develop statistical power formulas to identify requisite sample sizes and guide the planning of studies probing mediation under two- and three-level partially nested designs. Method: We investigate multilevel mediation in partially nested structures and models for two- and three-level designs. Results: Well-powered studies probing mediation using partially nested designs will typically require moderate to large sample sizes or moderate to large effects. Discussion: We implement these formulas in the R package PowerUpR and a simple Shiny web application (https://poweruprshiny.shinyapps.io/PartiallyNestedMediationPower/) and demonstrate their use to plan studies using partially nested designs.

Optimization of Ceramic Paste Viscosity Use for the Elaboration of Tubular Membrane Support by Extrusion and Its Application

The objective of this work was to determine the optimum size and amount of raw materials which influence the viscosity of ceramic paste using the experimental design for the production of tubular support by the extrusion technique and its application in microfiltration. The Box Behnken design was used to optimize the viscosity of the ceramic paste. ANOVA was used to model the system represented by independent parameters and dependent output response and to optimize the system by estimating the statistical parameters. A three-factor and three-level design was used generating thus 15 experiments. The independent factors were the amount of porogen, size of porogen and amount of binder and dependent factor the viscosity of the ceramic paste. The minimum (−1), intermediate (0) and maximum (+1) level of the amount of porogen, size of porogen and amount of binder used were 20 g, 30 g and 40 g, 50 μm, 100 μm and 150 μm, and 2 g, 3.5 g and 5 g respectively. The statistical analyses showed that the values of the answers would adapt to a second degree polynomial model. The R-square value obtained was greater than 95%, the Biais factor was equal to the unit and the Absolute Average Deviation (AAD) equal to the zero thus validating the model. The optimal size of raw material was found to be 100 μm for an amount of clay of 66 g, amount of porogen of 30 g and amount of binder of 4 g. The optimum viscosity of the ceramic paste was found to be 26.7 Pa∙s which is close to the viscosity of the clay paste only found to be 28.5 Pa∙s, thus good for shaping by the extrusion technique. The ceramic paste showed a pseudo-plastic behavior. The tubular porous support was sintered at 950°C and the dimensions, such as outer and inner diameters and length of the tube were 4 cm, 2 cm, and 19 cm, respectively. The sintered membrane possesses a porosity of 43.5%, water permeability of 244.9 L/h∙m2 bar, an average pore size of 2.4 μm and mechanical strength of 9.2 MPa with very good corrosion resistance in acidic and basic conditions. The membrane was subjected to microfiltration of synthetic clay suspension at various combinations of applied pressures (0.5 - 2 bar) with a feed concentration of 100 NTU. An increase in the applied pressure leads to an increase in the flow rate and retention rate. The flow rate decreases steadily with time. The highest retention was obtained at 2 bar with permeability of 184.69 L/h∙m2 bar and a retention of 96% decreasing the turbidity to about 3.5 NTU which is below the acceptable value of 5 NTU.

The effect of holding time before solidification on the properties of aluminium castings

SYNOPSIS The properties of aluminium castings are strongly affected by their inclusion content, particularly double oxide film defects, or bifilms. Such defects have been reported not only to decrease the tensile and fatigue properties of Al casting, but also to increase their variability, making the properties of such alloys unreliable and unreproducible. Earlier research suggested that the bifilm atmosphere might be consumed by reaction with the surrounding melt, which could improve the mechanical properties of the castings. In this work, the effect of holding an Al casting in the liquid state for up to 20 minutes before solidification was studied using a three-level general factorial design of experiments. Two responses were considered, the ultimate tensile strength (UTS) and elongation of the resulting castings. The results showed that the holding treatment had a significant effect on the elongation of the castings produced. In addition, the UTS and elongation peaked at a holding time of 10 minutes. Scanning electron microscopy (SEM) investigation detected many oxide fragments inside pores on the fracture surfaces, reflecting the role of entrained defects in the formation of porosity. The results suggest that two opposing phenomena may take place during the holding treatment. Thus, the consumption of air inside the entrained defects due to reaction with the surrounding molten metal may lead to improvements in mechanical properties, but this may be accompanied by hydrogen passing into the defects, which has a deleterious effect on properties. Keywords: oxide film, aluminium casting, porosity, defects, hydrogen, design of experiments.

Response surface methodology based on polyamide incorporated with biolubricant for optimisation of operating parameters in heavy vehicles

In this paper, the coefficient of friction (COF) and wear of pure and filled polyamide incorporated with and without bio lubrication prediction models based on response surface methodology (RSM) are exhibited in heavy vehicles. A special purpose vehicle is a motor vehicle or trailer, other than an agricultural vehicle or a tow truck, built for a purpose other than carrying goods, or a concrete pump or fire truck (both of which carry water). Examples of a special purpose vehicle include a mobile crane, a concrete pump, drill rig or fire truck. The models were developed based on three-level design of experiments conducted on pure polyamide such as Polyamide6, Polyamide66 and filled polyamide like Polyamide66 filled with glass fibre 30 and Polyamide66 filled with molybdenum disulfide, considering with load, speed and sliding distance as process parameters. Numerical models of second order RSM clearly show that the prediction capabilities of response surface methodology models are more desirable. This implementation identifies the insignificant main factors and contact factors or insignificant quadratic expressions in the model and in this manner can diminish the complexity of the problem.