Fractional Factorial Design Method Research Articles

Toxicity evaluation of microplastics to aquatic organisms through molecular simulations and fractional factorial designs

Molecular docking, molecular dynamics modelling, and fractional factorial design methodologies were used in the current work to examine the harmful effects of ten microplastic (MPs) such as polystyrene (PS), polyvinylchloride (PVC), polyurethane (PU), polymethyl methacrylate (PMMA), polyamide (PA), polyethylene terephthalate (PET), polyethylene (PE), polypropylene (PP), polychloropene (PCP) and polycarbonate (PC) on the aquatic organism (zebrafish). The toxicity was evaluated based on the docking of the MPs on cytochrome P450 (CYP P450) protein crystals. The binding affinities (ΔG) followed the order, PC (−6.9 kcal/mol) > PET (−6.1 kcal/mol) > PP (−5.8 kcal/mol) > PA (−5.6 kcal/mol) > PS (−5.1 kcal/mol) > PU (−4.1 kcal/mol) > PMMA (−3.9 kcal/mol) > PCP (−3.3 kcal/mol) > PVC (−2.4 kcal/mol) > PE (−2.1 kcal/mol). The primary driving factors for the binding of the MPs and the protein were hydrophobic force, and hydrogen bonding based on the molecular dynamics analysis and surrounding amino acid residues. Furthermore, a 210−5 fractional factorial design method was estimated to identify the main effect and second-order effects of MPs in a composite contamination system on binding affinity/energy to CYP450 receptor protein of zebrafish, combined with a fixed effects model. The findings showed that different MPs combinations had varying impacts on aquatic toxicity; as a consequence, the best combination of MPs with the lowest aquatic toxicity effect could be excluded. The factorial designs showed that the PU-PS and PP-PA combination and single PCP, has the most significant main effect on CYP450 receptor protein of zebrafish which translates to an optimum toxicity level of −4.61 kcal/mol. The investigation offers a theoretical foundation for identifying the hazardous impacts of MPs on aquatic life.

Seismic response sensitivity and optimal design of an isolated multi-span continuous highway bridge with self-centering SMA RC bridge piers and superelastic SMA restrainers

The use of superelastic shape memory alloy (SMA) in reinforced concrete (RC) pier and restrainers between girder and pier/abutment has been proposed in an earlier study to improve the seismic performance of highway bridges. This paper aims at identifying the significant factors that affect the seismic response of such a novel bridge system. A sequential fractional factorial design method is performed to statistically evaluate the effects of six design factors (three geometry-related and three material-related) as well as their interactions. Additionally, a multi-criteria optimization technique is implemented to determine the most efficient combination of the design parameters for SMA RC piers and SMA restrainers. Results demonstrate that the geometry-related factors and their interactions have large effects (with a contribution greater than 91%) on the relative displacement between the girder and pier. The target residual drift of the pier, design target displacement of the restrainer, and their interaction are the three most significant factors (with contributions approximately 30%–68%) affecting the base shear of the pier. The residual drift of the pier is sensitive to the design target displacement of the restrainer, its interaction with the forward transformation stress of SMA, and material-related factors with regard to the energy dissipation of SMA.

Understanding the combination of fractional factorial design and chemometrics analysis for screening super-saturable quercetin-self nano emulsifying components

Quercetin is formulated in a super saturable - self-nano emulsifying (SS-SNE) to increase its stability and bioavailability. This study focuses on the screening design for SS-SNE components with a fractional factorial design (FrFD) approach and chemometric analysis. The FrFD method was chosen because it provides comprehensive benefits. The oil components used are canola and grape seed oil. Croduret 50-SS was selected as a surfactant and PEG 400 as a co-surfactant. The interaction of SNE components was evaluated using FTIR-ATR instrumentation. SNE droplet morphology was observed using a transmission electron microscope (TEM). The selected formulas were grape seed oil as oil phase at 19.6%, croduret at 60%, and PEG 400 as co-surfactant with a concentration of 16.6%. The selected formula has a droplet size of 133.27 nm, PDI of 0.181, the zeta potential of 17.00 mV, electrophoretic mobility of 1.332 µmcm/Vs, emulsification time of 10.05 seconds, a viscosity of 370.147 mPa.s, and a drug load of 31.70 mg/mL. The components of grape seed oil, croduret, and PEG 400 resulted in a quercetin carrier SNE formula that met the criteria. FrFD design and chemometric analysis in the screening process can help determine the selected formula very effectively and efficiently.

Core-shells of magnetite nanoparticles decorated by SBA-3-SO3H mesoporous silica for magnetic solid phase adsorption of paraquat herbicide from aqueous solutions

Paraquat, the most well-known herbicides of toxicological class I, is widely used as an effective herbicide despite its high toxicity for humans and animals. In the current research, a simple synthesis approach was utilized to prepare Fe3O4 @SiO2 @SBA-3-SO3H core-shell mesoporous magnetic nanoparticles (MMNPs) as effective adsorbent for paraquat removal from the aqueous solutions. The characterization of nanoparticles was examined by XRD, BET, FT-IR, FESEM, VSM, mapping and TEM. To optimize the various experimental variables affecting the removal efficiency of paraquat, the effects of four experimental parameters at four levels including solution pH, adsorbent amount, contact time and ionic strength were evaluated by Taguchi fractional factorial design method (OA16). Based on the ANOVA results, ionic strength (80.69%) was recognized as the most significant factor contributing to the paraquat removal efficiency followed by the adsorbent mass (12.67%), pH of the solution (3.52%), and stirring time (0.141%). At the optimum conditions (sample volume = 50 mL, adsorbent dose = 2.4 g L−1, solution pH = 7 and ionic strength = without salt addition), the four kinetic models for the paraquat adsorption on the Fe3O4 @SiO2 @SBA-3-SO3H MMNPs were studied at two concentrations of 25 and 75 mg L−1 in the time range of 0.5–120 min. According to the results, the pseudo-second order kinetic model is the best model (R2 > 0.99, qe, cal =80.0 mg g−1), confirming diffusion plays a key role in determining the rate of adsorption process. Adsorption equilibrium data were investigated by four known isotherm models and the results demonstrated the best fitting with the Langmuir model. From the thermodynamic studies, ΔH°, ΔS°, ΔG°, and Ea of adsorption process were obtained as − 4697.08 J mol−1, − 3.938 J mol−1 K−1, − 3523.45 J mol−1 and − 4246.46 J mol−1, respectively. The negative ΔH° and ΔG° values indicated the exothermic and spontaneous nature of paraquat sorption on the surface of nanoparticles, respectively. Moreover, the obtained values of ΔH°, ΔG° and Ea confirmed the physisorption nature of interaction. The negative ΔS° and Ea shows a decrease in the randomness at the interface of solution-adsorbent with the progress of the sorption process and exothermic nature of adsorption, respectively. The calculated sticking probability (S*) showed the high probability of sticking to the surface. The proposed adsorbent showed very good adsorption behavior and showed reusability more than six cycles without significant reduction in its performance that makes it as a proper adsorbent for paraquat removal.

Multi-objective design optimization of dental implant geometrical parameters.

In-silico investigations are becoming an integral part of the development of novel biomedical devices, including dental implants. Using computer simulations can streamline the process by tuning different geometrical and structural features, emphasizing the osseointegration of the implant design a priori, leading to the optimal designs in preparation for in-vivo trails. This research aims to elucidate the interrelationship between 12 geometrical variables that holistically define the shape of the implant. The approach to achieve optimality hinged on coupling the finite element analysis results with the fractional factorial design method. The latter was used to determine the most influential variables during the screening process, followed by the parameter optimization process using the response surface method, regarding four different objectives, namely: bone-implant contact area, volume of trabecular bone dead cells, volume of cortical bone dead cells, and axial displacement. This resulted in reducing the number of virtual experiments and substantially decreasing the computational cost without compromising the accuracy of the solution. It was found that the optimized values improved the performance significantly. The validity of all models was verified by comparing optimized responses with simulation results. A sensitivity analysis was performed on all five optimized models to address the effect of friction coefficient on the implant-bone joint interaction. It was shown that the mechanical behavior of implant-bone would be independent in higher friction coefficients. The significance of this study is demonstrated in determining the most effective and optimized values of all possible geometrical parameters considering their singular or interactive effects.

Statistical analysis on the effect of premixed ratio, EGR, and diesel fuel injection parameters on the performance and emissions of a NG/Diesel RCCI engine using a DOE method

In reactivity-controlled compression ignition (RCCI) engines, the ignition and combustion of premixed low reactive fuel (LRF) such as natural gas (NG) is controlled by the injection of high reactive fuel (HRF) such as diesel fuel during the compression stroke. In this study, the effects of six different input parameters on the performance and emissions of the natural gas/diesel fueled RCCI engine are studied using fractional factorial design (FFD) method, which is one of the design of experiment (DOE) methods. In this method, the effects of the interactions of input parameters, referred to as “factors,” on the outputs, referred to as “responses,” are investigated. The factors include premixed ratio (PR), start of first injection (SOI1), spray angle (SA), exhaust gas recirculation (EGR), start of second injection (SOI2), and mass fraction of first injection. Sixteen runs were conducted to evaluate the effects of the interaction between input factors on performance and emissions of a RCCI engine using a validated computational fluid dynamics (CFD) model. DOE results indicate that in order to increase gross indicated efficiency (GIE), higher premixed ratio, 85%, with wider spray angle, 150°, is an effective way. Meanwhile, carbon monoxide (CO) and unburned hydrocarbons (UHC) emissions as well as ringing intensity (RI) are decreased at this condition. To reduce NOx emissions, it is beneficial to raise premixed ratio from 55% to 85% or to use 40% EGR, independently.

Assessment of the devulcanization process of EPDM waste from roofing systems by combined thermomechanical/microwave procedures

Ethylene-propylene-diene rubber (EPDM) is a elastomer widely used in common industrial applications. EPDM can be shaped into sheets and employed as isolating material for roofing systems. In this study, scraps of EPDM from commercial, industrial and residential roofing systems were treated by combined thermo-mechanical and microwave devulcanization processes including peroxide of benzoyl (BPO). The devulcanized EPDM (Dev-EPDM) was characterized by cross-link density, Horikx plot, sol fraction content, SEM and TGA analysis. In order to assess the effect of the different factors implied (type of devulcanization process, temperature and amount of BPO), the Fractional Factorial Design (FFD) method has been applied. The obtained results show that, when thermo-mechanical and microwave methods are combined, produce an intense devulcanization effect. It was also found that the presence of BPO has significative influence in the devulcanization and that the effect of the temperature is related to the amount of BPO.

Magnetic restricted-access carbon nanotubes for the extraction/pre-concentration of organophosphates from food samples followed by spectrophotometric determination

In this work, magnetic restricted-access carbon nanotubes (M-RACNTs) were synthesized, characterized and used in the dispersive solid-phase extraction (d-SPE) of organophosphate pesticides (OPPs) from food samples (broccoli, eggplant, cauliflower, and soy milk), followed by spectrophotometric determination in a flow injection analysis system. Fe3O4 nanoparticles were incorporated in the multi-walled carbon nanotubes employing dimethylformamide. The dimethylformamide was used as a solvent in the incorporation process, forming the suspension of both particles. The resulting M-CNTs were covered with an external bovine serum albumin (BSA) layer, chemically crosslinked. M-RACNTs were able to efficiently capture OPPs, excluding about 95% of the proteins from food matrices. The analyses were carried out in a flow injection analysis system (FIA), with the spectrophotometric detection (at 560nm) of the complex formed by the reaction between OPPs, N-bromosuccinimide and rhodamine B. A fractional factorial design method was used to optimize the experimental parameters. The addition/recovery test showed results from 95.5% to 108.9%. Accuracies were checked by comparing the results obtained with the proposed and standard HPLC methods, which were in agreement. The proposed method was linear from 5 to 90μgL-1 of OPPs, with limits of detection and quantification of 0.74 and 5μgL-1 and precision of 3.67%, expressed as relative standard deviation. The pre-concentration factor was about 164 times.

Investigation of Factors Affecting Biogas Production from Cassava Peels by Fractional Factorial Design Experimental Methodology

The aim of this study was to investigate parameters affecting biogas production from cassava peels by using fractional factorial design method. The parameters studied were initial pH, organic loading rate, particle size and co-substrate type. Eight biodigesters (TH1, TH2, TH3, TH4, TH5, TH6, TH7 and TH8) in duplicate were performed to produce biogas from cassava peels. The experimental results showed that organic loading rate (X2), particle size (X3) and co-substrate (X4) have significant effect on the yield of biogas. The full mathematical model developed includes two main effects (X2 and X3) and three interactions (X1X2, X2X3 and X1X2X3). Reduced model was introduced in the present study. The highest volume of biogas (2252 mL) was obtained in digester TH2 under the following conditions: initial pH 7.8, 5% TS, ≤2 mm of particle and urea as co-substrate, while digester TH8 had slightly low biogas yield (2129.5 mL). Thus, the best conditions to produce biogas from cassava peels are those of TH2.

Investigating the co-effect of twist and hot drawing processes on the bio-based yarns properties

Biodegradable fibres made from branched polymer grade were spun, hot drawn and twisted. To model the process parameters’ effect, samples had been characterised and analysed under a fractional factorial design method as functions of the process parameters using statistical methods. Drawing ratio, drawing temperature and the number of drawing stages had a positive effect on thermal shrinkage, tenacity and modulus and had a negative effect on elongation at break. The drawing stage had a negative effect on abrasion positively affected by the drawing ratio. With a one-stage drawing process, the tension was very high, and then the spin finish played an important role in the filament slippage on the last roller after the applied spin finish. Twist values did not have a significant effect on thermal shrinkage value itself; twist affected negatively on modulus and positively on abrasion of drawn biodegradable yarn. Results and statistical analysis indicated combinations of factor levels which controlled the production processes of environmentally friendly biodegradable textiles to suit different purposes.

Plasma-induced poly(acrylic acid)-TiO2 coated polyvinylidene fluoride membrane for produced water treatment: Synchrotron X-Ray, optimization, and insight studies

A super-hydrophilic, polyvinylidene fluoride (PVDF) membrane was obtained through plasma-induced poly (acrylic acid) (PAA) polymerization followed by titanium dioxide nano particles (TiO2 NPs) self-assembly for oily produced water treatment. Fractional factorial design method was applied to investigate the effects of experimental factors and their interactions on membrane modification. The mechanism of TiO2 NPs self-assembly was explored through synchrotron-based X-ray analyses and comprehensive membrane characterization. It was found that nano-TiO2 was immobilized onto the membrane surface through PAA layer without valence change. For the first time, the mechanism of nano-TiO2 immobilization was confirmed to be the coordination of Ti4+ with carboxylic group. After modification, the TiO2 NPs were strongly and uniformly fixed on membrane surface, dramatically improving the hydrophilicity of the PVDF membrane surface. The permeation flux was increased more than four times, and the oil rejection rate was higher than 92%. The modified PVDF membrane has great potential in the application for various water-recovery systems, and this study provided a new insight into the nature of functionalized polymer membrane.

A predictive formula for the Nusselt number of compressible laminar fluid flow passing the thermal developing zone of a hot tube

AbstractMany of the industrial and engineering problems need to know the value of the convective heat transfer coefficient of fluid flows within various tools, systems, or tubes. In the present study, a predictive formula has been obtained for the Nusselt number for compressible laminar flows passing the velocity developed and thermal developing zone of a hot tube with different angles with the horizon. A fractional factorial experimental design method and an optimization method have been utilized for obtaining a width range and accurate formula. Finally, the ability of this formula has been examined using a set of testing data.

Voltammetric method for simultaneous determination of ascorbic acid, paracetamol and guaifenesin using a sequential experimentation strategy

Cold is a leading cause of school and work absenteeism. Most cold over-the-counter medicines (OTC) contain paracetamol (PA), guaifenesin (GU) and other active ingredients. Ascorbic acid (AS) in pharmaceutical preparations is designed for preventing and treating respiratory viral infections. Thus, we report a robust voltammetric method for simultaneous determination of AS, PA and GU in their effervescent dosage form. The advantages of nanotechnology and chemometrics were combined to enhance the performance of electroanalysis. Fractional factorial design (FrFD) and dual response surface method (DRSM) were sequentially conducted. The method was validated in agreement with ICH guidelines; it showed accuracy over the concentration range of 11.3–108.9, 14.6–140.3, 4.6–43.9 μg ml−1 for AS, PA and GU, respectively. Based on findings, a robust and not time-consuming procedure was applied.

Interference Adsorption Mechanisms of Dimethoate, Metalaxyl, Atrazine, Malathion and Prometryn in a Sediment System Containing Coexisting Pesticides/Heavy Metals Based on Fractional Factor Design(Resolution V) Assisted by 2D-QSAR

The mechanisms of adsorption of pesticides(dimethoate, metalaxyl, atrazine, malathion and prometryn) and heavy metals(Cu, Cd, Pb, Zn and Ni) coexisting in sediments, with pesticides as target pollutants, and the influence of their main effects and double-order interaction effects were studied using the experimental design module in the Minitab software package with a 210‒3 fractional factorial design method at resolution V. The main, double-order interaction, synergistic and antagonistic effect values of pollutant concentrations influencing the adsorption of pesticides were set as dependent variables, while various quantum chemical parameters of pesticides were set as independent variables, and two-dimensional quantitative structure activity relationship(2D-QSAR) models were established by stepwise regression to reveal the adsorption mechanisms of pesticides in a composite contamination system. The main effects of pollutants concentration played the primary role in the adsorption of dimethoate and malathion(the rates of contributions were 53.54% and 56.46%, respectively), while double-order interaction effects were primarily responsible for metalaxyl, atrazine and prometryn adsorption(the rates of contributions were 79.05%, 60.21% and 57.89%, respectively) in the pesticide/heavy metals coexisting sediment system. The synergistic effects of the main effects and double-order interaction effects of pollutants concentration(synergistic effects) played a leading role in adsorption of malathion and prometryn(the rates of contributions were 70.61% and 69.61%, respectively), while antagonistic effects of the main effects and double-order interaction effects of pollutants(antagonistic effects) played a dominant role in the adsorption of dimethoate, metalaxyl and atrazine(the rates of contributions were 58.82%, 56.89% and 58.24%, respectively). Moreover, the correlation coefficient value(R2) ranged from 0.986 to 0.999(>0.8783) in the 2D-QSAR model, while the standard deviation(SD) ranged from 0.006 to 0.066 and the F test values were 22.684―199.544, indicating the model has good predictive ability and fit. The 2D-QSAR model revealed a significant correlation(P=0.05) between the main effects of pollutants concentrations on pesticides adsorption(main effect values) and the most positive hydrogen atomic charge( $$q_{H^+}$$ ), the highest occupied molecular orbital energy(EHOMO) and the dipole moment(μ). Furthermore, double-order interaction effect values of pollutant concentrations influenced the adsorption of pesticides(double-order interaction effect values), and the most positive atomic charge(q+), $$q_{H^+}$$ , and the lowest occupied molecular orbital energy(ELUMO) were significantly correlated. The qH+, ELUMO and μ of pesticides were found to be significant factors promoting pesticides adsorption, while the q+ and ELUMO of pesticides were significant inhibiting factors(P=0.05). Overall, this study provides a theoretical basis for further realization of combined pollution control of pesticide pollutants in complex environmental systems.

Characterizing the Effects of Micro Electrical Discharge Machining Parameters on Material Removal Rate during Micro EDM Drilling of Tungsten Carbide (WC-Co)

Micro-dies, molds and miniaturized products can be manufactured using micro EDM process. In this research, EDM machine and on-machine fabricated CuW micro-electrode were utilized to produce the micro holes in WC-16%Co. The effects of voltage, current, pulse ON time, pulse OFF time, capacitor and rotating speed on Material removal rate (MRR) during micro EDM drilling of WC-16% Co was analyzed using fractional factorial design method. ANOVA analysis shows that increasing current, rotating speed, capacitor and decreasing voltage and pulse ON time lead to the amplify in MRR. It was found that out of all the factors, current and capacitor had the most significant effect on MRR, while the effect of capacitor was more than current. Eventually, it can be concluded that micro holes can be produced using EDM machine.

Critical operating factors of a jetting dispenser driven by piezostack actuators: statistical analysis of experimental results

In this work, critical operating factors of a jetting dispenser driven by a dual type of the piezostack actuators are experimentally identified. As a first step, geometrical information and working principle of the jetting dispenser are briefly addressed. Subsequently, in order to investigate jetting performance eight important operating (or working) factors of the dispenser such as exciting stroke and frequency are chosen based on two levels for each factor. Then, in order to reduce the number of experiments, one-sixteenth fractional factorial design method is adopted and an experimental apparatus to measure the weight of a single dot is established. After measuring the weight of a single dispensed dot under each test condition, the effect of each operating factor on the jetting performance is analyzed using a statistical program. The main effects and interaction effects on the average and standard deviation of the weight of a single dispensed dot are then analyzed and discussed in details. In addition, the analysis of variance results for average single dot weight is undertaken to determine the specific values of the critical factors which can provide optimal jetting performances. Consequently, critical operating factors for a small amount and small weight variation of a single dot are identified, which directly represent the performances of a non-contact jetting dispenser driven by piezostack actuators such as dotting accuracy and dotting speed.

Application of the fractional factorial design in multiple W/O/W emulsions

ABSTRACTIn presented research, multiple W/O/W emulsions were developed by using experimental design method. A 24-1 fractional factorial design was performed by varying the following input parameters: primary polymeric emulsifier (PEG 30-dipolyhydroxystearate) concentration (0.8% and 2.4%), secondary polymeric emulsifier (Poloxamer 407) concentration (0.8% and 1.2%), electrolyte magnesium sulfate heptahydrate (0.08% and 0.4%) and electrolyte sodium chloride (0.08% and 0.4%). Multiple emulsions were prepared by a two-step emulsification process. Obtained emulsions were characterized with rheological measurements, conductivity and centrifugation tests. Factorial analysis revealed that the concentration of the primary emulsifier was the predominant factor influencing the phase separation, conductivity and maximal apparent viscosity. Additionally, electrolyte magnesium sulfate heptahydrate was more efficient in stabilizing these systems, compared to sodium chloride. The applied fractional factorial design method enabled determination of the optimal concentrations of the primary and secondary emulsifier, as well as the concentration of electrolytes, in order to obtain W/O/W emulsions with desired maximal apparent viscosities, low values of conductivity and without phase separation after centrifugation.

Uncertainty propagation in FE modelling of a fire resistance test using fractional factorial design based model reduction and deterministic sampling

In this paper, fractional factorial design (FFD) and deterministic sampling (DS) are applied to a finite element (FE) model of a fire resistance test of a loaded steel beam, to investigate how uncertainties are propagated through the FE model. The sought quantity was the time when the deflection of the beam exceeded 225mm. The FFD method was used as a model reduction technique which reduced the number of uncertain parameters from 5 to 3. The DS method was compared to a reference Monte Carlo (MC) method of 1000 simulations from all 5 uncertain parameters, which was the minimum number of simulations in order for the statistical moments to converge. The combined FFD and DS method successfully computed the propagation of the mean and standard deviation in the model, compared to the MC method. Given the uncertainties in the FE model, the fractional factorial design reduced the number of simulations required in the DS method by 82%. The combined method of FFD and DS reduced the number of required simulations by 96% compared to the MC method. The DS method did not capture the tails of the probability distribution and is therefore not a suitable candidate for probabilistic evaluation of the time of failure at the edges of the domain of possible failure times. Future research could very well be on improving the tails in DS. However, the DS method provides a conservative 95% coverage interval of 6min for the time to failure of the steel beam.

A study on improving bone conduction speaker performance by electromagnetic prediction and performance distribution by statistical analysis method

The present paper is focused on the stochastic characteristics of the electromagnetic force, one of the performance parameters for the bone conduction speaker which is one of the devices in the “smart glass”. The design parameters were taken as significant, affecting the electromagnetic force. Characteristic analysis of significant parameters was considered by using the factorial design method. Significant factor of main effect was selected via fractional factorial design method. Main effect and interaction of selected factor were analyzed applying the full factorial design method. The independency of the selected parameter and their significant interaction were examined by using the F-test method. Linear and non-linear characteristics for the selected parameters and performance were examined by creation of the median point within the analysis results for significance analysis. Therefore, prediction model derived non-linear regression model from the central composite design of response surface method. For probability distribution of the electromagnetic characteristics, related prediction model and Monte Carlo simulation method were applied. Electromagnetic performance prediction result showed 98.5 % level and improved maximum 99.8 % reliability level under 3σ level of dimensional management. In view of this, such stochastic design approach could improve design efficiency via verification of individual design parameters’ effect on the performance levels, thereby proving design reliability based on the object levels.

Seismic behavior of deficient reinforced concrete bridge piers confined with FRP – A fractional factorial analysis

Material properties, amount of longitudinal and transverse steel, external confinement, axial load and shear span-depth ratio affect the lateral load capacity, ductility and failure mode of retrofitted bridge piers under seismic load. These parameters are considerably different in old reinforced concrete (RC) bridge piers compared to the seismically designed bridges. This research investigates the effects of these factors and their interactions on the limit states of carbon fiber reinforced polymer (CFRP) confined seismically deficient RC circular bridge piers using fractional factorial design method. CFRP-confined bridge piers are modelled using a fiber modelling approach and nonlinear static pushover analyses of the bridge piers are conducted in order to determine the sequence of different limit states such as yielding, buckling and fracture of reinforcement, and concrete crushing along with ductility capacity of the piers. This study shows that the shear span-depth ratio, yield strength and longitudinal reinforcement ratio, axial load and CFRP confinement significantly affect the lateral load capacity, ductility and the failure mode of retrofitted bridge piers under seismic load.