Second-order Response Surface Methodology Research Articles

A Study on the Shrinkage and Compressive Strength of GGBFS and Metakaolin Base Geopolymer under Different NaOH Concentrations.

Geopolymers (GPs) are gaining prominence due to their low carbon emissions and sustainable attributes. However, one challenge with GPs, particularly those made with ground granulated blast furnace slag (GGBFS), is their significant shrinkage during the geopolymerization process, limiting its practical applicability. This study focuses on how the substitution ratio of metakaolin (MK) and the concentration of sodium hydroxide (NaOH) in the activator can influence the shrinkage and strength of a GGBFS-based GP. The experimental approach employed a 3 × 3 parameter matrix, which varied MK substitution ratios (0%, 50%, and 100%) and adjusted the NaOH concentration (6 M, 10 M, and 14 M). The results revealed that increasing MK substitution, particularly with 6 M NaOH activation, reduced the GP shrinkage but also diminished compressive strength, requiring higher NaOH concentrations for strength improvement. Statistical tools, including analysis of variance (ANOVA) and second-order response surface methodology (RSM), were employed for analysis. ANOVA results indicated the significant impacts of both the MK content and NaOH concentration on compressive strength, with no observable interaction. However, the shrinkage exhibited a clear interaction between MK content and NaOH concentration. The RSM model accurately predicted compressive strength and shrinkage, demonstrating a high predictive accuracy, for which the coefficients of determination (R2) were 0.99 and 0.98, respectively. The model provides a reliable method for determining the necessary compressive strength and shrinkage for GGBFS-based GP based on MK substitution and NaOH concentration. Within the optimization range, the RSM model compared with experimental results showed a 6.04% error in compressive strength and 0.77% error in shrinkage for one interpolated parameter set. This study establishes an optimized parameter range ensuring a GP performance that is comparable to or surpassing OPC, with a parameter set achieving a compressive strength of 34.9 MPa and shrinkage of 0.287% at 28 days.

RSM modelling and optimization for performance evaluation of biodiesel production process from livistona jenkinsiana using NaOH as a catalyst

The production of biodiesel from conventional vegetable oils is limited by the high cost and competition with food supply. Therefore, there is a need to explore new and underutilized feedstocks that can provide abundant and low-cost oil for biodiesel production. Livistona jenkinsiana is a palm species that grows in tropical and subtropical regions of Asia. It produces oil-rich fruits that are usually discarded as waste. In this work, biodiesel was produced from Livistona jenkinsiana through transesterification reaction, and the parametric analysis was carried out. The process parameters such as reaction temperature, molar ratio, reaction time, and catalyst amount were studied, and yield (Y) was modelled using response surface methodology (RSM) as a modelling tool in MINITAB@17.1.0 software. A second-order RSM model for biodiesel yield was developed as a function of temperature, catalyst, and the molar ratio, which could predict the biodiesel yield. ANOVA results showed that temperature, catalyst, and molar ratio played an important role in the transesterification process. The optimization result showed that the optimal conditions were attained at a temperature of 61.78 °C, methanol to oil molar ratio 9.25:1, and catalyst concentration of 0.86 wt%. The highest biodiesel yield predicted was 94.47%. The reaction was carried out at a constant reaction speed of 500 rpm for 1.5 h of reaction time. The physicochemical properties of the produced biodiesel indicate that the biodiesel from Livistona jenkinsiana oil (LJO) is ideal for the production of biodiesel.

Next-Generation High-Density PCB Development by Fan-Out RDL Technology

High-density interconnect (HDI) printed circuit boards (PCBs) are in high demand for smartphones, particularly those with fifth generation (5G) functionality, due to their smaller form factors, higher interconnection densities, and improved integrative ability. Various advanced PCB technologies are available, including HDI PCBs and substrate-like PCBs (SLPs). However, even for substrate-like PCBs, the line width (L) and spacing (S) of the copper traces are limited to <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$25~\mu \text{m} / 25~\mu \text{m}$ </tex-math></inline-formula> , and fine-line development also faces yield and cost challenges. Accordingly, the present study utilizes an redistribution layer (RDL) first fabrication process to develop a fine line width/spacing ( <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$10~\mu \text{m} / 10~\mu \text{m}$ </tex-math></inline-formula> ) Fan-out interposer (FOI) on PCB architecture with a higher I/O (Input/Output) density, greater yield, and lower cost. A three-dimensional (3D) ANSYS finite element (FE) model combined with volume fractions approach applied to equivalent thermomechanical properties of the multilayer RDL is introduced. The validity of the simulation model is confirmed by comparing the numerical results for the out-of-plane deformation of the top surface of the FOI with the experimental observations. Then, the effects of five design parameters on the warpage and solder joint stress performance of the FOI-PCB architecture are identified through parametric analysis. Finally, a second-order response surface methodology (RSM) model and Box-Wilson central composite design (CCD) method are employed to examine the interactive effects of the structural design factors of the FOI-PCB architecture on the FOI warpage under typical manufacturing thermal loading conditions. It is shown that a smaller overall size of the FOI is beneficial in reducing the warpage by minimizing the coefficient of temperature expansion (CTE) mismatch between the interposer and the PCB.

The Efficiency of Seven-Variable Box-Behnken Experimental Design with Varying Center Runs on Full and Reduced Model Types

Response Surface Methodology is widely used in the optimization of industrial processes and products that depend on several experimental variables. One of the most tested and efficient second-order Response Surface Methodology designs is the Box-Behnken Design. This research explores the efficiency of a seven-variable Box-Behnken design with varying center runs, on full and reduced quadratic models. Backward Elimination and Forward Selection techniques are employed as the variable selection techniques for obtaining the reduced models, based on the Akaike Information Criterion. Fit Statistics and Design Efficiency values are obtained for the reduced models and are compared with those of the full model. Generally, results show that the reduced quadratic models perform best under one center-point run, thereby making the reduced models the most preferred in terms of the model fit and D-efficiency. Comparative analysis, based on G-efficiency, reveals that the full quadratic model performs better than the reduced models under one center-point Box-Behnken design.

Comprehensive Optimization of the Dispersion of Mixing Particles in an Inert-Particle Spouted-Bed Reactor (IPSBR) System

Effective gas dispersion and liquid mixing are significant parameters in the design of an inert-particle spouted-bed reactor (IPSBR) system. Solid particles can be used to ensure good mixing and an efficient rate of mass and heat transfer between the gas and liquid. In this study, computational fluid dynamics (CFD) coupled with the discrete phase model (DPM) were developed to investigate the effect of the feed gas velocity (0.5–1.5 m/s), orifice diameter (0.001–0.005 m), gas head (0.15–0.35 m), particle diameter (0.009–0.0225 m), and mixing-particle-to-reactor-volume fraction (2.0–10.0 vol.%) on the solid mass concentration, average solid velocity, and average solid volume fraction in the upper, middle, and conical regions of the reactor. Statistical analysis was performed using a second-order response surface methodology (RSM) with central composite design (CCD) to obtain the optimal operating conditions. Selected parameters were optimized to maximize the responses in the middle and upper regions, and minimize them in the conical region. Such conditions produced a high interfacial area and fewer dead zones owing to good particle dispersion. The optimal process variables were feed gas velocity of 1.5 m/s, orifice diameter of 0.001 m, gas head of 0.2025 m, a particle diameter of 0.01 m, and a particle load of 0.02 kg. The minimum average air velocity and maximum air volume fraction were observed under the same operating conditions. This confirmed the novelty of the reactor, which could work at a high feed gas velocity while maintaining a high residence time and gas volume fraction.

Research on tool wear factors for milling wood-plastic composites based on response surface methodology

A high-speed milling experiment on wood-plastic composites was performed using cemented carbide tools, and the resulting wear pattern was studied. The influence of the cutting parameters, the cutting speed, feed speed, and axial cutting depth on the tool wear was studied via response surface methodology, and the influence of the interaction of the cutting parameters on tool wear was analyzed. Three-dimensional surface graphs and contour plots of the tool wear results were established. According to the experimental results, a mathematical model of the tool wear based on the second-order response surface methodology was established, and the model was utilized to verify its feasibility. The results show that the nose width (NW) increases with the increase of the cutting speed and axial cutting depth and decreases with the increase of feed speed. Among the factors affecting tool wear, the cutting speed had the greatest influence, followed by the feed rate, with the axial cutting depth affecting tool wear the least. According to the results of the interaction between the tool wear and the cutting parameters, a low feed speed and small axial cutting depth can be selected to ensure long tool life; for low-speed cutting, a high feed speed and large axial cutting depth can be adopted to ensure tool life while improving machining efficiency.

Wind Turbine Blade Optimal Design Considering Multi-Parameters and Response Surface Method

Within the framework of blade aerodynamic design, the maximum aerodynamic efficiency, power production, and minimum thrust force are the targets to obtain. This paper describes an improved optimization framework for blade aerodynamic design under realistic conditions, while considering multiple design parameters. The relationship between the objective function and the design parameters, such as the chord length, maximum chord, and twist angle, were obtained by using the second-order response surface methodology (RSM). Moreover, the identified parameters were organized to optimize the aerodynamic design of the blades. Furthermore, the initial and optimized blade geometries were compared and showed that the performance of the optimized blade improved significantly. In fact, the efficiency was increased by approximately 10%, although its thrust was not varied. In addition, to demonstrate the improvement in the resulting optimized blades, the annual energy production (AEP) was estimated when installed in a specific regional location. The result showed a significant improvement when compared to the baseline blades. This result will be extended to a new perspective approach for a more robust optimal design of a wind turbine blade.

The effect of intrinsic and extrinsic factors on moisture sorption characteristics of hard candy

This study assessed effects of intrinsic factors, composition and candy size, and extrinsic factors, storage temperature, and humidity, on moisture sorption characteristics of hard candy. Nine types of plain hard candy with various percentage of sucrose (45.0 to 65.0% wt/wt) and citric acid (0.0 to 1.0% wt/wt) were prepared. The prepared samples had surface area per weight ratio (SA/W) of 2.05 to 3.69 cm2/g. Moisture sorption isotherms of all candy formulations were built at 25 °C and 35 °C and were well-represented by Guggenheim-Anderson-de Boer (GAB) model (R2 between 0.9634 and 0.9960). Compositions and SA/W significantly affected moisture sorption characteristics of hard candies. Increasing citric acid content increased rate of moisture uptake, while increasing SA/W decreased absorption rate. Additionally, the predictive models for rate of moisture uptake of candies with different compositions and SA/W at 25 °C and 35 °C and 75% relative humidity based on second-order response surface methodology were developed and validated. Practical applications Moisture sorption isotherms built and the obtained models of moisture uptake could be used as a guideline to predict moisture sorption characteristics or to estimate shelf life of hard candies, with known compositions and/or storage conditions.

Application of Response Surface Methodology for Coffee Effluent Treatment by Ozone and Combined Ozone/UV

ABSTRACTThis paper reports a study using ozone (O3) and combined ozone/ultraviolet (O3/UV) processes for color removal and caffeine degradation from synthetic coffee wastewater using a second-order response surface methodology (RSM) with a three-level central composite face-centered (CCF) design. The effects of O3 concentration, initial pH, and reaction time were examined for both processes. The reaction time and pH were statistically significant for caffeine degradation and color removal. In the ozonation process, higher caffeine degradation and color removal were observed in alkaline pH, indicating that ozone attacks indirectly, consequently generating hydroxyl radicals. Regarding the ozone/UV process, it was observed that lower caffeine degradation and color removal occurred at neutral pH, indicating an adverse effect due to lower ozone dissolution and consequently the production of a smaller amount of free hydroxyl radicals. The achieved results showed that the techniques were efficient for color removal (85% and 99%, respectively) and caffeine degradation (88% and 98%, respectively).

Optimal Design of IPM Motors With Different Cooling Systems and Winding Configurations

Performance improvement of permanent magnet (PM) motors through optimization techniques has been widely investigated in the literature. Oftentimes the practice of design optimization leads to derivation/interpretation of optimal scaling rules of PM motors for a particular loading condition. This paper demonstrates how these derivations vary with respect to the machine ampere loading and ferrous core saturation level. A parallel sensitivity analysis using a second-order response surface methodology followed by a large-scale design optimization based on evolutionary algorithms are pursued in order to establish the variation of the relationships between the main design parameters and the performance characteristics with respect to the ampere loading and magnetic core saturation levels prevalent in the naturally cooled, fan-cooled, and liquid-cooled machines. For this purpose, a finite-element-based platform with a full account of complex geometry, magnetic core nonlinearities, and stator and rotor losses is used. Four main performance metrics including active material cost, power losses, torque ripple, and rotor PM demagnetization are investigated for two generic industrial PM motors with distributed and concentrated windings with subsequent conclusions drawn based on the results.

Alternative Second-Order N-Point Spherical Response Surface Methodology Design and Their Efficiencies

The equiradial designs are studied as alternative second-order N-point spherical Response Surface Methodology designs in two variables, for design radius ρ = 1.0. These designs are seen comparable with the standard second-order response surface methodology designs, namely the Central Composite Designs. The D-efficiencies of the equiradial designs are evaluated with respect to the spherical Central Composite Designs. Furthermore, D-efficiencies of the equiradial designs are evaluated with respect to the D-optimal exact designs defined on the design regions of the Circumscribed Central Composite Design, the Inscribed Central Composite Design and the Face-centered Central Composite Design. The D-efficiency values reveal that the alternative second-order N-point spherical equiradial designs are better than the Inscribed Central Composite Design though inferior to the Circumscribed Central Composite Design with efficiency values less than 50% in all cases studied. Also, D-efficiency values reveal that the alternative second-order N-point spherical equiradial designs are better than the N-point D-optimal exact designs defined on the design region supported by the design points of the Inscribed Central Composite Design. However, the N-point spherical equiradial designs are inferior to the N-point D-optimal exact designs defined on the design region supported by the design points of the Circumscribed Central Composite Design and those of the Face-centered Central Composite Design, with worse cases with respect to the design region of the Circumscribed Central Composite Design.

Optimization of blade setting angles of a counter-rotating type horizontal-axis tidal turbine using response surface methodology and experimental validation

SUMMARY This paper describes an optimization method for blade setting angles of a counter-rotating type horizontal-axis tidal turbine(HATT). Both of the front and rear blades were designed by the traditional blade element momentum (BEM) theory, whichfails to simulate the interaction between the dual rotors. However, the computational fluid dynamics (CFD) analysis canpredict the mutual performance accurately to make up the drawback of BEM theory. A second-order response surfacemethodology (RSM) with the aid of three-dimensional Reynolds-averaged Navier–Stokes (RANS) analysis was employedto obtain the optimal match of front and rear blade setting angles. Furthermore, experimental tests in the wind tunnel werecarried out to verify the numerical predictions. The performance of the optimal turbine has been proven to be greatlyimproved by both of CFD predictions and experimental results. Copyright © 2015 John Wiley & Sons, Ltd. KEY WORDScounter-rotating; HATT; CFD; RSMCorrespondence*Bin Huang, Faculty of Engineering, Kyushu Institute of Technology, Kitakyushu, Japan.

Investigating and Modeling the Machinability of Al 6061 Using Response Surface Methodology

Decreasing the effect of temperature, surface roughness and vibration amplitude during turning process will improve machinability. Mathematical model has been developed to predict responses of the surface roughness, temperature and vibration in relation to machining parameters such as the cutting speed, feed rate, and depth of cut. The Box-Behnken First order and second-order response surface methodology was employed to create a mathematical model, and the adequacy of the model was verified using analysis of variance. The experiments were conducted on aluminium 6061 by cemented carbide. The direct and interaction effect of the machining parameters with responses were analyzed. It was found that the feed rate, cutting speed, and depth of cut played a major role on the responses, such as the surface roughness and temperature when machining mild steel AISI 1018. This analysis helped to select the process parameters to improve machinability, which reduces cost and time of the turning process.

Prediction of optimized composition for enhanced mechanical and electrochemical response of Zr-C-N-Ag coatings for medical devices

The necessity of improving the performance of existing biocompatible materials promotes the investigation of new approaches to solve biocompatibility problems caused by low chemical stability and poor mechanical performance of implanted materials. Envisioning those problems and considering the current reported complications of implanted stainless steel 316L devices, this work aimed to produce new Zr-C-N-Ag coatings and to predict an optimal composition to provide the required electrochemical stability and mechanical performance to the stainless steel 316L. The coatings were deposited by dual unbalance magnetron sputtering and characterized in terms of chemical, structural, mechanical and electrochemical properties to optimize their functional properties by means of a second-order response surface methodology. The optimization process revealed that the best mechanical and electrochemical performance was reached when stoichiometric ZrC0.5N0.5 phase is the main constituent of the materials, with low amounts of silver (<8at.%) and residual oxygen, mainly explained by the electrochemical stability and mechanical performance of the Zr-C-N solid solution. The current density applied to the silver target was identified as the main parameter affecting the final properties of the films due to its direct relation to the incorporation of metallic silver in the system. However, the reactive gases, as well as the high amount of residual oxygen, were also found to be significant in the process.

Process parameter optimization for fused deposition modeling using response surface methodology combined with fuzzy inference system

Fused deposition modeling (FDM) is gaining distinct advantages because of its ability to fabricate the 3D physical prototypes without the restrictions of geometric complexities, while when it comes to accuracy and efficiency, the advantages of FDM is not distinct, and so how to improve them is worthy of study. Focusing on process parameter optimization, such parameters as line width compensation, extrusion velocity, filling velocity, and layer thickness are selected as control factors, input variables, and dimensional error, warp deformation, and built time are selected as output responses, evaluation indexes. Experiment design is assigned according to uniform experiment design, and then the three output responses are converted with fuzzy inference system to a single comprehensive response. The relation between the comprehensive response and the four input variables is derived with second-order response surface methodology, the correctness of which is further validated with artificial neural network. Fitness function is created using penalty function and is solved with genetic algorithm toolbox in Matlab software. With confirmation test, the results are obtained preferring to the results of the experiment 1 with the best comprehensive response among the 17 experiment runs, which confirms that the proposed approach in this study can effectively improve accuracy and efficiency in the FDM process.

Optimization of sulfamethoxazole degradation by TiO2/hydroxyapatite composite under ultraviolet irradiation using response surface methodology

A titanium dioxide/hydroxyapatite/ultraviolet (TiO2/HAP/UV-A) system was used to remove sulfamethoxazole (SMX) from water in a second-order response surface methodology (RSM) experiment with a three-level Box-Behnken design (BBD) for optimization. The effects of both the primary and secondary interaction effects of three photocatalytic reaction variables were examined: the concentration of SMX (X1), dose of TiO2/HAP composite (X2), and UV intensity (X3). The UV intensity and TiO2/HAP dose significantly influence the SMX and total organic carbon (TOC) removal (p<0.001). However, the SMX and TOC removal are enhanced with increasing TiO2/HAP dose up to certain levels, and further increases in the TiO2/HAP dose result in adverse effects due to hydroxyl radical scavenging at higher catalyst concentrations. Complete removal of SMX was achieved upon UV-A irradiation for 180min. Under optimal conditions, 51.2% of the TOC was removed, indicating the formation of intermediate products during SMX degradation. The optimal ratio of SMX (mg L−1) to TiO2/HAP (g L−1) to UV (W/L) was 5.4145 mg L−1 to 1.4351 g L−1 to 18W for both SMX and TOC removal. By comparison with actual applications, the experimental results were found to be in good agreement with the model’s predictions, with mean results for SMX and TOC removal of 99.89% and 51.01%, respectively.

A comparative analysis of tool wear prediction using response surface methodology and artificial neural networks

The research reported herein is to study the comparison between a response surface methodology (RSM) and artificial neural network (ANN) in the modelling and prediction of tool wear during face milling of hybrid composites. Aiming to achieve this goal, several milling experiments were performed with polycrystalline diamond (PCD) inserts at different machining parameters namely feed rate, cutting speed, depth of cut and weight fraction of alumina (Al2O3). The experiment was carried out using 6061 aluminium alloy reinforced with alumina of size 65 ßm and graphite of size 60 ßm particles which are prepared using stir casting method. Mathematical model is created using central composite face centred second-order RSM and the adequacy of the model was verified using analysis of variance. With regard to the machining test, it was observed that feed rate is the dominant parameter that affects tool wear of PCD inserts. The comparison results show that models provide accurate prediction of tool wear in which ANN perform better than RSM. The data predicted from ANN is very nearer to experimental results compared to RSM, therefore we can use this ANN model to determine the tool wear for various composites and also for various machining parameters.

Optimization of Vehicle Handing and Stability Based on RSM

Based on the theory of multi-body system dynamics and simulation software ADAMS/Car, the whole vehicle model was established. Afterwards by means of pylon course slalom, the accuracy of modeling was tested. The analysis and evaluation were later made to draw a conclusion that the handling stability of model needed improved. So as to improve the handling stability, the index lateral acceleration, yaw rate, side slip angle were taken as target function while suspension stiffness parameters were designed variables. Optimization of vehicle handing stability was practiced by applying second-order Response Surface Methodology (RSM) model. The relationship could be obtained by least square method obviously. Moreover applying with linear interpolation the final objective function was decided. The minimum of final objective function was the optimal result. Simulation analysis was performed again for the whole vehicle model by parameters modification. Subsequently, the results showed that this method greatly improved handling stability.

Application of Response Surface Methodology to systematically optimize image quality in computer tomography: A case study using fresh chestnuts (Castanea spp.)

The objective of this study is to describe a method that will systematically and efficiently obtain a model of computerized tomographic (CT) scanning factor levels, which returns optimized high quality CT images. Chestnut (Castanea spp.) two-dimensional CT images were used to describe this optimization procedure, considered to be a critical step in the development of a fast, nondestructive technique, capable of assessing fresh internal quality attributes and components of chestnuts, and other agricultural commodities. Response Surface Methodology (RSM), using a three-factor, three-level Box–Behnken statistical design and digital image processing, were used to optimize the factors affecting image quality, which include X-ray voltage, current, and slice thickness. Response variables representing image quality were digitally and automatically inferred from fresh chestnut image Signal to Noise Ratio, Teflon® cylinder reference volume accuracy, quality assurance (QA) High Contrast Spatial Resolution phantom, and QA Low Contrast Detectability phantom. Second-order RSM prediction models for each response variable reflected a combined maximized CT image quality at a voltage, current, and slice thickness equal to 120kV, 170mA, and 2.5mm respectively. The experiment yielded optimal chestnut CT images that can accurately reflect internal decay of fresh chestnuts with an overall accuracy rate equal to 96%, taking as reference data the of Subjective Quality Rating of five trained chestnut experts.

Development of RSM- and ANN-based models to predict and analyze the effects of process parameters of laser-hardened commercially pure titanium on heat input and tensile strength

Laser transformation hardening (LTH) is an innovative and advanced laser surface modification technique as compared to conventional transformation hardening processes and has been employed in aerospace, marine, chemical applications, heat exchangers, cryogenic vessels, components for chemical processing and desalination equipment, condenser tubing, airframe skin, and nonstructural components which introduces the advantageous residual stresses into the surface, improving the mechanical properties like wear, resistance to corrosion, tensile strength, and fatigue strength. In the present study, LTH of commercially pure titanium, nearer to ASTM grade 3 of chemical composition was investigated using continuous wave 2 kW, Nd: YAG laser. The effect of laser process variables such as laser power, scanning speed, and focused position was investigated using response surface methodology (RSM) and artificial neural network (ANN) keeping argon gas flow rate of 10 lpm as fixed input parameter. This paper describes the comparison of the heat input (HI) and ultimate tensile strength (σ) (simply called as tensile strength) predictive models based on ANN and RSM. The paper also presents the effect of laser process variables on the HI and ultimate σ. The research work also emphasizes on the effect of HI on σ. The experiments were conducted based on a three-factor, three-level Box–Behnken surface statistical design. Quadratic polynomial equations were developed for proper process parametric study for its optimal performance characteristics. The experimental results under optimum conditions were compared with the simulated values obtained from the RSM and ANN model. Adequacy of the developed models was tested by analysis of variance technique. A multilayer feed-forward neural network with a Levenberg–Marquardt back-propagation algorithm was adopted to develop the relationships between the laser hardening process parameters, HI, and ultimate σ. The performance of the developed ANN models were compared with the second-order RSM mathematical models of HI and σ. There was good agreement between the experimental and simulated values of RSM and ANN. The comparison clearly indicates that the ANN models provide more accurate prediction compared to the RSM models. It has been found that there is a trend of increased tensile strength with the decrease of hardening heat input and a trend of increased tensile strength with the increase of hardening cooling rate. As heat input decreases, there will be a faster cooling rate. Considering the effect of HI on ultimate σ, it was found that the lower the heat input, the faster cooling rate. The details of experimentation, model development, testing, validation of models, effect of laser process variables on heat input and ultimate σ, effect of HI on σ, and performance comparison of RSM and ANN models are presented in the paper. The results of Box–Behnken design of RSM and ANN models also indicate that the proposed models predict the responses adequately within the limits of input parameters being used. It is suggested that regression equations can be used to find optimum conditions for HI and σ of laser-hardened commercially pure titanium material.