Axial Points Research Articles

The Utilization of Central Composite Design for the Production of Hydrogel Blends for 3D Printing

Central composite design (CCD) is a statistical experimental design technique that utilizes a combination of factorial and axial points to study the effects of multiple variables on a response. This study focused on optimizing hydrogel formulations for 3D printing using CCD. Three biopolymers were selected: sodium alginate (SA), gelatin (GEL), and carboxymethyl cellulose (CMC). The maximum and minimum concentrations of each polymer were established using a Google Scholar search, and CCD was employed to generate various combinations for hydrogel preparation. The hydrogels were characterized in accordance with their swelling degree (SD) in phosphate-buffered saline (PBS) and Dulbecco’s Modified Eagle Medium (DMEM), as well as their printability in 2D and 3D assays. The formulation consisting of 7.5% SA, 7.5% GEL, and 2.5% CMC exhibited the best swelling properties and exceptional printability, surpassing all other tested formulations. This study highlights the effectiveness of design of experiment methodologies in accelerating the development of optimized hydrogel formulations for various applications in 3D printing and suggests avenues for future research to explore their performance in specific biological contexts.

Comparison of the Three Types of Central Composite Designs Over Subsets of Reduced Models by Design Optimality Criteria

The purpose of this article is to compare the 3 important types of central composite designs (CCDs) consisting of central composite circumscribed design (CCCD), central composite inscribed design (CCID), and central composite face-centroid design (CCFD) in response surface methodology (RSM). The difference among these designs is the distance from the center design to the axial points. The comparison was performed across the full second-order response surface model and across a set of reduced models for 3, 4, and 5 design factors ( 3, 4, and 5) including 1, 3, and 5 center runs ( 1, 3, and 5). This study used D-, A-, and G- optimality criteria to evaluate the performance of CCDs by presenting the design optimality criteria comparison ranking throughout the reduced-model subsets of 43, 224, and 839 models for 3, 4, and 5 design variables, respectively. The results showed that CCCD was superior to CCID and CCFD according to A- and D- optimality criteria, while CCCD and CCID performed better than CCFD based on G- optimality criterion over a set of reduced models for 3, 4, and 5 design factors. It was observed that D-, A-, and G- optimality efficiencies were robust to changes in the linear and cross-product terms and sensitive to deviation in the square terms. The study will provide recommendations to assist the experimenters in the choice of the best design among the candidate designs for practice applications when some model effects may be insignificant. HIGHLIGHTS Comparison of 3 classifications of CCD. Assessment by using D-, A-, and G- optimality criteria over the reduced-model subsets for the full second-order response surface model. Generated the reduced models by using weak heredity. CCCD was superior to CCID and CCFD according to A- and D- optimality criteria, while CCCD and CCID performed better than CCFD based on G- optimality criterion over a set of reduced models for 3, 4, and 5 design factors. GRAPHICAL ABSTRACT

Modified Slope Rotatability for Balanced Ternary Designs of Second Order Response Surfaces

Objective: To evaluate the best optimal solutions of modified Second Order Slope Rotatable Designs (SOSRD) using Balanced Ternary Designs (BTD) and to compare with different methods of Modified SOSRD for 3≤v≤8. Methods: To estimate the parameters of the response surface design of second order the principle of least squares was applied for design of experiments, we also evaluated modified slope rotatable value and variance of estimated responses. Findings: The outcome of this research reveals the influence of various design parameters on key aspects such as the variance of the estimated response, slope rotatable value, axial points, central points and also total number of design points of modified SOSRD framework. Novelty: The variance of the estimated responses in the new method of Modified SOSRD using BTD provides the best optimal solutions with minimum variances while compared to different methods of Modified SOSRD. Keywords: Response ­ Surface Experimental Designs, Second Order Rotatable Designs, Second ­ Order Slope ­ Rotatability, Second ­ Order Modified Slope ­ Rotatability, Balanced Ternary Designs

A Comparative Evaluation of Marginal and Internal Fitness of Zirconia Monolithic Crown Fabricated with Different CAD\CAM Systems: (In Vitro Study)

The precision of computer-aided design/computer-aided manufacturing (CAD/CAM) systems is reliant upon their technical attributes and reliability in producing the designated restorations. The evaluation of this precision is primarily conducted through the examination of the marginal and internal fitness of said restorations. Consequently, the objective of this research endeavor was to analyze and compare the marginal and internal fitness of zirconia crowns fabricated using various CAD/CAM systems. The samples were categorized into four groups, each consisting of 10 samples, based on the specific CAD/CAM equipment employed for crown fabrication as follows: Group I fabricated using Sirona CAD\CAM milling machine, Group II fabricated using Dentium CAD\CAM machine, Group III fabricated using XTCERA CAD\CAM machine and Group IV fabricated using IMES-ICORE CAD\CAM machine. Tooth preparation done following the guidelines recommended by KATANA TM Zirconia (Kurary Noritake Dental Inc., Japan). To ensure standardization, one CAD/CAM program designed parameters was selected to be used for all CAD/CAM machines. Cement thickness was directly measured using sectioning technique to assess the crown's internal and marginal fitness. After performing sectioning, measurements were conducted using a digital microscope with a magnification of 230x. Eleven predetermined measuring locations were selected for each sample, representing four distinct areas: two marginal points, two chamfer points, four axial points, and three occlusal points. Results showed that none of four CAD\CAM machines tested was able to accurately reproduce the designed cement space parameter except Group I (Sirona) showed the closest results. As a conclusion, no CAD\CAM system is 100% accurate however, crowns fabricated using Sirona CAD\CAM milling machine showed the closest recordings to selected parameters among other CAD\CAM milling machines tested.

Multipoint kinetics model with power reactivity defect for the axial offset control in the VVER-1200 nuclear reactor during the load following mode of operation

This article proposes the multipoint kinetics model consisting with different number of point kinetics model (two points, four points, six points, eight points, ten points) in the axial direction for the VVER-1200 nuclear reactor. Each node is coupled with others through the coupling coefficients determined from the diffusion approach. For more precise description of the dynamical modes of the reactor operation, the proposed model integrates the power reactivity feedback derived from temperature reactivity coefficients and Mann’s thermal hydraulic model which assumes one fuel node adjacent to two coolant nodes. On the model with four axial points, additionally was tested the influence of the different number of delayed neutrons groups on the accuracy results and model running time during the load-following mode of operation. Moreover, the novel model of the control rods is introduced, utilizing a combination of sign functions to sequentially influence all nodes during insertion or withdrawal. The computational results show that the accuracy of the proposed model is satisfactory, and general assumptions about transients align with their physical definitions. This research contributes to the advancement of the point-like nuclear reactor modeling for improvement of the automatic power controller synthesis.

109 Evaluation of net energy, standardized ileal digestible lysine, and soybean meal content interaction in 13 to 25 kg pigs using a central composite design

Abstract Pigs [n = 4,683; 337 × 1050, PIC; initial body weight (BW) = 13.0 ± 0.01 kg] were used in a 21-d trial to investigate the interaction of net energy (NE), standardized ileal digestible lysine (SID Lys), and soybean meal (SBM) content used at five different levels on growth performance of nursey pigs. Pigs were housed in mixed sex pens with 35 pigs per pen and assigned in a randomized complete block design to 15 dietary treatments using a circumscribed central composite design (CCD). Factorial and axial points had 7 repetitions, and the central points had a total of 24. Eight diets were formulated to various levels of NE, SID Lys, and SBM and blended to create the 15 dietary treatments. The NE ranged from 2,334 to 2,762 kcal/kg, SID Lys from 1.08 to 1.52%, and SBM from 25.5 to 35.9%. Diets were corn-soybean meal based and soy hulls and soybean oil were added to reduce or increase NE content of the diet. Feed grade amino acids and SBM were used to adjust SBM and SID Lys content and to maintain SID Thr, Trp, Met, Val, and Ile ratios relative to SID Lys. For NE, a linear effect (P ≤ 0.052) was observed for average daily gain (ADG) and average daily feed intake (ADFI), and linear and quadratic effect was found (P ≤ 0.047) for gain to feed ratio (G:F) with a reduction in growth performance as NE increased due to reduction in SID Lys:calorie. When increasing SID Lys, ADG (P ≤ 0.044) and G:F (P ≤ 0.020) increased quadratically (Table). Increasing SBM content linearly improved ADG (P = 0.039) and G:F (P < 0.001), respectively. There was also a significant interaction between SID Lys and SBM for G:F (P = 0.082), where SID Lys positively impacted G:F as SBM increased in the diet. When including the significant terms, the resulting models can be used to predict the ADG (kg) response = [0.579392 + (-0.0063389 × NE) + (0.0260796 × Lys) + (0.0067428 × SBM%) + (-0.0065721 × Lys²) adjusted R2 = 0.36], and G:F (kg/kg) response = [0.7013215 + (0.0035198 × NE) + (0.0264389 × Lys) + (0.0060863 × SBM%) + (-0.0048012 × NE²) + (-0.0031838 × Lys²) + (-0.0034413 × Lys × SBM) adjusted R2 = 0.65]. In conclusion, using a CCD, increasing SID Lys resulted in a quadratic improvement in ADG and G:F, with this improvement being greater when SBM also increased. Overall, we observed few interactions between SID Lys, SBM, and NE.

Investigating the adsorption potential of char derived from waste latex for methylene blue removal

This study presents the adsorption of methylene blue (MB) dye using latex char derived from pyrolysis of latex gloves. The adsorption process was investigated systematically using Response Surface Methodology (RSM) with a Central Composite Design (CCD). The effects of four key variables, namely pH, time, temperature, and adsorbent dosage, were studied using a factorial design enriched with center points and axial points. Experimental data were analyzed using a second-order polynomial regression model to construct a response surface model, which elucidated the relationship between the variables and MB removal efficiency. The study found that the char obtained at 800 °C exhibited the highest adsorption capacity due to its increased carbonization, expanded surface area, and diverse pore structure. Analysis of Variance (ANOVA) confirmed the significance of the quadratic model, with remarkable agreement between predicted and experimental outcomes. Diagnostic plots validated the model's reliability, while 3D contour graphs illustrated the combined effects of variables on MB removal efficiency. Optimization using DoE software identified optimal conditions resulting in a 99% removal efficiency, which closely matched experimental results. Additionally, adsorption isotherms revealed that the Freundlich model best described the adsorption behavior, indicating heterogeneous surface adsorption with multilayer adsorption. This comprehensive study provides valuable insights into the adsorption process of MB dye using latex char, with implications for wastewater treatment and environmental remediation.

Visualization of Deformation and Stress Waves in Wooden Solid and Glued Elements of Building Structures.

The basis of the research hypothesis is the assumption that in wooden structures, deformations and stresses propagate in waves. The numerical experiment demonstrated a correct qualitative visual picture of the wave propagation of deformations, with wave manifestations and characteristic effects on the surface of the sample, at axial and corner points. Visually, the numerical model showed Rayleigh waves on the surface layer of the sample, depending on the ratio of the external geometric dimensions of the sample model, with pronounced wave interference on the outer shell. The visual manifestation of deformation on the outer sides (faces) and the reflection of deformation waves from the outer boundaries of the elastic medium of the sample in the form of Rayleigh waves confirm the correctness of the general hypothesis and the implemented model. Visualization of the process of emergence, propagation and attenuation of deformation waves on the surface of the sample shows that in the quantitative description of the deformation gradient, areas dangerous for the material can be identified.

Optimization of Wall Materials for Astaxanthin Powder Production from Shrimp Shell Extract Using Simplex Lattice Mixture Design

Shrimp shell waste is an attractive source of value-added bioactive-rich by-products. Shrimp shell extract containing astaxanthin was recovered by solvent extraction method (petroleum ether/acetone/water with a ratio of 15 : 75 : 10) and ultrasound process (amplitude 20% for 15 min at 35°C). The extract was then encapsulated by freeze-drying using wall materials such as maltodextrin (with the dextrose equivalent (DE) of 7 (MD7) and 20 (MD20)) and modified starch (Hi-Cap 100) incorporated at different ratios. Simplex lattice with augmented axial points in the mixture design was applied for the optimization of wall material. The optimal wall materials were 29.4% (MD7), 34.0% (Hi-Cap 100), and 36.6% (MD20), with encapsulation yield (Y) of 94.6%, encapsulation efficiency (EE) of 91.8%, astaxanthin content (Ast) of 46.1 μg/g DW, and DPPH scavenging capacity of 64.0%, respectively. The optimized microcapsules had spongy morphology and brittle and flaky mass. The degradation kinetics of bioactive astaxanthin in UV light was evaluated and found to follow first-order reaction kinetics. The microcapsules obtained under optimal wall composition exhibited the highest UV light stability with half-life values of 76.8 h, demonstrating a high stability.

Thomson scattering measurements in the krypton plume of a lanthanum hexaboride hollow cathode in a large vacuum test facility

Laser Thomson scattering is a minimally intrusive diagnostic technique for determining electron temperature, density, and bulk velocity in plasma systems. Advances in technology have made possible the application of Thomson scattering to electric propulsion-relevant plasma systems, with reported electron number-density detection limits as low as 1×1016 m−3, and electron temperatures from one-to-tens eV. However, the implementation of laser Thomson scattering in large vacuum testing facilities, wherein electric propulsion devices are tested, remains a challenge. This work presents the implementation of a laser Thomson scattering system in a large vacuum test facility at the Georgia Tech High Power Electric Propulsion Laboratory. The diagnostic was optimized for maximum light-collection efficiency and ease of re-alignment while the facility is at vacuum. The high light-collection efficiency allowed reduced accumulation times to achieve the target detection limit of 1×1017 m−3. The diagnostic is used to measure axial electron property profiles in the near-field plume of a lanthanum hexaboride hollow cathode operating at 25 A on krypton at a background pressure of 1.3×10−6 Torr—Kr. The diagnostic is quantitatively compared to similar systems in the literature. The resulting axial points, collected from 2 to 8 mm downstream of the cathode keeper orifice, are qualitatively and quantitatively compared with simulations and experimental measurements made with electrostatic probes and laser-induced fluorescence. The main quantitative difference between measured values and results is the one to two order of magnitude difference in the peak electron density, being attributed to the relative size and location of the external anode with respect to the cathode keeper.

Implementation of Grey Wolf, Multi-Verse and Ant Lion Metaheuristic Algorithms for Optimizing Machinability of Dry CNC Turning of Annealed and Hardened UNIMAX® Tool Steel

Advances in machining technology and materials science impose the identification of optimal settings for process-related parameters to maintain high quality and process efficiency. Given the available resources, manufacturers should determine an advantageous process parameter range for their settings. In this work, the machinability of a special tool steel (UNIMAX® by Uddeholm, Sweden) under dry CNC turning is investigated. The working material is examined under two states; annealed and hardened. As major machinability indicators, main cutting force Fz (N) and mean surface roughness Ra (μm) were selected and studied under different values for the cutting conditions of cutting speed, feed rate, and depth of cut. A systematic experimental design was established as per the response surface methodology (RSM). The experimental design involved twenty base runs with eight cube points, four center points in the cube, six axial points, and two center points in the axial direction. Corresponding statistical analysis was based on analysis of variance and normal probability plots for residuals. Two regression models referring to main cutting force and surface roughness for both the annealed and hardened states of the material were developed and used as objective functions for subsequent evaluations by three modern meta-heuristics under the goal of machinability optimization, namely multi-objective grey wolf algorithm, multi-objective multi-verse algorithm and multi-objective ant lion algorithm. All algorithms were found capable of providing beneficial Pareto-optimal solutions for both main cutting force and surface roughness simultaneously whilst regression models achieved high correlation among input variables and optimization responses.

Exploration of Temperature Inversion in Intermediate Joints of 10 kV Three-Core Cable

In order to precisely ascertain the temperature at the hot spot within the intermediate joint of a three-core cable, this study focused on a 10 kV three-core cable joint as its primary subject. A three-dimensional finite element model of the cable joint was constructed, enabling the calculation of both the steady-state hot spot temperature field distribution and the transient temperature rise curve of the joint. Employing a one-dimensional transient thermal path model for the cable body, a radial inversion model for the cable core temperature was established. Through simulating the transient temperature field of the cable joint under varying currents, a fitting relationship was determined for the axial temperature points of the cable core. Subsequently, an inversion perception model was devised to calculate the hot spot temperature of the cable joint based on temperature measurements at specific points on the outer surface of the cable. Under both continuous and periodic loads, the inversion results revealed a consistent trend in the temperature at the joint crimping point with the finite element calculation outcomes, demonstrating a maximum error of within 3 degrees Celsius. This verification underscores the precision of the temperature combination inversion method when applied to three-core cable joints.

Experimental Study on Gas–Liquid Two-Phase Flow Upstream and Downstream of U-Bends

In this study, the influence of U-bends on the flow and pressure propagation characteristics of a gas–liquid two-phase flow in upstream and downstream straight pipes was investigated experimentally. The superficial velocities of the gas and liquid are 0.18–25.11 m/s and 0.20–1.98 m/s, respectively, covering plug flow, slug flow, and annular flow. The experiments were conducted in U-tubes with inner diameters of 9 mm and 12 mm and with a curvature ratio of 8.33. The U-tube was C-shaped. The pressure fluctuations at the axial measurement points of the straight tubes were measured. Flow images of the distal straight tubes and U-bends were obtained. The disturbance from U-bends in the two-phase flow in the vicinity of the bend is very obvious. The perturbation from U-bends in the fluid in the adjacent straight tubes is highly related to the incoming flow pattern. The slug flow has the most significant influence, whereas the effects of the plug and annular flows are small. Fundamentally, it mainly depends on the weight relationship between the gravity, centrifugal force, and inertial force of the gas–liquid two-phase fluid. The pressure fluctuation propagates in the form of a wave with the same dominant frequency in the straight pipes of the U-tube. The pressure pulsation energy in the straight tubes strengthens with decreasing distance from the 180° return bend. In addition, the pressure fluctuation energy downstream of the U-bend is greater than that upstream of the return bend.

Superfície de resposta para quantificação dos efeitos de NaCl e pH em alface

Abstract The objective of this work was to evaluate the response surface methodology (RSM), with a large sample size, to investigate the effects of NaCl and pH on the root elongation of lettuce (Lactuca sativa) in vitro. For this, 20 lettuce seeds were placed in sterile Petri dishes with two filter papers at the bottom and 3.0 mL of the sample being tested. A rotatable 2x2 factorial arrangement was used, with two factors and a two-level matrix, incorporating two center points and ±1.41 α axial points. Each treatment group consisted of 40 replicates, resulting in 400 experimental observations. Increasing NaCl concentration from 0.0065 to 2,700 g L-1 caused a 19.3% decrease in lettuce root elongation. When pH decreased from 7.0 to 1.5, there was a 68.8% decrease in root elongation, but, when it increased from 7.0 to 12.5, there was a 44.9% decrease. The analysis of combined effects showed that the increase in NaCl concentration reduced the ability of the plant to resist changes in pH. The RSM was effective in evaluating the statistical significance of the NaCl and pH factors, including their second-order effects and interactions, as well as in quantifying their effects on the root elongation of lettuce under the experimental conditions. Therefore, the RSM is a valuable tool for interpreting the results and evaluating the sensitivity of multi-factor research, even when dealing with a large sample size.

Minimal lattice points in the Newton polyhedron and application to normal ideals

Let a1,...,an be positive integers and let ∆=NP(a1,...,an) be the Newton polyhedron associated to these integers, that is, the convex hull in Rn of the axial points that haveaiin the xi-axis. We give some characterization of the minimal elements of ∆, and then use this characterization to give an alternative simpler proof of a main result of [7] on the normality of monomial ideals.

Central composite designs with three missing observations

In an experiment, there are many situations when some observations are missed, ignored or unavailable due to some accidents or high cost experiments. A missing observation can make the results of a response surface model quite misleading. This work therefore investigates the impact of a three missing observation of them various design points: factorial, axial and center points, on the estimation and predictive capability of the central composite design (CCD). Therefore minimaxloss CCD is formulated under a minimaxloss criterion. The minimaxloss CCD is considered to be robust to three missing observation and the investigation has been made in this article. The general formulas for the efficiency of the design when missing three observations, are presented in closed form as a function of α, where α is the value used in the CCDs' axial part. For the first time in this paper, these are calculated explicitly for CCDs from k=2 to k=7 factors and displayed in tables for practitioners to use. The corresponding graphs for the efficiencies are presented and suggestions are made for the values of α to maximize the robustness and estimability of the design for all cases.

Optimization of the Heat-Drying Conditions of Drone Pupae by Response Surface Methodology (RSM).

Recent research has been conducted on various types of pre-processing methods for insects, including freeze-drying, microwave drying, hot air heat drying, and non-heat drying. This study aimed to identify the factors that have the greatest impact on heat drying conditions and establish the optimal heat drying conditions for drone pupae (Apis melifera L.) using response surface methodology (RSM) to minimize quality changes. Drone pupae were treated under various conditions, including blanching time (53-187 s) (X1), drying temperatures (41.6-58.4 °C) (X2), and drying time (266-434 min) (X3). The effect of these treatments on response variables, including the color parameter (WI, YI, BI, △E, and BD), AV, and TB of the dried drone pupae, was evaluated using a central composite design. The whole design consisted of 20 experimental points carried out in random order, which included eight factorial points, six center points, and six axial points. The optimal drying conditions for drone pupae were determined to be a blanching time of 58 s, a drying temperature of 56.7 °C, and a drying time of 298 min. The response variables were most affected by drying temperature and drying time and to a lesser extent by blanching time. The processed drone pupae using the optimized drying conditions resulted in the color parameters (WI, BI, YI, ΔE, and BD) being found to be 66.67, 21.33, 26.27, 31.27 and 0.13, respectively. And TB (log CFU/g) and AV (mg/g) values were found to be 3.12 and 4.33, respectively. The estimated and actual values for dried drone pupae showed no significant difference (p < 0.05). Comparing the physicochemical and microbiological properties of freeze-dried and optimal heat-dried drone pupae, the L and b value as well as PV were significantly lower in the heat-dried samples, while no significant difference was observed in the a value and AV (p < 0.05). Our study suggests that the model we developed can be applied to the large-scale production of drying conditions for use in the pharmaceutical and food industries.

Hopf bifurcation in a delayed prey–predator model with prey refuge involving fear effect

This work investigates a prey–predator model featuring a Holling-type II functional response, in which the fear effect of predation on the prey species, as well as prey refuge, are considered. Specifically, the model assumes that the growth rate of the prey population decreases as a result of the fear of predators. Moreover, the detection of the predator by the prey species is subject to a delay known as the fear response delay, which is incorporated into the model. The paper establishes the preliminary conditions for the solution of the delayed model, including positivity, boundedness and permanence. The paper discusses the existence and stability of equilibrium points in the model. In particular, the paper considers the discrete delay as a bifurcation parameter, demonstrating that the system undergoes Hopf bifurcation at a critical value of the delay parameter. The direction and stability of periodic solutions are determined using central manifold and normal form theory. Additionally, the global stability of the model is established at axial and positive equilibrium points. An extensive numerical simulation is presented to validate the analytical findings, including the continuation of the equilibrium branch for positive equilibrium points.

A coupled-lines system to determine the anteroposterior position of maxillary central incisors for smiling profile esthetics.

To develop a coupled-lines system to determine the anteroposterior position of maxillary central incisors (U1) for smiling profile esthetics. Thirty Asian females with ordinary and good facial harmony were selected as the study sample and the control sample, respectively. Three-dimensional facial images and 45°- and 90°-angled profiles were collected. The anteroposterior relationships between U1 and upper- and mid-facial soft tissue landmarks were measured. By morphing photos of the study sample, two artificial images were created to represent the well-balanced 45°- and 90°-angled profiles and were further processed with combined variations of soft tissue subnasale (SSn)-Glabella and the mid-point of facial axial points of the bilateral central incisor (mFA)-SSn distances. Esthetic assessments were performed on these images by layperson (n = 94) and orthodontist (n = 94) raters. Both upper- and mid-facial soft tissue landmarks were indispensable in assessing anteroposterior positions of U1 for well-balanced smiling profiles. As assessed in 45°- and 90°-angled profiles, the most esthetically sensitive parameters were mFA-Glabella and mFA-SSn distances. A coupled-lines system was constructed, comprising the Glabella and SSn vertical lines. In smiling profiles with optimal esthetics, the mFA point was at 2 to 5 mm posterior to the Glabella vertical and concomitantly 4 to 7 mm posterior to the SSn vertical, as perceived by orthodontists. Laypersons gave a wider range for mFA-Glabella distances, at 2 to 6 mm. The coupled-lines system could serve as a reliable reference for determining esthetically optimal anteroposterior positions of U1 for female facial profiles.

On the robustness of central composite designs when missing two observations

AbstractQuite often, many situations arise in experimental work where some experimental runs that may not be feasible because of certain circumstances or existing constraints in the system under investigation. A lot of work has been done in studying classical designs, such as the central composite designs (CCDs), with missing observations. In this paper our interest is to research the losses that may occur when one or two observations are missing. The general formulas for missing two observations are presented in a closed form as a function of α, where α is the value used in the axial part in the CCDs. These are calculated explicitly for CCDs up to factors, for the first time in this paper, and are displayed in tables for practitioners to use. The losses for any value of α, in the axial points of the design, can be derived by simply replacing α with the desirable value in the provided formulas. A detailed comparison between our findings and results already known in the literature also been made.