Warpage Values Research Articles

Advanced FOPoP technology in heterogeneous integration: Finite element analysis with element birth and death technique

This research investigates the advanced applications of Fan-Out Package-on-Package (FOPoP) technology within heterogeneous integration, highlighting its critical role in artificial intelligence (AI), big data analytics, and 5 G communication systems. Heterogeneous integration technology, which merges diverse components and technologies into a single package, is essential for addressing the increasing demands of modern electronic systems. However, wafer warpage during the FOPoP manufacturing process poses a significant challenge, impacting yield, chip alignment, and handling. We employ Finite Element Analysis (FEA) to tackle this issue using the element birth and death technique for process-oriented simulations. Our method innovatively utilizes both the backside and frontside Redistribution Layer (RDL) to create vertical interconnections within the FOPoP structure. The simulation process includes 11 stages: backside RDL electroplating, Polyimide (PI) curing, Molding Compound (MC) curing, frontside RDL electroplating, and PI curing. Comparing the simulated FOPoP wafer warpage values at each stage with experimental data, we consistently found discrepancies under 10 %, validating the accuracy of our simulations. Additionally, we identify effective strategies to reduce FOPoP wafer warpage through parameter analysis, such as lowering copper trace density in the RDL and increasing the die area ratio, thereby improving manufacturing yield. This research advances the understanding of FOPoP technology in heterogeneous integration and provides a robust framework for its application in next-generation electronic systems.

Finite element analysis of 2.5D packaging processes based on multi-physics field coupling for predicting the reliability of IC components

The 2.5D packaging technology is a high–performance method for electronic packaging. This study addresses the reliability issues of 2.5D packaging during the manufacturing process. A multi–physics field coupling Finite Element Method (FEM) has been developed, combined with sub–modeling techniques, to investigate the curing of underfill adhesive, the curing of Epoxy Molding Compound (EMC), and the reflow soldering between the interposer and substrate in a 2.5D packaging entity during various manufacturing procedures. The focus is on the thermo–mechanical–chemical behavior of viscoelastic components within the packaging structure, as well as the viscoplastic characteristics of the micro solder balls and microbumps. A systematic analysis is conducted on the warpage deformation and stress distribution of the 2.5D packaging at crucial time points. The results demonstrate that after curing, the overall warpage of the packaging exhibits a ‘concave’ warpage profile. Additionally, as the thickness of the EMC above the chip increases, the warpage value of the packaging also increases. The warpage value defined by linear elasticity is larger than that defined by viscoelasticity. The maximum Von Mises stress value in the key areas of the submodel is greater than the maximum Von Mises stress value in the corresponding key areas of the global model. After reflow soldering, the stress concentration in the micro solder balls occurs at the edge of the micro solder ball array. The maximum stress values for each component of the packaging are observed in the interface areas between the components. Packaging components that undergo the curing process have notably higher warpage and Von Mises stress values than those that do not undergo the curing process. The simulation method established in this study can accurately predict the warpage deformation and stress distribution state of 2.5D packaging, providing significant engineering application value for process optimization and reliability enhancement of 2.5D packaging in the production process.

Anisotropic mechanism of monocrystalline silicon on surface quality in precision diamond wire saw cutting

The surface quality of wire-saw cut monocrystalline silicon is affected by its anisotropy. This work investigates the effect of anisotropy on the surface quality of monocrystalline silicon (100), (110), and (111) crystalline surfaces in wire-saw cutting processing. The material properties of monocrystalline silicon in different crystal directions are analyzed, and the expressions of elastic modulus of monocrystalline silicon (100), (110), and (111) crystal surfaces are derived, and the influences of material properties and process parameters on macroscopic sawing force and material removal are investigated. The single abrasive grains scratching the surface of monocrystalline silicon and the wire saw cutting and processing process were simulated, and the diamond wire saw cutting and processing of monocrystalline silicon experiment was carried out. The experiment results show that: When the wire saw cuts and processes the (100), (110), and (111) crystal surfaces, the cutting angle with better sawing performance is 30°. The macroscopic normal and tangential average sawing forces on the crystalline surface of monocrystalline silicon (110) differed by 7.22N and 2.54N. The average error between the experiment value of surface warpage and the simulation value is 5.47 %, which indicates the accuracy of the surface morphology prediction model.

Research on warping optimization of automobile mesh based on artificial intelligence algorithm

Automobile mesh is a typical large plastic part prone to warping deformation in the manufacturing process, which seriously affects the quality of products. The traditional method is to find the optimal combination parameters to reduce warping deformation in the forming process through repeated trial or mold flow analysis with high cost. In this study, An optimization method based on an artificial intelligence algorithm is proposed to optimize the warping deformation of the automobile mesh. In the optimization method, artificial intelligence regression algorithm-support vector machine regression was used to establish the nonlinear function relationship (prediction function) between the molding process parameters and the warpage of automobile mesh, and the performance of the prediction function was optimized by a genetic algorithm. The optimized prediction function was taken as the fitness function, the warping value was regarded as the fitness value, and genetic algorithm is used again to obtain a set of optimal process parameters and minimum warpage values. Finally, the reliability of the optimization method is verified by the modal flow analysis software.

Analysis of warpage of a flip-chip BGA package under thermal loading: Finite element modelling and experimental validation

The objective of this study is to investigate warpage of a Flip-Chip Ball Grid Array (FCBGA) package experimentally and numerically. Projection Moiré technique was used to measure full-field warpage during heating experiment from room temperature up to 250 °C. As temperature changes within the FCBGA package, different thermal strains are generated in the package resulting from the mismatch in the Coefficient of Thermal Expansion (CTE) between the constituent material layers. A finite element model and analytical equations based on the classical bending theory were used to analyze the thermally induced deformations of package under test. The results show that a maximum warpage value of 67 μm with a concave or smiling shape occurred at the neighborhood of 70 °C during heating and 87 μm warpage with a convex crying shape at 250 °C by assuming a stress-free temperature at 175 °C. Warpage analysis showed that the studied FCBGA package exhibits a different curvature in the die region at the center of the package compared to the region outside the die. At temperatures higher than 175 °C, a concave or smiling warpage shape was shown in the die region while a convex or crying shape in the region outside the die. In contrast, at room temperature, the die area has a convex shape warpage, while outside this area presented a concave shape.Furthermore, the good agreement between warpage of the studied package from finite element simulation and measurements was achieved thanks to the use of the measured material's thermal-mechanical properties of the substrate and Molding Compound (MC) rather than using datasheet data. In-plane CTE and Young's modulus of the substrate were measured using stereo-digital image correlation. Moreover, temperature dependent Young's modulus of the MC was measured by nanoindentation.

Residual stress and warpage of additively manufactured SCF/PLA composite parts

With the rapid development of novel technologies, additive manufacturing of carbon fiber-reinforced composites is drawing increasing attention in various industrial applications. In this study, we develop numerical models to predict and analyze the stress distribution, crystallinity and warpage mechanisms of two commonly used structural parts, i.e., a square tube (ST) and a circular tube (CT), made of short carbon fiber-reinforced polylactic acid (SCF/PLA) with additive manufacturing using fused filament fabrication (FFF). First, a multi-physics field model considering thermoelastic relations and crystallization kinetics was developed to simulate the FFF printing process using numerical “activated elements.” Then, the most important numerical parameters were experimentally evaluated to refine the numerical model for prediction and analysis. The results show that the composite ST specimens have a significant residual stress distribution and are prone to stress concentrations at the edges and corners. Specifically, the maximum warpage value, i.e., at the corner of ST specimens (100.47 µm), is higher than that of CT specimens (88.45 µm). Overall, the difference in crystallinity for additively manufactured composite tubes with different configurations is small (average crystallinities of ST and CT specimens are 5.22% and 6.1%, respectively). However, the crystallinity tends to generally decrease along the tube height direction, from the bottom upwards to the upper area beneath the printing nozzle.

Нейросетевая модель для определения регламентных параметров технологического процесса переработки рудного сырья

Machine learning methods are currently widely used to solve various production problems, the problems of defects diagnosing and predicting for items in mass production, in particular. One of the most important problems is defects diagnosing and predicting, basing on its solution the regulations for the technological processes parameters and raw materials used can be determined, that insures the minimum probability of defects and the highest possible quality of manufactured products. The solution of this urgent problem with the help of a neural network model is shown on the example of the technological process for manufacturing products from fine ore material. The proposed model is based on the neural network trained on the set of historical data including examples of manufacturing products with different sets of technological parameters and raw ore material. The predicted parameter is warping of the product in one of its sections. Designing and training of the proposed neural network structure allowed achieving the coefficient of determination R2 between the predicted and actual warpage values of 92%. The dependences for the warpage value on the most significant parameters of the technological process, including thermophysical and chemical power technological processes of raw materials processing were constructed by conducting computer experiments using the method of partial freezing for input parameters. Due to these dependencies, the regulations for the most significant parameters of the production process are determined, which ensures the product to be without violating the tolerance for the warpage value specified by the design documentation. Thus, a specific example shows the possibility of using neural network modeling to solve the problem of setting regulations for the production process parameters, which compliance ensures the minimum amount of rejects and, accordingly, a higher quality of a production batch.

Correction of mould cavity geometry for warpage compensation

Warpage is one of the most challenging defects occurring in plastic injection moulded parts. Various approaches to overcome this issue have been proposed in the literature, but they all provide only partial solutions to the problem. This paper proposes a new method for the compensation and minimisation of warpage. The method is based on Mould Cavity (MC) correction. In contrast to other similar methods, here the MC correction is accomplished through a direct comparison of the local deviations of the warped part’s geometry to the desired geometry of the part. Modifying the MC shape accordingly yields parts with a lower shape discrepancy from the desired geometry compared to the nonadjusted shape. The key novelty of the paper is the development of software that iteratively adjusts the MC shape to minimise local deviations. In every iteration, the warped part is compared to the desired geometry in order to compute local deviations between both geometries. Computation is done first by determining the point normal vector of the warped geometry mesh and its piercing point through desired geometry mesh. Second, distance between the base point and the piercing point is calculated. After all local deviations are determined, the MC geometry is adjusted accordingly. Two case studies demonstrate the method’s capabilities. In the first case we present a curved thin-walled plate part. The maximum warpage value of 0.005 mm (0.7% of the initial maximum warpage) was reached after three iterations of MC geometry correction and remained stable afterwards. In the second case the method was tested on the box-shaped part. The maximum warpage dropped from initial 0.711 mm to 0.066 mm after three iterations.

Non-Dominant Genetic Algorithm for Multi-Objective Optimization Design of Unmanned Aerial Vehicle Shell Process.

This paper uses Pareto-optimized frames and injection molding process parameters to optimize the quality of UAV housing parts with multi-objective optimization. Process parameters, such as melt temperature, filling time, pressure, and pressure time, were studied as model variables. The quality of a plastic part is determined by two defect parameters, warpage value and mold index, which require minimal defect parameters. This paper proposes a three-stage optimization system. In the first stage, the main node position of the electronic chip in the module is collected by the unified sampling method, and the chip calculation index of these node positions is analyzed by the mold flow analysis software. In the second stage, the kriging function predicts the mathematical relationship between the mold index and warpage value and the process parameters, such as melt temperature, filling time, packing pressure, and packing time. In the third stage, using LHD sampling and non-dominant rank genetic algorithm II, a convergence curve of warp value is found near the Pareto optimal frontier. In the fourth stage, the fitting degree of Pareto optimal leading edge curve points was verified by analytical experiments. According to experimental verification, it can be seen that the injection molding factors are pressure and pressure time, because the injection molding time and pressure time are completely positively correlated with the mold indicators, the correlation is the strongest, the mold temperature and glue temperature are not the main influencing factors, and the mold temperature shows a certain degree of negative correlation. In this experiment, the die index is mainly improved by injection time and pressure, optimal injection parameter factor combination and minimum injection index, the optimization rate of the die index is up to 96.2% through genetic algorithm optimization nodes and experimental verification, the average optimization rate of the four main optimization nodes is 91.2%, and the error rate with the actual situation is only 8.48%, which is in line with the needs of actual production, and the improvement of the UAV IME membrane is realized.

Using Sequence-Approximation Optimization and Radial-Basis-Function Network for Brake-Pedal Multi-Target Warping and Cooling.

This paper uses a multi-objective optimization method to optimize the injection-molding defects of automotive pedals. Compared with the traditional automotive pedal material, aluminum alloy, the polymer pedal containing glass fibers not only reduces the aluminum pedal by at least half, but also improves the strength and hardness of the fibers by adjusting the orientation of the fibers in all directions. Injection factors include: filling time, filling pressure, melt temperature, cooling time, injection time, etc. For the optimization process influencing factors, herein, we focus on warpage analyzed via flow simulation, and setting warpage parameters and cycle time as discussed by setting different cooling distributions, pressures and temperature schemes. The multi-objective optimization design was mainly used to describe the relationship between cycle time and warpage, and the Pareto boundary was used for cycle time and warpage to identify the deviation function and radial-basis-function network. We worked with a small DOE for building the surface to run SAO programming—which improved the accuracy of the response surface by adding sampling points—terminating the time when the warpage value met the solution requirements, to find out the global optimal solution of the warpage value under different cooling times. Finally, the results highlighted four influencing parameters that match the experimental image of the actual production.

Analysis of the Warpage Phenomenon of Micro-Sized Parts with Precision Injection Molding by Experiment, Numerical Simulation, and Grey Theory.

In this study, we determined the effects of design and processing parameters of precision injection molding (PIM) to minimize warpage phenomena of micro-sized parts using various plastics (polyoxymethylene (POM), acrylonitrile-butadiene-styrene (ABS), polypropylene (PP), polyamide (PA), and ABS+ polycarbonate (PC)). We applied a numerical simulation (Moldflow) to determine the runner’s balance in multi-cavities of the micro-sized part and simulate the warpage phenomenon of micro-parts with PIM. We used simulation data to fabricate a steel mold by computer numerical control (CNC) machining. In this, we study manufactured a micro-sized part and measured its warpage value using various PIM process parameters (melt temperature, mold temperature, injection pressure, and filling time). In order to obtain optimal results (i.e., minimum warpage), we employed the Taguchi method and grey theory to discern the influence of each process parameter on PIM. Finally, we determined that the most significant PIM process parameter influencing the warpage phenomenon of micro-sized parts was the mold temperature, regardless of whether in terms of the experimental results, numerical simulations, or grey theory. The PA material had the most suitable properties for application for micro-sized parts, regardless of whether in terms of experimental results, numerical simulations, or grey theory for PIM. This study also illustrates that micro-sized parts can be fabricated by PIM without the use of micro-injection molding, and we determined that the mold temperature required for molding does not need to be higher than the glass-transition temperature of the material.

Optimization of the Warpage of Fused Deposition Modeling Parts Using Finite Element Method.

Fused deposition modeling (FDM) is one of the most affordable and widespread additive manufacturing (AM) technologies. Despite its simplistic implementation, the physics behind this FDM process is very complex and involves rapid heating and cooling of the polymer feedstock. As a result, highly non-uniform internal stresses develop within the part, which can cause warpage deformation. The severity of the warpage is highly dependent on the process parameters involved, and therefore, currently extensive experimental studies are ongoing to assess their influence on the final accuracy of the part. In this study, a thermomechanical Finite Element model of the 3D printing process was developed using ANSYS. This model was compared against experimental results and several other analytical models available in the literature. The developed Finite Element Analysis (FEA) model demonstrated a good qualitative and quantitative correlation with the experimental results. An L9 orthogonal array, from Taguchi Design of Experiments, was used for the optimization of the warpage based on experimental results and numerical simulations. The optimum process parameters were identified for each objective and parts were printed using these process parameters. Both parts showed an approximately equal warpage value of 320 μm, which was the lowest among all 10 runs of the L9 array. Additionally, this model is extended to predict the warpage of FDM printed multi-material parts. The relative percentage error between the numerical and experimental warpage results for alternating and sandwich specimens are found to be 1.4% and 9.5%, respectively.

Warpage Simulation Study by Trace Mapping Method for FCCSP with ETS Substrate

Abstract ETS (Embedded trace substrate) has become as the mainstream substrate for FCCSP since it has fine trace, better trace dimension control and low cost advantages which compared to normal substrate. But it usually encountered more serious warpage issue for bare substrate and complete package which may influence D/B (die bonding) and SMT yield rate due to its coreless characteristic. Especially for ETS substrate with special trace pattern design (ex. larger Copper area), bare substrate may appear peculiar warpage contour and led to serious non-wetting issue at specific location during D/B process. Thus, if it can predict warpage value and contour accurately for bare substrate and package is an important topic. In this paper, a FCCSP package with ETS substrate was chosen to study trace impact. Bare substrate and package warpage simulation models w/ and w/o considering trace pattern by trace mapping method were performed and compared to shadow moiré results. Analysis results showed that simulation w/ considering trace pattern could get more accurate warpage value and more similar warpage contour for bare substrate and package warpage.

Optimisation of Mould Design for Injection Moulding – Numerical Approach

Computer simulation of injection moulding process is a powerful tool for optimisation of moulded part geometry, mould design and processing parameters. One of the most frequent faults of the injection moulded parts is their warpage, which is a result of uneven cooling conditions in the mould cavity as well as after part ejection from the mould and cooling down to the environmental temperature. With computer simulation of the injection moulding process it is possible to predict potential areas of moulded part warpage and to apply the remedies to compensate/minimize the value of the moulded part warpage. The paper presents application of simulation software Moldex 3D in the process of optimising mould design for injection moulding of thermoplastic casing.

Increase in Warpage Prediction Accuracy for Glass Filled Polyamide Material (PA66) through Integrative Simulation Approach

The warpage prediction accuracy of the simulation software depends on part geometry, material model and methodology. However, the material model in the existing simulation software’s does not consider factors such as nonlinear mechanical properties, temperature dependent behaviour, viscoelastic behaviour and transient description of warpage leading to less accuracy. Using an integrative simulation approach, BASF has developed Ultrasim® tool to overcome limitations in the material model of existing simulation software. In the new material model thermomechanical properties, stress relaxation behaviour and nonlinear mechanical properties were considered and this new material model is added to Ultrasim® tool. The model also considers time dependent descriptions of the warpage starting from packing phase of the moulding process, followed by actual ejection and cooling. In this paper warpage results predicted through new integrative simulation approach and existing simulation approach are compared with actual experimental results for 50% glass filled polyamide material (Ultramid®A3WG10). The results revealed that warpage values predicted by integrative simulation based Ultrasim® tool are closer to actual experimental results compared to values predicted by existing simulation technologies. Therefore an integrative simulation approach can be used prior to making real parts to reduce manufacturing cost.

Warpage Optimisation Using Recycled Polycar-bonates (PC) on Front Panel Housing.

Many studies have been done using recycled waste materials to minimise environmental problems. It is a great opportunity to explore mechanical recycling and the use of recycled and virgin blend as a material to produce new products with minimum defects. In this study, appropriate processing parameters were considered to mould the front panel housing part using R0% (virgin), R30% (30% virgin: 70% recycled), R40% (40% virgin: 60% recycled) and R50% (50% virgin: 50% recycled) of Polycarbonate (PC). The manufacturing ability and quality during preliminary stage can be predicted through simulation analysis using Autodesk Moldflow Insight 2012 software. The recommended processing parameters and values of warpage in x and y directions can also be obtained using this software. No value of warpage was obtained from simulation studies for x direction on the front panel housing. Therefore, this study only focused on reducing the warpage in the y direction. Response Surface Methodology (RSM) and Genetic Algorithm (GA) optimisation methods were used to find the optimal processing parameters. As the results, the optimal ratio of recycled PC material was found to be R30%, followed by R40% and R50% materials using RSM and GA methods as compared to the average value of warpage on the moulded part using R0%. The most influential processing parameter that contributed to warpage defect was packing pressure for all materials used in this study.

Enhancement of thermal and mechanical properties of silicone rubber with γ-ray irradiation-induced polysilane-modified graphene oxide/carbon nanotube hybrid fillers.

In this study, a polysilane-modified graphene oxide (GO) and carbon nanotube (CNT) nanocomposite (GO/CNTs-Si) was prepared as a thermal conductive nanofiller to enhance the thermal and mechanical properties of silicone rubber composites. By γ-ray-radiation 3-methacryloxypropyltrimethoxy silane (MPTMS) was polymerized on the surface of GO and CNTs to improve the interfacial interaction between the GO/CNTs-Si and SR matrix. FTIR characterization results demonstrated that polysilane modified the GO/CNTs successfully. The pristine GO/CNTs and resultant GO/CNTs-Si were individually incorporated into α,ω-dihydroxypolydimethylsiloxane to vulcanize SR composites. Compared with SR–GO/CNTs, SR–GO/CNT-Si exhibited better mechanical and thermal performance. Moreover, the time-dependent complex modulus of SR–GO/CNTs-Si was much higher than that of SR–GO/CNTs, which indicates longer service time and more stable performance. In terms of electronic packaging, SR–GO/CNTs exhibited better performance than the 1180B counterpart. The low value of warpage of chip packaged by SR–GO/CNTs implied that SR–GO/CNTs-Si could have potential application as the thermal interface electronic packaging material.

Study of Warpage Evolution and Control for Six-Side Molded WLCSP in Different Packaging Processes

A six-side molded wafer-level chip scale package (mWLCSP) is a novel and attractive packaging method for smart phone applications due to its lower cost, better electrical performance, and higher long-term reliability. Nevertheless, wafer warpage in different manufacturing processes is a significant issue for the six-side mWLCSP. This article focuses on wafer warpage evolution in different packaging processes and the development of control method for the six-side mWLCSP. A quarter wafer-level finite-element (FE) model and a strip-level FE model were established to simulate the actual packaging processes by element birth and death method and restart technology. Both the FE models were proved quite efficient and accurate for warpage prediction compared to the experimental results. The effects of geometric parameters and material parameters on the maximum warpage value were studied based on the two established FE warpage models, and some recommendations were given for warpage optimization. Based on the above studies, an improved manufacturing process flow for the six-side mWLCSP was presented and proved feasible to control the maximum warpage value under 3 mm. It offers an insight work for the development and warpage control of the six-side mWLCSP and other wafer-level molded packages.

A hybrid back-propagation neural network and intelligent algorithm combined algorithm for optimizing microcellular foaming injection molding process parameters

The microcellular foaming injection molding process can effectively reduce the product weight and facilitate the realization of automobile lightweight, which is greatly affected by process parameters. Warpage of microcellular foaming material will increase, affecting the dimensional stability of the product, unless the process parameters are effectively controlled by process parameters. Warpage of microcellular foaming material has been based on key process variables including mold temperature, melt temperature, coolant temperature, coolant Reynolds number, v/p switch over, initial foaming volume, initial bubble radius and initial gas concentration. In order to reduce warpage of microcellular foaming material, the input and output data obtained from the Finite Element (FE) simulations are used to train BP neural network, GABP neural network and PSOBP neural network as prediction model for the warpage. Comparing the performance of the three methods in prediction error and training time, PSOBP is considered as the best prediction model for the warpage of microcellular foaming material. It has been proved that the prediction model has the ability to predict the warpage of the plastic within an error range of 1 %. The prediction model can be optimized by genetic algorithm to find the best combination of process parameters. The optimized warpage value is 0.7038 mm, which effectively reduces warpage of microcellular foaming material. Finally, finite element simulation and physical tests are carried out to verify the accuracy of the method to optimize microcellular foaming injection molding process parameters.

YAKLAŞIK ÇÖZÜM TEKNİKLERİNİ KULLANARAK PLASTİK ENJEKSİYON PROSESİNİN TASARIM METODOLOJİSİ

Bu çalışmada, istatistiksel deney tasarım yöntemleri kullanılarak hazırlanan deney setine uygun olarak yapılan akış analizleri ile enjeksiyon parametreleri optimize edilmiştir. Elde edilen sonuçları değerlendirmek için, ilk olarak istatistiksel deney yazılımı olan MiniTab vasıtası ile uygun bir regresyon modeli oluşturulmuştur, model katsayılarının doğruluğunu saptamak için F testi, parametrelerin sonuçlar üzerindeki etkisini saptamak için ANOVA testi uygulanmıştır. İkinci olarak süreç, bir hipoteze dayanan değişken yaratılarak, Monte Carlo simülasyonu ile optimize edilmiştir. Monte Carlo simülasyonu, analitik olarak belirsiz durumlarda varsayımlara dayanan hesaplamaları yapmak için kullanılır. Kalıp sıcaklığı, soğutma suyu sıcaklığı, enjeksiyon basıncı gibi işlem parametreleri sabit değildir. Bu belirsizliği gidermek için süreç hipoteze dayalı değişken üretmek suretiyle optimize edilmiştir. Son aşamada farklı optimizasyon yöntemleri kullanılarak elde edilen sonuçlar karşılaştırılarak, hangi yöntemin daha doğru sonuç verdiği değerlendirilmiştir. Sonuç olarak Monte Carlo simülasyonu ile minimum çarpılma değeri elde edilmiştir. Sonuç bölümünde yer alan Tablo 7 ve Grafik 1 üzerinden bu sonuç daha net anlaşılmaktadır. Plastik enjeksiyon işlemi gibi birçok parametrenin sonuç üzerinde etkin olduğu üretim yöntemleri için yapılacak optimizasyon çalışmalarında, belirsizlikleri gidermek için hipoteze dayalı rastsal parametre değerleri ile çalışmak avantaj sağlamaktadır.