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Because of the high computational efficiency, response surface method (RSM) has been widely used in structural reliability analysis. However, for a highly nonlinear limit state function (LSF), the approximate accuracy of the failure probability mainly depends on the design point, and the result is that the response surface function composed of initial experimental points rarely fits the LSF exactly. The inaccurate design points usually cause some errors in the traditional RSM. The purpose of this paper is to present a hybrid method combining adaptive moving experimental points strategy and RSM, describing a new response surface using downhill simplex algorithm (DSA-RSM).

In DSA-RSM, the operation mechanism principle of the basic DSA, in which local descending vectors are automatically generated, was studied. Then, the search strategy of the basic DSA was changed and the RSM approximate model was reconstructed by combining the direct search advantage of DSA with the reliability mechanism of response surface analysis.

The computational power of the proposed method is demonstrated by solving four structural reliability problems, including the actual engineering problem of a car collision. Compared to specific structural reliability analysis methods, the approach of modified DSA interpolation response surface for structural reliability has a good convergent capability and computational accuracy.

This paper proposes a new RSM technology based on proxy model to complete the reliability analysis. The originality of this paper is to present an improved RSM that adjusts the position of the experimental points judiciously by using the DSA principle to make the fitted response surface closer to the actual limit state surface.

The purpose of this study is to improve the efficiency and accuracy of response surface method (RSM), as well as its robustness.

By introducing cut-high-dimensional representation model (HDMR), the delineation of cross terms and the constitution analysis of component function, a new adaptive RSM is presented for reliability calculation, where a sampling scheme is also proposed to help constructing response surface close to limit-state.

The proposed method has a more feasible process of evaluating undetermined coefficients of each component function than traditional RSM, and performs well in terms of balancing the efficiency and accuracy when compared to the traditional second-order polynomial RSM. Moreover, the proposed method is robust on the parameter in a wide range, indicating that it is able to obtain convergent result in a wide feasible domain of sample points.

This study constructed an adaptive bivariate cut-HDMR by introducing delineation of cross-terms and constitution of univariate component function; and a new sampling technique is proposed.

The purpose of this paper is to find the optimal values of process parameters in injection molding when both warpage and shrinkage are minimized.

In finding the optimal values, advantages of finite element software, Moldflow, and dual response surface method (dual RSM) combined with the nonlinear programming technique by Lingo are exploited. Considering the nine process parameters, injection time, injection pressure, packing pressure, packing time, cooling time, coolant temperature, mold‐open time, melting temperature and mold surface temperature, a series of mold analyses are performed to exploit the warpage and shrinkage data. In the analyses, warpage is considered the primary response, whereas shrinkage is the secondary response.

The results indicate that dual RSM combined with the nonlinear programming technique can outperform the Taguchi's optimization method. The optimal process values are also confirmed by re‐running experiments on Moldflow. Additionally, an auxiliary dual RSM model is proposed to search for a better result based on the given findings by dual RSM at the cost of running extra experiments. Based on dual RSM, a multiple objective optimization for the whole plastic product is finally suggested to integrate the dual RSM models that are developed for the individual nodes or edges.

This paper proposes a new method to find the optimal process for plastic injection molding.

Based on univariate dimension-reduction model, this study aims to propose an adaptive anisotropic response surface method (ARSM) and its high-order revision (HARSM) to balance the accuracy and efficiency for response surface method (RSM).

First, judgment criteria for the constitution of a univariate function are derived mathematically, together with the practical implementation. Second, by combining separate polynomial approximation of each component function of univariate dimension-reduction model with its constitution analysis, the anisotropic ARSM is proposed. Third, the high-order revision for component functions is introduced to improve the accuracy of ARSM, namely, HARSM, in which the revision is also anisotropic. Finally, several examples are investigated to verify the accuracy, efficiency and convergence of the proposed methods, and the influence of parameters on the proposed methods is also performed.

The criteria for constitution analysis are appropriate and practical. Obtaining the undetermined coefficients for every component functions is easier than the existing RSMs. The existence of special component functions is useful to improve the efficiency of the ARSM. HARSM is helpful for improving accuracy significantly and it is more robust than ARSM and the existing quadratic polynomial RSMs and linear RSM. ARSM and HARSM can achieve appropriate balance between precision and efficiency.

The constitution of univariate function can be determined adaptively and the nonlinearity of different variables in the response surface can be treated in an anisotropic way.

Balancing accuracy and efficiency is an important evaluation index of response surface method. The purpose of this paper is to propose an adaptive order response surface method (AORSM) based on univariate decomposition model (UDM).

First, the nonlinearity of the univariate function can be judged by evaluating the goodness of fit and the error of curve fit rationally. Second, combining UDM with the order analysis of separate component polynomial, an easy-to-implement AORSM is proposed. Finally, several examples involving mathematical functions and structural engineering problems are studied in detail.

With the proposed AORSM, the orders of component functions in the original response surface can be determined adaptively and the results of those cases in this paper indicate that the proposed method performs good accuracy, efficiency and robustness.

Because just the cases with single failure mode and single MPP are studied in this paper, the application in multi-failure mode and multi-MPP cases need to be investigated in the coming work.

The nonlinearity of the univariate in the response surface can be determined adaptively and the undetermined coefficients of each component function are obtained separately, which reduces the computation dramatically.

The multisource uncertainties, including material dispersion, load fluctuation and geometrical tolerance, have crucial effects on fatigue performance of turbine bladed disks. In view of the aim of this paper, it is essential to develop an advanced approach to efficiently quantify their influences and evaluate the fatigue life of turbine bladed disks.

In this study, a novel combined machine learning strategy is performed to fatigue assessment of turbine bladed disks. Proposed model consists of two modeling phases in terms of response surface method (RSM) and support vector regression (SVR), namely RSM-SVR. Two different input sets obtained from basic variables were used as the inputs of RSM, then the predicted results by RSM in first phase is used as inputs of SVR model by using a group data-handling strategy. By this way, the nonlinear flexibility of SVR inputs is improved and RSM-SVR model presents the high-tendency and efficiency characteristics.

The accuracy and tendency of the RSM-SVR model, applied to the fatigue life estimation of turbine bladed disks, are validated. The results indicate that the proposed model is capable of accurately simulating the nonlinear response of turbine bladed disks under multisource uncertainties, and SVR-RSM model provides an accurate prediction strategy compared to RSM and SVR for fatigue analysis of complex structures.

The results indicate that the proposed model is capable of accurately simulate the nonlinear response of turbine bladed disks under multisource uncertainties, and SVR-RSM model provides an accurate prediction compared to RSM and SVRE for fatigue analysis of turbine bladed disk.

In a multistage process, the final quality in the last stage not only depends on the quality of the task performed in that stage but is also dependent on the quality of the products and services in intermediate stages as well as the design parameters in each stage. One of the most efficient statistical approaches used to model the multistage problems is the response surface method (RSM). However, it is necessary to optimize each response in all stages so to achieve the best solution for the whole problem. Robust optimization can produce very accurate solutions in this case.

In order to model a multistage problem, the RSM is often used by the researchers. A classical approach to estimate response surfaces is the ordinary least squares (OLS) method. However, this method is very sensitive to outliers. To overcome this drawback, some robust estimation methods have been presented in the literature. In optimization phase, the global criterion (GC) method is used to optimize the response surfaces estimated by the robust approach in a multistage problem.

The results of a numerical study show that our proposed robust optimization approach, considering both the sum of square error (SSE) index in model estimation and also GC index in optimization phase, will perform better than the classical full information maximum likelihood (FIML) estimation method.

To the best of the authors’ knowledge, there are few papers focusing on quality-oriented designs in the multistage problem by means of RSM. Development of robust approaches for the response surface estimation and also optimization of the estimated response surfaces are the main novelties in this study. The proposed approach will produce more robust and accurate solutions for multistage problems rather than classical approaches.

The purpose of this paper is to discuss the capability of finite element analysis (FEA) in performing the virtual thermal cycling reliability test to evaluate the reliability of solder joints in a ball grid array (BGA) package.

Thermal cycling test has been used to evaluate the reliability or fatigue life of the solder joints in BGA package using commercially available FEA software, ANSYS™. The effect of different temperature cycling condition is studied by applying different value of dwell time and ramp rate. Two types of analyses are used namely, the physics‐based analysis and the statistical‐based analysis. Two screening design methods namely, central composite design (CCD) and Box‐Behnken Matrix Design method are used to isolate the most important factors amongst six selected design variables. The optimization process is carried out using response surface methodology (RSM).

It is observed that changes in ramp rate produce significant effect in solder fatigue life than changes in dwell time but the dwell time at high temperature has a negligible contribution to solder fatigue life. It has been found that the thickness of the mold has a significant effect on the performance of the solder joint reliability (more than 50 percent) as compared to that from other factors. Besides, the effect of individual factor, the interaction among factors also changes the solder joint reliability. RSM based on Box‐Behnken Matrix design offers the highest characteristic solder joint fatigue life with a value of 2,861 cycles.

This paper provides a comprehensive method to evaluate the reliability of solder joints in terms of physics and statistical‐based analysis.

This paper aims to establish the predictive equations of height, area and volume of printed solder paste during solder paste stencil printing (SPSP) process in surface mount technology (SMT) to better understand the effect of process parameters on the printing quality.

An experiment plan is proposed based on the response surface method (RSM). Experiments with 30 different combinations of process parameters are performed using a solder paste printer. After printing, the volume, area and height of the printed SAC105 solder paste are measured by a solder paste inspection machine. Using RSM, the predictive equations associated with the printing parameters and the printing quality of the solder paste are formed.

The optimal printing parameters are 175.08 N printing pressure, 250 mm/s printing speed, 0.1 mm snap-off height and 15.7 mm/s stencil snap-off speed if the target height of solder paste is 100 µm. As the target printing area of solder paste is 1.1 mm × 1.3 mm, the optimized values of the printing parameters are 140.29 N, 100.52 mm/s, 0.63 mm and 20.25 mm/s. When both the target printing height and area are optimized together, the optimal values for the four parameters are 86.67 N, 225.76 mm/s, 0.15 mm and 1.82 mm/s.

A simple RSM-based experimental method is proposed to formulate the predictive polynomial equations for height, area and volume of printed solder paste in terms of important SPSP parameters. The predictive equation model can be applied to the actual SPSP process, allowing engineers to quickly predict the best printing parameters during parameter setting to improve production efficiency and quality.

The purpose of this paper is to develop a mathematical model for surface roughness and delamination through response surface methodology (RSM) and analyse the influences of the entire individual input machining parameters (cutting speed, fibre orientation angle, depth of cut and feed rate) on the responses in milling of glass fibre reinforced plastics (GFRP) composites with solid carbide end mill cutter coated with PCD.

Four factors, five level central composites and a rotatable design matrix in response surface methodology were employed to carry out the experimental investigation. “Design Expert 8.0” software was used for regression and graphical analysis of the data were collected. The optimum values of the selected variables were obtained by solving the regression equation and by analyzing the response surface contour plots. Analysis of variance (ANOVA) was applied to check the validity of the model and for finding the significant parameters.

The developed second order response surface model was used to calculate the surface roughness and delamination of the machined surfaces at different cutting conditions with the chosen range with 95 per cent confidence intervals. Using such a model, remarkable savings in time and cost can be obtained.

The effect of fibre orientation during milling of GFRP laminates using RSM has not been previously attempted for analysis.