Improvement of the superconvergent patch recovery technique by the use of constraint equations: the SPR‐C technique

The superconvergent patch recovery (SPR) technique is widely used in the evaluation of a recovered stress field σ ^* from the finite element solution σ _fe. Several modifications of the original SPR technique have been proposed. A new improvement of the SPR technique, called SPR‐C technique (Constrained SPR), is presented in this paper. This new technique proposes the use of the appropriate constraint equations in order to obtain stress interpolation polynomials in the patch σ that locally satisfy the equations that should be satisfied by the exact solution. As a result the evaluated expressions for σ will satisfy the internal equilibrium and compatibility equations in the whole patch and the boundary equilibrium equation at least in vertex boundary nodes and, under certain circumstances, along the whole boundary of the patch coinciding with the boundary of the domain. The results show that the use of this technique considerably improves the accuracy of the recovered stress field σ ^* and therefore the local effectivity of the ZZ error estimator. Copyright © 2006 John Wiley & Sons, Ltd.     

Quadrature for meshless methods

In this paper we discuss quadrature schemes for meshless methods. We consider the Neumann problem and derive an estimate for the energy norm error between the exact solution, u, and the quadrature approximate solution, u, in terms of a parameter, h, associated with the family of approximation spaces, and quantities η, τ, and ε that measure the errors in the stiffness matrix, in the boundary data, and in the right‐hand side vector, respectively, due to the quadrature. The major hypothesis in the estimate is that the quadrature stiffness matrix has zero row sums, a hypothesis that can be easily achieved by a simple correction of the diagonal elements. Copyright © 2008 John Wiley & Sons, Ltd.     

Improved radial basis function fluid–structure coupling via efficient localized implementation

Previous work by the authors has developed a universal interpolation scheme, using radial basis functions (RBFs), which results in a unified formulation for robust fluid–structure interpolation and high‐quality mesh motion. The method has several significant advantages. Primarily, all volume mesh, structural mesh, and flow‐solver‐type dependence is removed entirely, as all operations are performed on totally arbitrary point clouds of any form. Hence, all connectivity requirements are removed from both the coupling and mesh motion problems. Furthermore, only matrix‐vector multiplications are required during unsteady simulation because dependence relations are computed once prior to any simulation and then remain constant. This property means that the method is both perfectly parallel and totally independent from the flow‐solver. However, the full method is expensive, since the dependence matrix between two sets of points is N × N. The fluid–structure coupling behaviour can also be influenced by parameters used in the interpolation. To alleviate these difficulties a more efficient form of the RBF fluid–structure coupling is presented, which also greatly reduces the interpolation parameter influence. A pointwise form of the partition of unity approach is developed that localizes the interpolation, with results presented for static aeroelastic simulations of the Brite‐Euram multi‐disciplinary optimization wing using a very fine mesh containing 58 000 surface points. It is shown that a 58 × reduction in data size is achieved, and equally importantly the interpolation has a much smaller influence on final aeroelastic results. Copyright © 2009 John Wiley & Sons, Ltd.     

Capability assessment for processes with multiple characteristics: A generalization of the popular index Cpk

Process capability index C_pk is the most popular capability index widely used in the manufacturing industry. Existing research on the yield‐based measure index C_pk to date is restricted to processes with single characteristics. However, many manufacturing processes are commonly described with multiple characteristics, for example, the gold bumping process in the TFT‐LCD (thin film transistor‐liquid crystal display) manufacturing industry. In the gold bumping process, gold bumps have multiple characteristics all having effects on the process yield. Obtaining accurate gold bumping manufacturing yield is very important for quality assurance and in providing guidance toward process improvement. To obtain accurate yield assessment for processes with multiple characteristics, we propose a new overall yield‐measure index C, which is a generalization of the index C_pk, and a natural estimator of C. For the purpose of making inferences on the process capability, we derive a quite accurate approximation of the distribution of since the distribution is analytically intractable. With this distribution, we tabulate the lower confidence bounds of the new index under various sample sizes for in‐plant applications. In addition, we construct a statistical test on the new yield‐measure index in order to examine whether the yield meets the customers' requirements. For illustration purpose, a real case in a gold bumping factory located in the Science‐based Industrial Park at Hsinchu, Taiwan is presented. Copyright © 2011 John Wiley & Sons, Ltd.     

Filter‐based compressed sensing MRI reconstruction

Compressed sensing (CS) enables to reconstruct MR images from highly undersampled k‐space data by exploiting the sparsity which is implicit in the images. In this article, an MR image as a combination of a high‐frequency component and a low‐frequency component through a pair of filters has been proposed to express. Since exhibits a sparser representation in the wavelet transform domain, reconstructing and separately yields a better result than reconstructing directly. Two parameters, normalized sparsity (NS) and power ratio (PR), are defined to design the filters, that is, the high‐pass filter H _HP and the low‐pass filter H _LP. H _HP is applied to pick out high‐frequency k‐space data for the reconstruction of high‐frequency image ; while H _LP is used for filtering , which is reconstructed from the entire undersampled k‐space data to obtain the low‐frequency reconstruction . Summing and leads to the final reconstruction of . Experimental results demonstrate that the proposed method outperforms the conventional CS‐MRI method. It provides 2–4 dB improvement in peak signal to noise ratio (PSNR) value and preserves more edges and details in the images. © 2016 Wiley Periodicals, Inc. Int J Imaging Syst Technol, 26, 173–178, 2016     

Free mesh radial basis function collocation approach for the numerical solution of system of multi‐ion electrolytes

The main objective of this work is to show the versatility of an innovative mesh‐free numerical scheme, which allows the solution of the coupled transport equations governing the evolution of a system of multi‐ion electrolytes, by mean of the use of radial basis functions interpolation and a nesting approach. The nesting approach is used in order to capture the detail behaviour of the solution near a solid wall i.e. at the diffusion–reaction layer. As a numerical example the problem of silver deposition on a rotating disk is analysed. The versatility of the proposed numerical scheme is proved by solving the proposed electrochemical phenomena imposing three different kinds of boundary conditions at the solid wall (Dirichlet, Neumann and Robin). The obtained numerical results are compared with simplified analytical approximation of the corresponding problems. The effect of the ligand concentration on the others species is considered and a comparison between the obtained concentration profiles for the complex AgS₂O and Ag(S₂O₃) when the concentration of the ligand S₂O takes different values is shown. Copyright © 2005 John Wiley & Sons, Ltd.     

Charts with Variable Sample Size,Sampling Interval,and Warning Limits

The notion of variable warning limits is proposed for variable sample size and sampling interval (VSSI) charts. The basic purpose is to lower down the frequency of switches between the pairs of values of the sample sizes and sampling interval lengths of VSSI charts during their implementations. Expressions for performance measures for the variable sample size, sampling interval, and warning limits (VSSIWL) charts are developed. The performances of these charts are compared numerically with that of VSSI and VSSI (1, 3) charts, where VSSI (1, 3) charts are the VSSI charts with runs rule (1, 3) for switching between the pairs of values of sample sizes and sampling interval lengths. Runs rule (1, 3) greatly reduces the frequency of the switches; however, it slightly worsens the statistical performances of the VSSI charts in detecting moderate shifts in the process mean. It is observed that the out‐of‐control statistical performance and overall switching rate of VSSIWL charts are adaptive for the same in‐control statistical performances. These charts can be set to yield exactly similar performances as that of VSSI (1, 3) charts, to yield tradeoff performances between that of VSSI (1, 3) and VSSI charts, or to yield significantly lower switching rate than even that of VSSI (1, 3) charts at the cost of slightly inferior statistical performances than that of VSSI (1, 3) charts. Copyright © 2012 John Wiley & Sons, Ltd.     

An iterative defect‐correction type meshless method for acoustics

Accurate numerical simulation of acoustic wave propagation is still an open problem, particularly for medium frequencies. We have thus formulated a new numerical method better suited to the acoustical problem: the element‐free Galerkin method (EFGM) improved by appropriate basis functions computed by a defect correction approach. One of the EFGM advantages is that the shape functions are customizable. Indeed, we can construct the basis of the approximation with terms that are suited to the problem which has to be solved. Acoustical problems, in cavities Ω with boundary T, are governed by the Helmholtz equation completed with appropriate boundary conditions. As the pressure p(x,y) is a complex variable, it can always be expressed as a function of cosθ(x,y) and sinθ(x,y) where θ(x,y) is the phase of the wave in each point (x,y). If the exact distribution θ(x,y) of the phase is known and if a meshless basis {1, cosθ(x,y), sinθ (x,y) } is used, then the exact solution of the acoustic problem can be obtained. Obviously, in real‐life cases, the distribution of the phase is unknown. The aim of our work is to resolve, as a first step, the acoustic problem by using a polynomial basis to obtain a first approximation of the pressure field p(x,y). As a second step, from p(x,y) we compute the distribution of the phase θ(x,y) and we introduce it in the meshless basis in order to compute a second approximated pressure field p(x,y). From p(x,y), a new distribution of the phase is computed in order to obtain a third approximated pressure field and so on until a convergence criterion, concerning the pressure or the phase, is obtained. So, an iterative defect‐correction type meshless method has been developed to compute the pressure field in Ω. This work will show the efficiency of this meshless method in terms of accuracy and in terms of computational time. We will also compare the performance of this method with the classical finite element method. Copyright © 2003 John Wiley & Sons, Ltd.     

On the Performance of Shewhart‐type Synthetic and Runs‐rules Charts Combined with an Chart

A synthetic chart is a combination of a conforming run‐length chart and an chart, or equivalently, a 2‐of‐(H + 1) runs‐rules (RR) chart with a head‐start feature. However, a synthetic chart combined with an chart is called a Synthetic‐ chart. In this article, we build a framework for Shewhart Synthetic‐ and improved RR (i.e., 1‐of‐1 or 2‐of‐(H + 1) without head‐start) charts by conducting an in‐depth zero‐state and steady‐state study to gain insight into the design of different classes of these schemes and their average run‐length performance using the Markov chain imbedding technique. More importantly, we propose a modified side‐sensitive Synthetic‐ chart, and then using overall performance measures (i.e., the extra quadratic loss, average ratio of average run‐length, and performance comparison index), we show that this new chart has a uniformly better performance than its Shewhart competitors. We also provide easy‐to‐use tables for each of the chart's design parameters to aid practical implementation. Moreover, a performance comparison with their corresponding counterparts (i.e., synthetic and RR charts) is conducted. Copyright © 2015 John Wiley & Sons, Ltd.     

Process Yield for Multivariate Linear Profiles with One‐sided Specification Limits

The new investigation of profile monitoring is focused mainly on a process with multiple quality characteristics. Process yield has been used widely in the manufacturing industry, as an index for measuring process capability. In this study, we present two indices and to measure the process capability for multivariate linear profiles with one‐sided specification limits under mutually independent normality. Additionally, two indices and are proposed to measure the process capability for multivariate linear profiles with one‐sided specification limits under multivariate normality. These indices can provide an exact measure of the process yield. The approximate normal distributions for and are constructed. A simulation study is conducted to assess the performance of the proposed approach. The simulation results show that the estimated value of performs better as the number of profiles increases. Two illustrative examples are used to demonstrate the applicability of the proposed approach. Copyright © 2015 John Wiley & Sons, Ltd.     

Statistical Tests to Validate Predictive Models

This article presents validation tests to check a predictive model over time. These validation tests are like individuals, and S control charts. The individuals validation test is used when there are no replicates at the checked time points. The and S validation tests can be used when there are replicates. Their power is evaluated under various scenarios via a simulation study. Based on these results, the and S validation tests are recommended when there are replicate measurements. Copyright © 2014 John Wiley & Sons, Ltd.     

A Note on “Capability Assessment for Processes with Multiple Characteristics: A Generalization of the Popular Index Cpk”

The generalized yield index establishes the relationship between the manufacturing specifications and the actual process performance, which provides a lower bound on process yield for two‐sided processes with multiple characteristics. The results attended are very practical for industrial application. In this article, we extended the results in cases with one‐sided specification and multiple characteristics. The generalized index was considered, and the asymptotic distribution of the natural estimator was developed. Then, we derived the lower confidence bounds as well as the critical values of index . We not only provided some tables but also presented an application example. Copyright © 2012 John Wiley & Sons, Ltd.     

The Effect of Measurement Errors on the Synthetic Chart

Measurement errors often exist in quality control applications. In this paper, the performance of the synthetic chart is investigated when measurement errors exist using a linearly covariate error model. It is shown that the performance of the synthetic chart is significantly affected in the presence of measurement errors. The effect of taking multiple measurements for each item in a subgroup on the performance of synthetic chart is also investigated in this paper. An example is provided in order to illustrate the application of the synthetic chart with measurement errors. Copyright © 2014 John Wiley & Sons, Ltd.     

The Performance of Variable Sample Size Chart with Measurement Errors

The variable sample size (VSS) chart has been investigated by several researchers under the assumption of no measurement error. However, in practice, measurement errors may exist in quality control applications. In this paper, the overall performance of the VSS chart is investigated when measurement errors exist using a linearly covariate error model, and a methodology is proposed for choosing optimal parameters by considering measurement errors. It is shown that the overall performance of the VSS chart is significantly affected by the presence of measurement errors. The effect of taking multiple measurements for each item in a subgroup on the performance of VSS chart is also investigated in this paper. An example is provided to illustrate the application of the VSS chart with measurement errors. Copyright © 2015 John Wiley & Sons, Ltd.     

Geodesic finite elements on simplicial grids

We introduce geodesic finite elements as a conforming way to discretize partial differential equations for functions v : Ω → M, where Ω is an open subset of and M is a Riemannian manifold. These geodesic finite elements naturally generalize standard first‐order finite elements for Euclidean spaces. They also generalize the geodesic finite elements proposed for d = 1 in a previous publication of the author. Our formulation is equivariant under isometries of M and, hence, preserves objectivity of continuous problem formulations. We concentrate on partial differential equations that can be formulated as minimization problems. Discretization leads to algebraic minimization problems on product manifolds Mⁿ. These can be solved efficiently using a Riemannian trust‐region method. We propose a monotone multigrid method to solve the constrained inner problems with linear multigrid speed. As an example, we numerically compute harmonic maps from a domain in to S². Copyright © 2012 John Wiley & Sons, Ltd.     

Spectral equivalence and proper clusters for matrices from the boundary element method

The Galerkin matrices A_n from applications of the boundary element method to integral equations of the first kind usually need to be preconditioned. In the Laplace equation context, we highlight a family of preconditioners C_n that simultaneously enjoy two important properties: (a) A_n and C_n are spectrally equivalent, and (b) the eigenvalues of C A_n have a proper cluster at unity. In the Helmholtz equation context, we prove the spectral equivalence for the so‐called second Galerkin matrices and that the eigenvalues of C A_n still have a proper cluster at unity. We then show that some circulant integral approximate operator (CIAO) preconditioners belong to this family, including the well‐known optimal CIAO. Consequently, if we use the preconditioned conjugate gradients to solve the problems, the number of iterations for a prescribed accuracy does not depend on n, and, what is more, the convergence rate is superlinear. Copyright © 2000 John Wiley & Sons, Ltd.     

The steady‐state behavior of the synthetic and side‐sensitive synthetic double sampling charts

The steady‐state average run length is used to measure the performance of the recently proposed synthetic double sampling chart (synthetic DS chart). The overall performance of the DS chart in signaling process mean shifts of different magnitudes does not improve when it is integrated with the conforming run length chart, except when the integrated charts are designed to offer very high protection against false alarms, and the use of large samples is prohibitive. The synthetic chart signals when a second point falls beyond the control limits, no matter whether one of them falls above the centerline and the other falls below it; with the side‐sensitive feature, the synthetic chart does not signal when they fall on opposite sides of the centerline. We also investigated the steady‐state average run length of the side‐sensitive synthetic DS chart. With the side‐sensitive feature, the overall performance of the synthetic DS chart improves, but not enough to outperform the non‐synthetic DS chart. Copyright © 2014 John Wiley & Sons, Ltd.     

Control Chart Limits for Monitoring Process Mean Based on Downton's Estimator

Control charts are important tools in statistical process control used to monitor shift in process mean and variance. This paper proposes a control chart for monitoring the process mean using the Downton estimator and provides table of constant factors for computing the control limits for sample size (n ≤ 10). The derived control limits for process mean were compared with control limits based on range statistic. The performance of the proposed control charts was evaluated using the average run length for normal and non‐normal process situations. The obtained results showed that the control chart, using the Downton statistic, performed better than Shewhart chart using range statistic for detection of small shift in the process mean when the process is non‐normal and compares favourably well with Shewhart chart that is normally distributed. Copyright © 2015 John Wiley & Sons, Ltd.     

Robust and efficient monolithic fluid‐structure‐interaction solvers

We construct new robust and efficient preconditioned generalized minimal residual solvers for the monolithic linear systems of algebraic equations arising from the finite element discretization and Newton's linearization of the fully coupled fluid–structure interaction system of partial differential equations in the arbitrary Lagrangian–Eulerian formulation. We admit both linear elastic and nonlinear hyperelastic materials in the solid model and cover a large range of flows, for example, water, blood, and air, with highly varying density. The preconditioner is constructed in form of , where , , and are proper approximations to the matrices L, D, and U in the LDU block factorization of the fully coupled system matrix, respectively. The inverse of the corresponding Schur complement is approximated by applying a few cycles of a special class of algebraic multigrid methods to the perturbed fluid sub‐problem, which is obtained by modifying corresponding entries in the original fluid matrix with an explicitly constructed approximation to the exact perturbation coming from the sparse matrix–matrix multiplications. The numerical studies presented impressively demonstrate the robustness and the efficiency of the preconditioner proposed in the paper. Copyright © 2016 John Wiley & Sons, Ltd.     

Adaptive control charts for skew‐normal distribution

The standard Shewhart‐type chart, named FSS‐ chart, has been widely used to detect the mean shift of process by implementing fixed sample and sampling frequency schemes. The FSS‐ chart could be sensitive to the normality assumption and is inefficient to catch small or moderate shifts in the process mean. To monitor nonnormally distributed variables, Li et al [Commun Stat‐Theory Meth. 2014; 43(23):4908‐4924] extended the study of Tsai [Int J Reliab Qual Saf Eng. 2007; 14(1):49‐63] to provide a new skew‐normal FSS‐ (SN FSS‐ ) chart with exact control limits for the SN distribution. To enhance the sensitivity of the SN FSS‐ chart on detecting small or moderate mean shifts in the process, adaptive charts with variable sampling interval (VSI), variable sample size (VSS), and variable sample size and sampling interval (VSSI) are introduced for the SN distribution in this study. The proposed adaptive control charts include the normality adaptive charts as special cases. Simulation results show that all the proposed SN VSI‐ , SN VSS‐ , and SN VSSI‐ charts outperform the SN FSS‐ chart on detecting small or moderate shifts in the process mean. The impact of model misspecification on using the proposed adaptive charts and the sample size impact for using the FSS‐ chart to monitor the mean of SN data are also discussed. An example about single hue value in polarizer manufacturing process is used to illustrate the applications of the proposed adaptive charts.