Designing two mixed quick switching sampling plans for linear profiles

This study compares two proposed mixed quick switching sampling (QSS) plans for linear profiles as the quality characteristic. For the QSS plans, we recommend a binomial attribute plan for normal inspection and then a variable sampling plan for tightened inspection based on capability index C_puA of linear profiles with one-sided specifications. The difference between the two proposed QSS plans is in the tightened inspection. Tightened inspection of the first proposed plan is a single sampling using C_puA index, but tightened inspection of the second plan is a multiple dependent state repetitive (MDSR) plan based on C_puA index. The optimal parameters are obtained by nonlinear optimization. Simulation study for selecting parameters is conducted with various combinations of specified acceptable quality level (AQL), limited quality level (LQL), producer's risk, and consumer's risk. Simulation results confirm that the second proposed QSS plan which applies variable MDSR at tightened inspection performs better than another proposed plan. Hence, the approach of the second proposed plan is demonstrated in an illustrative example.     

Optimisation of burn-in time considering the hidden loss of quality deviations in the manufacturing process

The burn-in test time is an important parameter of the complex batch processing machine scheduling problem. The omission of the loss of quality deviations in manufacturing generates a non-comprehensive and imperfect result in the optimisation of burn-in time, which hinders the identification of proactive and economical optimisation strategies to prevent infant failure in manufacturing. To solve this problem, this study visualises and quantifies for the first time the hidden loss caused by quality deviations in manufacturing and uses it as a newly added constraint to optimise the burn-in time. Firstly, a quality loss model composed of visible yield loss and warranty costs related to measurable but undetectable reliability vulnerabilities is defined. Secondly, the loss effects of growing defects are measured during the burn-in test, and the optimal burn-in time expressed by the proposed quality loss model is traded off between the additional burn-in cost and the decreased quality loss for an acceptable low infant failure rate. Finally, the effectiveness of the proposed optimisation approach is demonstrated using actual data from a control board with a high infant failure rate. Results show that the proposed method can systematically combine the fundamental loss of quality deviations in the optimisation of burn-in time, which supplements the commonly used optimality criteria, with the upstream loss of quality deviations in the form of manufacturing defects.     

Multiple dependent state repetitive group sampling plan for Burr XII distribution

In material engineering application, the failure time of material due to weakness in material (fatigue) is usually caused by repeated variations of stress. The failure time is modeled by statistical distributions. In this article, an attribute multiple state repetitive group sampling plan is developed assuming that the life time follows the Burr Type XII distribution. The plan parameters are determined by considering two points on operating characteristic (OC) curve. Tables are given for the practical use. The advantages of the proposed plan are discussed over the single sampling plans. Examples are given to illustrate the proposed plan.     

Multi-state reliability demonstration tests

ABSTRACT

Reliability demonstration tests have important applications in reliability assurance activities to demonstrate product quality over time and safeguard companies’ market positions and competitiveness. With greatly increasing global market competition, conventional binomial reliability demonstration tests based on binary test outcomes (success or failure) at a single time point become insufficient for meeting consumers’ diverse requirements. This article proposes multi-state reliability demonstration tests (MSRDTs) for demonstrating reliability at multiple time periods or involving multiple failure modes. The design strategy for MSRDTs employs a Bayesian approach to allow incorporation of prior knowledge, which has the potential to reduce the test sample size. Simultaneous demonstration of multiple objectives can be achieved and critical requirements specified to avoid early/critical failures can be explicitly demonstrated to ensure high customer satisfaction. Two case studies are explored to demonstrate the proposed test plans for different objectives.     

Sampling plans for the zero‐inflated negative binomial distribution in the food industry

In this paper, we propose 3 new sampling plans, including resubmitted single sampling plan (RSSP), repetitive group sampling (RGS) plan, and multiple dependent state (MDS) sampling plan to study the zero‐inflated negative binomial distribution in microbiological food safety and quality assurance practices. The unity value approach is used to find optimal plan parameters. The proposed plans are compared with the single sampling plan (SSP). We found that degree of clustering and excess of zeros counts affect the performance of all sampling plans. The MDS plan outperforms the SSP, RSSP, and RGS plans with respect to minimum average sample number in most cases. Both RGS and MDS plans show a comparable performance. The average run length is calculated to evaluate the rejection capability of the plans and signal the deterioration of the quality of lots. An example from 9 Irish abattoirs is used to illustrate the application of the proposed methods.     

Acceptance Sampling Plans with Truncated Life Tests for the Length-Biased Weighted Lomax Distribution

In this paper, we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans (ASPs) where the life test is assumed to be truncated at a pre-assigned time. For the new suggested ASPs, the tables of the minimum samples sizes needed to assert a specific mean life of the test units are obtained. In addition, the values of the corresponding operating characteristic function and the associated producer’s risks are calculated. Analyses of two real data sets are presented to investigate the applicability of the proposed acceptance sampling plans; one data set contains the first failure of 20 small electric carts, and the other data set contains the failure times of the air conditioning system of an airplane. Comparisons are made between the proposed acceptance sampling plans and some existing acceptance sampling plans considered in this study based on the minimum sample sizes. It is observed that the samples sizes based on the proposed acceptance sampling plans are less than their competitors considered in this study. The suggested acceptance sampling plans are recommended for practitioners in the field.     

Failure time distributions for complex equipment

The exponential distribution is inadequate as a failure time model for most components; however, under certain conditions (in particular, that component failure rates are small and mutually independent, and failed components are immediately replaced or perfectly repaired), it is applicable to complex repairable systems with large numbers of components in series, regardless of component distributions, as shown by Drenick in 1960. This result implies that system behavior may become simpler as more components are added. We review necessary conditions for the result and present some simulation studies to assess how well it holds in systems with finite numbers of components. We also note that Drenick's result is analogous to similar results in other systems disciplines, again resulting in simpler behavior as the number of entities in the system increases.     

考虑泊松效应的材料/结构一体化设计方法

为实现含有不同泊松比组分复合材料的优化设计,并考虑宏观结构及复杂的边界条件,提出了考虑泊松效应的材料/结构一体化设计方法,其显著特征在于不同组分材料中引入了泊松比插值,假设宏观结构由周期性排列的复合材料组成,复合材料含两种各向同性且泊松比不同的组分材料,以静态问题中柔顺度最小化或动态问题中特征值最大化为目标以及宏微观体积比为约束建立了拓扑优化模型。采用均匀化理论预测了复合材料等效性能,推导了目标函数对宏微观密度变量的敏度表达式。分别采用密度过滤和敏度过滤来消除宏微观拓扑优化中的不稳定性现象。采用优化准则法分别更新宏观、微观密度变量,考察了微观体积比和组分材料泊松比参数对优化结果的影响。三维数值算例结果表明所提出的一体化方法具有可行性和优越性。     

A combined method using modified routh stability array and MSE criterion for the reduction of discrete‐time systems

Abstract

A new mixed method using modified stability array and mean‐square error (MSE) criterion is proposed for deriving reduced‐order 2‐transfer functions for discrete‐time systems. More precisely, the modified Routh stability array is used to obtain the reduced‐order denominator, thus ensuring stability preservation, while the numerator is obtained by minimizing the mean‐square error between the unit step responses of the original system and reduced model. The main feature of the method is that it does not actually evaluate the system and model responses in the step of minimizing mean‐square error.     

A risk-adjusted exponentially weighted moving average control chart for detection of the scale parameter in surgical quality monitoring

Risk-adjusted control charts have been widely used in monitoring surgical quality in detecting risks of surgical performance. Most of the previous approaches focus on shifts in the location parameter as well as the existence of the scale parameter, which cannot get the full measure of the scale parameter under different levels. Ignoring the magnitude of the scale parameter, the monitoring methods cannot detect different variations of surgical mortality that is measured by scale parameter and required to reflect surgical quality improvement. The method of detecting variations in surgical quality is of interest in surgical quality improvement. This paper uses a new weighted h-likelihood method to obtain a weighted score test for the surgical risks from the logistic model. Then an exponentially weighted moving average chart can be constructed to monitor the changes in the variance of risks, which could be of interest in practical surgical monitoring programs. Simulation results indicate that the proposed approach performs more efficiently than existing methods under various magnitudes of shifts in scale parameters on top of different pre-set threshold stability. In addition, the application of the proposed method to real surgical data from the Surgical Outcome Monitoring and Improvement Program in Hong Kong shows the improvement and deterioration in a hospital's outcomes.     

A hybrid direct‐automatic differentiation method for the computation of independent sensitivities in multibody systems

The usefulness of sensitivity analyses in mechanical engineering is very well‐known. Interesting examples of sensitivity analysis applications include the computation of gradients in gradient‐based optimization methods and the determination of the parameter relevance on a specific response or objective. In the field of multibody dynamics, analytical sensitivity methods tend to be very complex, and thus, numerical differentiation is often used instead, which degrades numerical accuracy. In this work, a simple and original method based on state‐space motion differential equations is presented. The number of second‐order motion differential equations equals the number of DOFs, that is, there is one differential equation per independent acceleration. The dynamic equations are then differentiated with respect to the parameters by using automatic differentiation and without manual intervention from the user. By adding the sensitivity equations to the dynamic equations, the forward dynamics and the independent sensitivities can be robustly computed using standard integrators. Efficiency and accuracy are assessed by analyzing three numerical examples (a double pendulum, a four‐bar linkage, and an 18‐DOF coach) and by comparing the results with those of the numerical differentiation approach. The results show that the integration of independent sensitivities using automatic differentiation is stable and accurate to machine precision. Copyright © 2014 John Wiley & Sons, Ltd.     

A generalized complex eigenvector method for dynamic analysis of heterogeneous viscoelastic structures

A generalized complex eigenvector method which can be used to a linear dynamic analysis of viscoelastic structures is described. Here dynamic analysis is understood as transient analysis and frequency response analysis. The generalized complex eigenvector method is based on finite element discretization of structure, approximation of viscoelastic properties by differential operators and mode superposition technique. Coefficients of differential operator are defined from the condition of best coincidence of complex characteristic of viscoelastic material and complex characteristic of differential operator in preset frequency range. Advantage of this method is that it allows to take into account the real changes of the viscoelastic property in frequency range. Also, the generalized complex eigenvector method permit to describe a viscoelastic properties by two functions (complex Young's modulus, complex Poisson's ratio). The method is verified with the help of comparing with solutions obtained by complex modulus method. An influence of viscoelastic Poisson's ratio on transient and frequency responses of structure is demonstrated. Copyright © 2001 John Wiley & Sons, Ltd.     

Approximations of tolerance intervals for normally distributed data

Tolerance intervals are lesser known relatives of confidence and prediction intervals. They can be very useful in many situations to make product or process quality assessments. Even for normally distributed data, their calculation is less trivial than confidence and prediction intervals, which makes them underutilized in practice. In addition, they are not always readily available in statistical software packages. As a result, there have been several approximate methods proposed in the literature to calculate them. After a review of tolerance intervals and their variations, we investigate those approximations and compare them with the exact values for one‐sided and two‐sided intervals. We first propose a modification of an approximation for a one‐sided interval. Then we propose new approximations for two‐sided intervals based on Bonferroni's Inequality. We find that these approximations are extremely satisfactory for practical applications. Copyright © 2008 John Wiley & Sons, Ltd.     

A simple boundary element method for problems of potential in non‐homogeneous media

A simple boundary element method for solving potential problems in non‐homogeneous media is presented. A physical parameter (e.g. heat conductivity, permeability, permittivity, resistivity, magnetic permeability) has a spatial distribution that varies with one or more co‐ordinates. For certain classes of material variations the non‐homogeneous problem can be transformed to known homogeneous problems such as those governed by the Laplace, Helmholtz and modified Helmholtz equations. A three‐dimensional Galerkin boundary element method implementation is presented for these cases. However, the present development is not restricted to Galerkin schemes and can be readily extended to other boundary integral methods such as standard collocation. A few test examples are given to verify the proposed formulation. The paper is supplemented by an Appendix, which presents an ABAQUS user‐subroutine for graded finite elements. The results from the finite element simulations are used for comparison with the present boundary element solutions. Copyright © 2004 John Wiley & Sons, Ltd.     

Hamilton's law of variable mass system and time finite element formulations for time‐varying structures based on the law

Traditional principles of mechanics are primarily conceived for constant mass systems, which are only valid if mass is gained or lost at null velocity with respect to an inertial reference frame for variable mass systems, thus the numerical algorithms for time‐varying structures based on these principles are only suitable for this special case. In this paper, Hamilton's law of variable mass system is derived based on Meshchersky's fundamental equation, and two classes of novel time finite element formulations for linear systems with arbitrary continuous time‐varying parameters are developed based on the previous law. The formulations are verified extensively through numerical examples in which the convergence and effectiveness of algorithms are evaluated. Numerical examples demonstrate that compared with the algorithms for time‐varying structures that developed based on traditional principles of mechanics, the proposed algorithms provide extended capabilities in both time‐varying mass problems that mass is gained or lost at any velocity (such as rocket problem) and moving‐mass problems (such as vehicle‐bridge interaction problem) besides the time‐varying stiffness and damping problems, the proposed algorithms have a wider range of application. In particular, Hamilton's law of variable mass system provides a solid theoretical foundation for further research on the algorithm design for time‐varying structures. Copyright © 2014 John Wiley & Sons, Ltd.     

A direct coupling method for 3D hydroelastic analysis of floating structures

This paper presents a complete formulation for three‐dimensional hydrodynamic analysis of floating flexible structures subjected to surface regular waves, as well as other excitation forces, by employing a direct tight coupling method. The continuum mechanics‐based finite element method is employed to model floating structures with arbitrary geometries, which can account for the geometric nonlinearities and initial stress effects that result from the hydrostatic analysis, whereas the boundary element method is used for the fluid via total potential formulation. The simplicity and generality of the present formulation are revealed as compared with the conventional formulation. Numerical examples demonstrate the general capability of the formulation proposed. Copyright © 2013 John Wiley & Sons, Ltd.     

A coupled BEM‐flexibility force method for bending analysis of internally supported plates

This paper presents a new method for the analysis of plates in bending with internal supports. The proposed method can be regarded as an extension of the well‐known force method (the flexibility matrix method) in the matrix analysis of structures. The solution is performed through two phases: the released plate phase, in which the plate is released from all internal supports and solved using the Boundary Element Method (BEM). The effect of internal supports is considered in the second phase, where a series of unit virtual loads is placed instead of the unknown redundant reactions at internal supports. The flexibility matrix is formed and compatibility of deformations at the locations of internal supports is satisfied. Hence, the corresponding system of equations is solved for the unknown redundant forces at internal supports. The final solution of the problem consists of the summation of two phases: the released plate phase and the cases of virtual unit loads phase. An efficient solution algorithm is developed to solve both phases simultaneously. The main advantages of the present formulation are: (1) the present formulation increases the versatility of the BEM as it allows the re‐usability of standard BEM codes for solution of plates in bending to be used in solving problems having internal supports, with even no modifications; and (2) the two solution phases are completely uncoupled; therefore it is easy to trace behaviour of the plate due to failure of one or more of the internal supports without re‐analysis. Several numerical examples are analysed. The results are compared to those of analytical and finite element models to demonstrate the accuracy and the validity of the present formulation. The present formulation is used also to study the differences between the finite element and boundary element modelling for building slabs. Copyright © 2002 John Wiley & Sons, Ltd.     

A finite element post-processed Galerkin method for dimensional reduction in the non-linear dynamics of solids. Applications to shells

In this paper we introduce the finite element version of the so-called post-processed Galerkin method into the field of solid mechanics and apply the new technique to the dynamics of shells. The proposed post-processed method provides low-cost means to lift low-dimensional solutions to high-dimensional solutions. It is the very fact that the kinematical fields are improved to higher orders which makes the method of great interest. Our shell theory is geometrically exact in the sense that all non-linearities are included in the formulation. For time integration an energy/momentum scheme is used to enhance integration stability. Two hierarchical enhanced finite elements are formulated, on the basis of which a specific post-processed method is then developed. With the help of some examples of non-linear shell vibrations, a critical examination and validation of the post-processed method is carried out.     

Optimisation of FDM process parameters by Taguchi method for imparting customised properties to components

Customisation of material properties by route of controlling the process parameters is a landmark ability of the additive manufacturing (AM) processes. Parametric optimisation of fused deposition modelling process using Fortus 250mc modeller is accomplished for conical primitives of constructive solid geometry in the present research. Experiments were designed according to the Taguchi technique for four factors at three levels each – slice height (SH), contour width (CW), raster width and air gap (AG). Analysis of signal-to-noise ratios is utilised for establishing the optimal process parameters and the relative percentage contribution of factors is estimated using ANOVA. Optimal levels of process parameters are found to vary with the variation in the type of basic shape of primitive. It has been established that AG has a maximum impact over the part build volume followed by CW and SH. Also, it can be safely concluded that the interaction effect of parameters is relatively less important.     

An advanced boundary element method for solving 2D and 3D static problems in Mindlin's strain‐gradient theory of elasticity

An advanced boundary element method (BEM) for solving two‐ (2D) and three‐dimensional (3D) problems in materials with microstructural effects is presented. The analysis is performed in the context of Mindlin's Form‐II gradient elastic theory. The fundamental solution of the equilibrium partial differential equation is explicitly derived. The integral representation of the problem, consisting of two boundary integral equations, one for displacements and the other for its normal derivative, is developed. The global boundary of the analyzed domain is discretized into quadratic line and quadrilateral elements for 2D and 3D problems, respectively. Representative 2D and 3D numerical examples are presented to illustrate the method, demonstrate its accuracy and efficiency and assess the gradient effect on the response. The importance of satisfying the correct boundary conditions in gradient elastic problems is illustrated with the solution of simple 2D problems. Copyright © 2010 John Wiley & Sons, Ltd.