Optimization design of the CUSUM and EWMA charts for autocorrelated processes

The traditional control charts produce frequent false alarm signals in the presence of autocorrelation. The implementation of the modified chart scheme is a way of handling the problem of autocorrelation in control charts. In modified charts, the standard control limits of the traditional charts are adjusted to offset the influence because of the autocorrelation. The exponentially weighted moving average– and cumulative sum–modified charts are 2 widely used charts for monitoring autocorrelated data. These charts have design parameters in their formulation, and the choice of these parameters play significant roles in the detection of out‐of‐control situations. In reality, the magnitude of the mean shift is uncertain, and this leads to a difficulty in the choice of design parameters by the practitioner. The use of optimal parameters can enhance process performance in such situations. In this paper, we determine optimal design parameters for the charts using an exhaustive search procedure. In the optimization process, we determine the parameters that produce the smallest extra quadratic loss (EQL) value for each autocorrelation coefficient. This criterion measures the anticipated loss attributed to poor quality in the process. The loss in quality is lowered by minimizing the EQL and the combination of parameters in the chart that yields the smallest EQL has a better detection ability over the entire shift range. For the purpose of this work, we concentrate on autocorrelation that can be specifically modelled with autoregressive models. This article provides the practitioner with optimal parameters that can be used to enhance the overall effectiveness of the charts over an entire shift range.     

A Robust Design Method in Product Quality Applications

1　IntroductionThe 1980bookletbyTaguchiwaswrittenatatimewhentheinitialsignal to noiseratioswerebeingdevel opedandhisthinkingwasbeingtranslatedfromJapaneseforthefirsttime.Histhinkingandourunder standingofhisthinkinghaveevolvedagreatdealduringtheensuing 2 1years.Taguchi′sapproachestooff linequalityimprovementhavegeneratedmuchinterestanddebateduringthelast2 1years.Foranaccountofthesetechniques ,seeTaguchiandWu( 1980 ) .Thishasinturnledresearcherstocloselyexaminehismeth odsandsuggestvariousimpr…     

The robustness of sufficient reduction methods for detecting shifts of various types in multivariate processes

Applications of shift detection are of interest in several disciplines. Sufficient reduction (SR) methods have been developed for detecting a shift in a multivariate process under different conditions in several studies. However, all methods were proposed to detect only a constant, but persistent, mean shift. In practice, there might be other types of (mean) shift to be considered. Our purpose here is to investigate the robustness of SR methods for detecting different types of shift in a multivariate process. Four shift types are considered. The performances of the SR methods are compared against other statistical techniques used in multivariate process control. The evaluation was conducted via simulation by estimating four measures. The results show that in a process of independent observations the Wessman method performs well for detecting all sizes of single spike shift and small constant, linear, and exponential shifts. In an autocorrelated process the Parallel, Frisén, and Wessman methods produce a high number of false alarms. The Siripanthana and Stillman method gives shorter delays for detecting small shifts of all types, while the vector autoregressive chart gives a shorter delay for a large constant shift. The applications of SR methods to real health surveillance data are illustrated, with examples from food poisoning and pneumonia monitoring in Thailand.     

An Integrated Approach for Enhancing the Quality of the Product by Combining Robust Design and Customer Requirements

Enhancing the quality of the product has always been one considerable concern of production process management, and this subject gave way to implementing so many methods including robust design. In this paper, robust design utilizes response surface methodology (RSM) considering the mean and variance of the response variable regarding system design, parameter design, and tolerance design. In this paper, customer requirements and robust design are regarded simultaneously to achieve enriched quality. Subsequently, with a non‐linear programming, a novel method for integrating RSM and quality function deployment has been proposed to achieve robustness in design. The customer requirements are regarded in every stage of product development process meaning system design, parameter design and tolerance design. To validate the applicability of the proposed approach, it has been implemented in a real case of chemical industry. Research findings show that the proposed method is much better than other existing methods including MSE and dual response methods. According to this method, the resulted mean is better than MSE method, and more importantly, the variance of the process is approximately 14% and 10% lesser than dual response and MSE method. Copyright © 2013 John Wiley & Sons, Ltd.     

ROBUST TOLERANCE ALLOCATION USING STOCHASTIC PROGRAMMING

Abstract

Tolerance allocation in manufacturing is a prominent industrial task for enhancing productivity and reducing manufacturing costs. The classical tolerance allocation problem can be formulated as a stochastic program to determine the assignment of component tolerances such that the manufacturing cost is minimized. However, tolerance design is a prerequisite to the overall quality and cost of a product; robust tolerance design is particularly important and should be considered. In this paper, robustness is considered in formulating the tolerance allocation problem by minimizing the manufacturing cost's sensitivity. Moreover, from a practical perspective, the process capability index for each component and the upper bound of the manufacturing cost are also considered. To effectively and efficiently resolve the robust tolerance allocation problem, a sequential quadratic programming algorithm embedded with a Monte Carlo simulation is developed. To demonstrate this design method's robustness, two commonly used test problems are solved. The designs devised in this paper have lower manufacturing costs and smaller variations in manufacturing costs than those in previous studies, indicating that the proposed method is highly promising in the robust tolerance design.     

A Bayesian model for the joint optimization of quality and maintenance decisions

We develop a model for the economic design of a Bayesian control chart for monitoring a process mean. The process may randomly suffer failures that result in a non‐operating state, and thus call for an immediate corrective maintenance action, as well as assignable causes that shift the process mean to an undesirable level. Quality shifts, apart from poorer quality outcome and higher operational cost, also result in higher failure rate. Consequently, their removal, besides improving the outcome quality and reducing the quality‐related cost, is also a preventive maintenance action since it reduces the probability of a failure. The proposed Bayesian model allows the determination of the design parameters that minimize the total expected quality and maintenance cost per time unit. The effectiveness of the proposed model is evaluated through the comparison of its expected cost against the optimum expected cost of the simpler variable‐parameter Shewhart chart. Copyright © 2010 John Wiley & Sons, Ltd.     

Probability Constrained Optimization as a Tool for Functional Design for Six Sigma

An important up-stream activity in the overall design of a system is the so-called functional design wherein the means and tolerances of the design variables are determined with respect to the competing demands of quality and cost. In this article probability constrained optimization is invoked to produce a functional design that focuses on the goal of design for Six Sigma (i.e., improved customer satisfaction, robustness, and predictable cost levels). Herein, a maximum system probability of nonconformance is obtained from a prescribed defect rate that in turn provides the primary design constraint. The production cost provides the objective function to be minimized in order to allocate the design parameters. All three quality metrics (e.g., target/larger/smaller-is-best) and robustness are inherent in the approach. The design of an electro-mechanical servo system serves as a case study wherein three responses are related to three control variables and two noise variables by mechanistic models. Designs for selected defect rates show the practicality and potential of the approach.     

Stochastic analysis and robust optimization for a deck lid inner panel stamping

FE-simulation and optimization are widely used in the stamping process to improve design quality and shorten development cycle. However, the current simulation and optimization may lead to non-robust results due to not considering the variation of material and process parameters. In this study, a novel stochastic analysis and robust optimization approach is proposed to improve the stamping robustness, where the uncertainties are involved to reflect manufacturing reality. A meta-model based stochastic analysis method is developed, where FE-simulation, uniform design and response surface methodology (RSM) are used to construct meta-model, based on which Monte-Carlo simulation is performed to predict the influence of input parameters variation on the final product quality. By applying the stochastic analysis, uniform design and RSM, the mean and the standard deviation (SD) of product quality are calculated as functions of the controllable process parameters. The robust optimization model composed of mean and SD is constructed and solved, the result of which is compared with the deterministic one to show its advantages. It is demonstrated that the product quality variations are reduced significantly, and quality targets (reject rate) are achieved under the robust optimal solution. The developed approach offers rapid and reliable results for engineers to deal with potential stamping problems during the early phase of product and tooling design, saving more time and resources.     

田口方法在冲压仿真建模参数优化中的应用研究

利用现有的有限元软件ABAQUS,建立了V形件冲压加工的有限元仿真模型。结合田口方法,通过实验数据和仿真结果对比,分析了各建模参数对仿真模型鲁棒性的影响,最终找出有利于提高鲁棒性的建模参数组合,建立了可运用于实际分析的鲁棒性有限元模型。给出了V形冲压件基于田口方法的有限元建模参数优化的计算实例。结果表明,所提方法是有效且实用的,为提高有限元建模的鲁棒性提供了依据。     

Allocation of manufacturers through internet-based collaboration for distributed process planning

The pursuit of lower cost, shorter time-to-market, and better quality has led to a shift toward global production in today's competitive business environment. This shift however, forces manufacturing enterprises to have separate design houses and manufacturing facilities. In general, design houses are located in the same regions as customers to enable them to respond to the rapidly changing demands of customers. By contrast, manufacturing facilities can be placed in regions in which production costs are lower. However, this physical and logical separation between designers and manufacturers (or between upstream manufacturers and downstream manufacturers) raises various integration issues. The present paper addresses two of these issues: the framework for representing the data necessary to communicate requirements and objectives of the designer, and the methodology for utilizing such data to optimize the business objectives related to production cost and quality. The proposed representation, collaboration framework, and methodology will enable design houses and manufacturing facilities to realize the benefits of global production and to accommodate the management of loosely integrated supply chains.     

A Game Theory Application in Robust Design

Parameter designs consider the objective of designing products/processes that are insensitive to different noise factors affecting the performance of them. Such designs are called robust designs. Robustness has brought a revolution in the research and development of industries to design new products and develop new processes. Practitioners have shown considerable interest in what are known as Taguchi Methods. There has been controversy concerning these methods from a statistical standpoint. Some have pointed out that certain techniques among them are inefficient and unnecessarily complicated. This is particularly true of signal to noise ratios (S/N ratios) and statistical analysis based on them. S/N ratios play a crucial role in measuring robustness of product and process design in quality engineering. In this paper, we give an interactive two-person zero-sum game formulation of the S/N ratio analysis to select a robust design. This approach has the advantage of presenting to the designer both the mean and the standard deviation corresponding to a design setting instead of a single number such as S/N ratio. We present here some new results and illustrate our method with examples.     

Misleading signals in joint schemes for the mean vector and covariance matrix

In multivariate statistical process control, it is recommendable to run two individual charts: one for the process mean vector and another one for the covariance matrix. The resulting joint scheme provides a way to satisfy Shewhart's dictum that proper process control implies monitoring both process location and spread. The multivariate quality characteristic is deemed to be out of control whenever a signal is triggered by either individual chart of the joint scheme. Consequently, a shift in the mean vector can be misinterpreted as a shift in the covariance matrix and vice versa. Compelling results are provided to give the quality control practitioner an idea of how joint schemes for the mean vector and covariance matrix are prone to trigger misleading signals that will likely lead to a incorrect diagnostic of which parameter has changed.     

Modelling robustness for manufacturing processes: a critical review

‘Robustness’ is an important concept used in quality engineering for the improvement of quality in a manufacturing process. A process which is insensitive to noise variation is called a robust process. The robustness is modelled by several researchers and practioners for its design and implementation in a manufacturing process. A review of all these approaches is essential in order to assess their strengths, limitations and applicability under different process conditions and constraints. Over the years, many of these approaches have found widespread application in measuring, assessing and modelling of process robustness in manufacturing and other industries. In this paper, an attempt has been made to review critically the existing approaches as proposed and applied for measuring and evaluating robustness of manufacturing processes. Based on the critical appraisal, the key issues are identified and a generic framework for modelling and measuring of process robustness in single- and multi-stage manufacturing processes is presented.     

A new inspection sampling plan under capacity constraints and multiple shifts

Various SPC models have been widely deployed in the quality control of different production systems. This paper considers a new design of SPC model with associated decision rules to control a process that produces items in finite lots and has a variance shift as well as a mean shift. Under both an inspection capacity constraint and a false alarm rate constraint, an inspection sampling plan that maximizes the yield of production is developed. Numerical examples are presented to illustrate and evaluate the approach. A semi-economic approach that computes the optimal quantity of inspection capacity is also presented.     

A Kullback-Leibler information control chart for linear profiles monitoring

Profile monitoring is referred to as monitoring the functional relationship between the response and explanatory variables. Traditionally, process control charts monitor the mean and/or the variance of a univariate quality characteristic. For several correlated quality characteristics, multivariate process control charts monitor the mean vector and/or the covariance matrix. However, monitoring the functional relationship between variables is sometimes more beneficial. One example is the power output of a Diesel engine and the amount of fuel injected should be related. In this paper, we propose a Kullback-Leibler information (KLI) control chart for linear profiles monitoring in Phase II. The plotted statistics of the KLI chart are calculated based on a backward procedure. The functional relationship is described by linear regression. The performance of the proposed KLI control chart is compared with those of other existing control charts, especially the Generalized Likelihood Ratio (GLR) chart for both KLI and GLR charts do not require design parameters. The results show that (1) the KLI control chart is better than the GLR control chart in detecting the shift of variance in terms of Average Time to Signal, and (2) if the shift of the regression coefficient is small, the GLR chart outperforms the KLI chart, but if the size of shift is large, the KLI chart outperforms the GLR chart. The plotted statistics of KLI are compared to that of GLR. Their similarity is discussed.     

针对发动机平面度的二维Fused LASSO多元统计控制图

针对具有二维平面自然顺序关系的多元数据,提出了一种基于二维Fused LASSO回归模型的多元统计过程控制图。由于二维Fused LASSO多元回归模型对相邻系数的差异进行惩罚,因此它对检测出变量间的自然顺序关系非常有效。通过数值仿真实验可以看到,二维Fused LASSO控制图能更加快速有效地检测出具有二维平面自然顺序的多元过程中均值发生的变化,且在偏移量越大的情况下优势更加明显。最后通过对发动机平面度数据的实例验证,给出了二维Fused LASSO控制图的步骤和适用性。     

Robust design of tuned mass dampers installed on multi-degree-of-freedom structures subjected to seismic action

This study deals with robust optimum design of tuned mass dampers installed on multi-degree-of-freedom systems subjected to stochastic seismic actions, assuming the structural and seismic model parameters to be uncertain. A new global performance index for evaluating the efficiency of protection systems is proposed, as an alternative to commonly used local performance indices such as the maximum interstorey drift. The latter can be considered a good estimator of seismic damage, but it does not measure the whole structural integrity. The direct perturbation method based on first order approximation is adopted to evaluate the effects of uncertainties on the response. The robust design is formulated as a multi-objective optimization problem, in which both the mean and the standard deviation of the performance index are simultaneously minimized. A comparison of the effectiveness and robustness of tuned mass dampers designed using local or global performance indices is carried out, considering different levels of uncertainty.     

On‐line Identification and Quantification of Mean Shifts in Bivariate Processes using a Neural Network‐based Approach

Many statistical process control (SPC) problems are multivariate in nature because the quality of a given process or product is determined by several interrelated variables. Various multivariate control charts (e.g. Hotelling's , multivariate cumulative sum and multivariate exponentially weighted moving average charts) have been designed for detecting mean shifts. However, the main shortcoming of such charts is that they can detect an unusual event but do not directly provide the information required by a practitioner to determine which variable or group of variables has caused the out‐of‐control signal. In addition, these charts cannot provide more detailed shift information, for example the shift magnitude, which would be very useful for quality practitioners to search the assignable causes that give rise to the out‐of‐control situation. This work proposes a neural network‐based model that can identify and quantify the mean shifts in bivariate processes on‐line. The performance evaluation performed by the simulation demonstrates that the proposed model outperforms the conventional multivariate control schemes in terms of average run length, and can accurately estimate the magnitude of the shift of each of the shifted variables in a real‐time mode. Extensive simulation is also carried out to examine the effects of correlation on the performance of the proposed model. A numerical example is presented to illustrate the usage of the proposed model. Although a mean shift identification and quantification tool for bivariate SPC is the particular application presented here, the proposed neural network‐based methodology can be applied to multivariate SPC in general. Copyright © 2006 John Wiley & Sons, Ltd.     

Probabilistic collocation for simulation-based robust concept exploration

In the early stages of an engineering design process it is necessary to explore the design space to find a feasible range that satisfies design requirements. When robustness of the system is among the requirements, the robust concept exploration method can be used. In this method, a global metamodel, such as a global response surface of the design space, is used to evaluate robustness. However, for large design spaces, this is computationally expensive and may be relatively inaccurate for some local regions. In this article, a method is developed for successively generating local response models at points of interest as the design space is explored. This approach is based on the probabilistic collocation method. Although the focus of this article is on the method, it is demonstrated using an artificial performance function and a linear cellular alloy heat exchanger. For these problems, this approach substantially reduces computation time while maintaining accuracy.     

Robust design of assembly and machining tolerance allocations

Tolerancing is one of the most important tasks in product and manufacturing process design. The allocation of design tolerances between the components of a mechanical assembly and manufacturing tolerances in the intermediate machining steps of component fabrication can significantly affect a product's quality and its robustness. This paper presents a methodology to maximize a product's robustness by appropriately allocating assembly and machining tolerances. The robust tolerance design problem is formulated as a mixed nonlinear optimization model. A simulated annealing algorithm is employed to solve the model and an example is presented to illustrate the methodology.