Multiresponse optimization of a multistage manufacturing process using a patient rule induction method

Most manufacturing industries produce products through a series of sequential stages, known as a multistage process. In a multistage process, each stage affects the stage that follows, and the process often has multiple response variables. In this paper, we suggest a new procedure for optimizing a multistage process with multiple response variables. Our method searches for an optimal setting of input variables directly from operational data according to a patient rule induction method (PRIM) to maximize a desirability function, to which multiple response variables are converted. The proposed method is explained by a step-by-step procedure using a steel manufacturing process as an example. The results of the steel manufacturing process optimization show that the proposed method finds the optimal settings of input variables and outperforms the other PRIM-based methods.     

Distributionally robust optimization for engineering design under uncertainty

This paper addresses the challenge of design optimization under uncertainty when the designer only has limited data to characterize uncertain variables. We demonstrate that the error incurred when estimating a probability distribution from limited data affects the out-of-sample performance (ie, performance under the true distribution) of optimized designs. We demonstrate how this can be mitigated by reformulating the engineering design problem as a distributionally robust optimization (DRO) problem. We present computationally efficient algorithms for solving the resulting DRO problem. The performance of the DRO approach is explored in a practical setting by applying it to an acoustic horn design problem. The DRO approach is compared against traditional approaches to optimization under uncertainty, namely, sample-average approximation and multiobjective optimization incorporating a risk reduction objective. In contrast with the multiobjective approach, the proposed DRO approach does not use an explicit risk reduction objective but rather specifies a so-called ambiguity set of possible distributions and optimizes against the worst-case distribution in this set. Our results show that the DRO designs, in some cases, significantly outperform those designs found using the sample-average or the multiobjective approach.     

Efficient optimization of process parameters in shadow mask manufacturing using NNPLS and genetic algorithm

A shadow mask, the primary component of a cathode ray tube (CRT), is used to prevent the outer edges of electron beams from hitting incorrect phosphor dots. It is fabricated by means of a photo-etching process consisting of a few hundred/thousand process parameters. A primary concern in the management of the process is to determine the optimal process parameter settings necessary to sustain the desired levels of product quality. The characteristics of the process, including a large number of process parameters and collinear observed data, make it difficult to accomplish the primary concern. To cope with the difficulties, a two-phase approach is employed that entails the identification of a few critical process parameters, followed by determination of the optimal parameter settings. The former is obtained through the operator's domain knowledge and the NNPLS-based prediction model built between process parameters and quality defects. The latter is obtained by solving an optimization problem using a genetic algorithm (GA). A comparative study shows that the proposed approach improves product quality greatly in the shadow-mask manufacturing process.     

A method for estimating intensity and impulse response functions offiltered Poisson processes

This paper presents a method for estimating the intensity and impulse response (IR) function of filtered Poisson processes. The case is considered where the filtered Poisson process is modeled as an output of the linear constant-coefficient ordinary differential equations having poles and zeros driven by Poisson impulse processes. It is shown that an explicit formula for estimating the intensity is derived by combining second-and third-order cumulants of the residual time series generated from the discretized filtered Poisson process. It is also shown that the IR function can be estimated from the parameters of the discretized filtered Poisson process. Then, Monte Carlo simulations demonstrate the validity of the proposed method in some specific examples. It is concluded that the proposed method can be extensively applied to actual phenomena appearing in engineering and science     

Optimization of correlated multi-response quality engineering by the upside-down normal loss function

Most of the published literature on robust design is basically concerned with a single response. However, the reality is that common industrial problems usually involve several quality characteristics, which are often correlated. Traditional approaches to multidimensional quality do not offer much information on how much better or worse a process is when finding optimal settings. Köksoy and Fan [Engineering Optimization 44 (8): 935–945] pointed out that the upside-down normal loss function provides a more reasonable risk assessment to the losses of being off-target in product engineering research. However, they only consider the single-response case. This article generalizes their idea to more than one response under possible correlations and co-movement effects of responses on the process loss. The response surface methodology has been adapted, estimating the expected multivariate upside-down normal loss function of a multidimensional system to find the optimal control factor settings of a given problem. The procedure and its merits are illustrated through an example.     

A Bayesian approach to sequential monitoring of nonlinear profiles using wavelets

We consider change‐point detection and estimation in sequences of functional observations. This setting often arises when the quality of a process is characterized by such observations, called profiles, and monitoring profiles for changes in structure can be used to ensure the stability of the process over time. While interest in phase II profile monitoring has grown, few methods approach the problem from a Bayesian perspective. We propose a wavelet‐based Bayesian methodology that bases inference on the posterior distribution of the change point without placing restrictive assumptions on the form of profiles. By obtaining an analytic form of this posterior distribution, we allow the proposed method to run online without using Markov chain Monte Carlo (MCMC) approximation. Wavelets, an effective tool for estimating nonlinear signals from noise‐contaminated observations, enable us to flexibly distinguish between sustained changes in profiles and the inherent variability of the process. We analyze observed profiles in the wavelet domain and consider two possible prior distributions for coefficients corresponding to the unknown change in the sequence. These priors, previously applied in the nonparametric regression setting, yield tuning‐free choices of hyperparameters. We present additional considerations for controlling computational complexity over time and their effects on performance. The proposed method significantly outperforms a relevant frequentist competitor on simulated data.     

基于敏度分析的框架抗震优化

针对目前结构抗震优化设计方法存在优化效率低下的问题,提出一种高效的框架抗震优化设计方法。在有限元法和Newmark法基础上导出一种高效的层间相对位移对设计变量一阶和二阶导数的算法,建立显含时间参数,以结构质量最小化为目标,同时满足层间相对位移和设计变量约束的优化数学模型,通过积分型内点罚函数将显含时间参数的不等式约束优化问题转变为一系列不含时间参数的无约束优化问题,利用层间相对位移对设计变量一阶和二阶导数的信息计算罚函数的梯度和海森矩阵,然后利用梯度和海森矩阵构造求解优化设计问题高效有效的优化算法。算例表明本文的抗震优化方法能获得结构的最优设计,具有简单、下降速度快、不需要进行一维搜索等特点。是一种有效和高效的框架抗震二阶优化方法。     

An interval approach to robust design with parameter uncertainty

In robust design, it is common to estimate empirical models that relate an output response variable to controllable input variables and uncontrollable noise variables from experimental data. However, when determining the optimal input settings that minimise output variability, parameter uncertainties in noise factors and response models are typically neglected. This article presents an interval robust design approach that takes parameter uncertainties into account through the confidence regions for these unknown parameters. To avoid obtaining an overly conservative design, the worst and best cases of mean squared error are both adopted to build an optimisation approach. The midpoint and radius of the interval are used to measure the location and dispersion performances, respectively. Meanwhile, a data-driven method is applied to obtain the relative weights of the location and dispersion performances in the optimisation approach. A simulation example and a case study using automobile manufacturing data from the dimensional tolerance design process are used to demonstrate the effectiveness of the proposed approach. The proposed approach of considering both uncertainties is shown to perform better than other approaches.     

Optimization of Dynamic Multi-Response Problems Using Grey Multiple Attribute Decision Making

While many of the previous Taguchi method applications dealt with a state system problem, dynamic multi-response problems have received only limited attention. This study presents a practical and systematic procedure to resolve dynamic multi-response problems based on Taguchi's parameter design. The quality loss function is initially applied to assess the quality performance for each response. The technique for order preference by similarity to the ideal solution (TOPSIS), associated with the multiple attribute decision-making (MADM) method, is then incorporated into the Grey relational model of the Grey system theory. The integrated Grey relational grade (IGRG) relative closeness to the ideal solution is determined as a multi-response performance index for determining the optimal parameter setting. The proposed procedure can not only efficiently determine the optimal parameter setting, but also reduce the conflicts when determining the optimal parameter setting for the multi-response problems. Experimental results obtained from the biological reduction of an ethyl acetoacetate process demonstrate the effectiveness of the proposed procedure.     

Estimation of Complicated Profiles in Phase I,Clustering and S‐estimation Approaches

Some quality characteristics are well defined when expressed as a function of an independent variable. This function is usually called a profile. If the functional form of the profile is known, parametric methods could be used to monitor the profile representing a process. However, some processes are complicated, and it is not suitable to use parametric models. In these cases, nonparametric methods may be used to monitor the profiles. One of the powerful nonparametric profile monitoring methods is to use wavelets. In this paper, the issue of estimating the complicated profiles in phase I is studied. In order to monitor the process using wavelets, it is required to estimate the vector of wavelet coefficients. Classical estimators are usually used to estimate the coefficients vector. These estimators should be used when the data do not contain outliers. However, it is possible that the data set is contaminated and includes some outliers. Thus, it is better to use robust estimators that are insensitive to the presence of outliers. In this paper, two robust estimators for estimating the complicated profiles using wavelets are proposed. In the first approach, the dimension of the coefficients vector is reduced by means of PCA incorporated into clustering. The second approach is based on the S‐estimation method. An extensive simulation study is performed using matlab ® software to evaluate the proposed methods and to compare the results with an existing classical method. The results show the well performance of the suggested methods in estimating the model parameters when the data set is not contaminated and in the presence of outliers. Copyright © 2016 John Wiley & Sons, Ltd.     

Optimizing settings by accounting for uncontrollable material and environmental variables

Process settings that work well for one batch may not work for another due to variation in the uncontrollable variables that characterize environmental and raw material properties, for example. This paper presents an optimization methodology to identify settings for a particular batch based on information about uncontrollable variables in the batch. Also, the methodology predicts whether the batch is likely to produce a successful output or if it should be scrapped. The batch process we consider, that is common in industries such as pharmaceuticals, petroleum, and food processing, is characterized by many, highly correlated input variables. Input variables include those that can be set, such as temperatures and flow rates, as well as the uncontrollable variables. A nonlinear mathematical program identifies the optimal process settings when the distribution of the uncontrollable variables is known. When the distribution is unknown, the optimal process settings are obtained by combining sequential sampling and a robust optimization procedure that takes into account the variability in the sample estimates. The work here is motivated by our research in multivariate process control for batch extrusion processes. We demonstrate the proposed methodology using an extrusion simulation.     

An upside-down normal loss function-based method for quality improvement

Traditional measures of process quality do not offer much information on how much better or worse a process is when finding optimal settings of a given problem. The upside-down normal loss function (UDNLF) is a weighted loss function that provides a more reasonable risk assessment to the losses of being off-target in product engineering research. The UDNLF can be used in process design and optimization to accurately reflect and quantify the losses associated with the process in a way which minimizes the expected loss of the upside-down normal (UDN). The function has a scale parameter which can be adjusted by the practitioners to account for the actual percentage of materials failing to work at specification limits. In this article, the ‘target is best’ case is addressed to estimate the expected loss of UDN due to variation from target in the robust process design and response surface modelling context. An approach is proposed to find the control factor settings of a system by directly minimizing the expected loss. The procedure and its merits are illustrated through an example.     

Optimizing machining parameters of wire-EDM process to cut Al7075/SiCp composites using an integrated statistical approach

Metal matrix composites (MMCs) as advanced materials, while producing the components with high dimensional accuracy and intricate shapes, are more complex and cost effective for machining than conventional alloys. It is due to the presence of discontinuously distributed hard ceramic with the MMCs and involvement of a large number of machining control variables. However, determination of optimal machining conditions helps the process engineer to make the process efficient and effective. In the present investigation a novel hybrid multi-response optimization approach is proposed to derive the economic machining conditions for MMCs. This hybrid approach integrates the concepts of grey relational analysis (GRA), principal component analysis (PCA) and Taguchi method (TM) to derive the optimal machining conditions. The machining experiments are planned to machine Al7075/SiCp MMCs using wire-electrical discharge machining (WEDM) process. SiC particulate size and its weight percentage are explicitly considered here as the process variables along with the WEDM input variables. The derived optimal process responses are confirmed by the experimental validation tests and the results showed satisfactory. The practical possibility of the derived optimal machining conditions is also analyzed and presented using scanning electron microscope examinations. According to the growing industrial need of making high performance, low cost components, this investigation provide a simple and sequential approach to enhance the WEDM performance while machining MMCs.     

Functional Process Capability Indices for Circular Profile

Profile is a relation between one response variable and one or more explanatory variables that represent quality of a product or performance of a process. On the other hand, process capability indices are measures to help practitioners in improving the processes to satisfy the customer's expectations. Few researches are done to account for the process capability index in the areas of profile monitoring. All of these researches are focused on process capability index in simple linear profile. In all of these methods, response variables in different levels of explanatory variable are considered, and the relationship in all range of explanatory variable is neglected. In this paper, a functional method is proposed to measure process capability index of circular profiles in all range of explanatory variable. The proposed method follows the traditional definition of process capability indices. The functional method uses reference profile, functional specification limits and functional natural tolerance limits to present a functional form of process capability indices. This functional form results in measuring the process capability in each level of explanatory variable in circular profile as well as a unique value of process capability index for circular profile. The application of the proposed method is illustrated through a real case in automotive industry. Copyright © 2013 John Wiley & Sons, Ltd.     

实施印刷生产标准化的技术实践

从调整印刷机状态和设置最佳印刷质量标准两个方面阐述了印刷生产标准化的具体实施步骤,并通过实例论述了利用SPC(statistical process control)质量统计工具分析得到的印刷质量标准数据。企业可利用得到的标准数据进行印刷状态实时修正,完成印刷生产过程控制,从而实现企业的印刷生产标准化。     

Life-cycle reliability-based robust design optimization for GP model with response uncertainty

Reliability-based robust design optimization (RBRDO) is a crucial tool for life-cycle quality improvement. Gaussian process (GP) model is an effective alternative modeling technique that is widely used in robust parameter design. However, there are few studies to deal with reliability-based design problems by using GP model. This article proposes a novel life-cycle RBRDO approach concerning response uncertainty under the framework of GP modeling technique. First, the hyperparameters of GP model are estimated by using the Gibbs sampling procedure. Second, the expected partial derivative expression is derived based on GP modeling technique. Moreover, a novel failure risk cost function is constructed to assess the life-cycle reliability. Then, the quality loss function and confidence interval are constructed by simulated outputs to evaluate the robustness of optimal settings and response uncertainty, respectively. Finally, an optimization model integrating failure risk cost function, quality loss function, and confidence interval analysis approach is constructed to find reasonable optimal input settings. Two case studies are given to illustrate the performance of the proposed approach. The results show that the proposed approach can make better trade-offs between the quality characteristics and reliability requirements by considering response uncertainty.     

A Bayesian method for robust tolerance control and parameter design

This paper proposes a Bayesian method to set tolerance or specification limits on one or more responses and obtain optimal values for a set of controllable factors. The existence of such controllable factors (or parameters) that can be manipulated by the process engineer and that affect the responses is assumed. The dependence between the controllable factors and the responses is assumed to be captured by a regression model fit from experimental data, where the data are assumed to be available. The proposed method finds the optimal setting of the control factors (parameter design) and the corresponding specification limits for the responses (tolerance control) in order to achieve a desired posterior probability of conformance of the responses to their specifications. Contrary to standard approaches in this area, the proposed Bayesian approach uses the complete posterior predictive distribution of the responses, thus the tolerances and settings obtained consider implicitly both the mean and variance of the responses and the uncertainty in the regression model parameters.     

Integrated predictive maintenance strategy for manufacturing systems by combining quality control and mission reliability analysis

Predictive maintenance (PdM) is an effective means to eliminate potential failures, ensure stable equipment operation and improve the mission reliability of manufacturing systems and the quality of products, which is the premise of intelligent manufacturing. Therefore, an integrated PdM strategy considering product quality level and mission reliability state is proposed regarding the intelligent manufacturing philosophy of ‘prediction and manufacturing’. First, the key process variables are identified and integrated into the evaluation of the equipment degradation state. Second, the quality deviation index is defined to describe the quality of the product quantitatively according to the co-effect of manufacturing system component reliability and product quality in the quality–reliability chain. Third, to achieve changeable production task demands, mission reliability is defined to characterise the equipment production states comprehensively. The optimal integrated PdM strategy, which combines quality control and mission reliability analysis, is obtained by minimising the total cost. Finally, a case study on decision-making with the integrated PdM strategy for a cylinder head manufacturing system is presented to validate the effectiveness of the proposed method. The final results shows that proposed method achieves approximately 26.02 and 20.54% cost improvement over periodic preventive maintenance and conventional condition-based maintenance respectively.     

Multi-objective optimization based on meta-modeling by using support vector regression

Practical engineering design problems have a black-box objective function whose forms are not explicitly known in terms of design variables. In those problems, it is very important to make the number of function evaluations as few as possible in finding an optimal solution. So, in this paper, we propose a multi-objective optimization method based on meta-modeling predicting a form of each objective function by using support vector regression. In addition, we discuss a way how to select additional experimental data for sequentially revising a form of objective function. Finally, we illustrate the effectiveness of the proposed method through some numerical examples.     

Assessing the error in bootstrap estimates with dependent data

Bootstrap estimates, like most random variables, are subject to sampling variation. Efron and Tibshirani (1993) studied the variability in bootstrap estimates with independent data. Efron (1992) proposed the jackknife-after-bootstrap, a method for estimating the variability from the bootstrap samples themselves. We address the issue of studying the variability in bootstrap estimates for dependent data. We modify Efron's method to render it suitable to operate through the block bootstrap. A simulation study is carried out to investigate the consistency of the modified method. The performance of this method is judged by using the same setting as that used by Efron and Tibshirani (1993). Our results confirm that this method is reliable and has an advantage in the context of dependent data.