Smaller-the-better Research Articles

Two-Tailed Fuzzy Hypothesis Testing for Unilateral Specification Process Quality Index

The quality characteristics with unilateral specifications include the smaller-the-better (STB) and larger-the-better (LTB) quality characteristics. Roundness, verticality, and concentricity are categorized into the STB quality characteristics, while the wire pull and the ball shear of gold wire bonding are categorized into the LTB quality characteristics. In terms of the tolerance, zero and infinity (∞) can be viewed as the target values in line with the STB and LTB quality characteristics, respectively. However, cost and timeliness considerations, or the restrictions of practical technical capabilities in the industry, mean that the process mean is generally far more than 1.5 standard deviations away from the target value. Researchers have accordingly proposed a process quality index conforming to the STB quality characteristics. In this study, we come up with a process quality index conforming to the LTB quality characteristics. We refer to these two types of indices as the unilateral specification process quality indices. These indices and the process yield have a one-to-one mathematical relationship. Besides, the process quality levels can be completely reflected as well. These indices possess unknown parameters. Therefore, sample data are required for calculation. Nevertheless, interval estimates can lower the misjudgment risk resulting from sampling errors more than point estimates can. In addition, considering cost and timeliness in the industry, samples are generally small, which lowers estimation accuracy. In an attempt to increase the accuracy of estimation as well as overcome the uncertainty of measured data, we first derive the confidence interval for unilateral specification process quality indices, and then propose a fuzzy membership function on the basis of the confidence interval to establish the two-tailed fuzzy testing rules for a single indicator. Lastly, we determine whether the process quality has improved.

Fuzzy Supplier Selection Method Based on Smaller-The-Better Quality Characteristic

Many important parts of tool machines all have the important smaller-the-better (STB) quality characteristics. The important STB quality characteristics will impact on the quality of the end-product. At the same time, supplier quality influences the quality and functionality of the end-product, so suppliers must be selected with caution. The six sigma quality index for the STB quality characteristics can directly reflect process quality levels. Besides, this index possesses a mathematical relationship with process yield. Nevertheless, the point estimation will cause the risk of misjudgment, due to sampling errors. As a result, this study applies the confidence interval of the index to a two-tailed fuzzy testing method, in order to select appropriate suppliers. Now that this method is on the basis of the confidence interval, the possibility of misjudgment caused by sampling errors will be reduced, while the precision of the selection will be enhanced. The method can help companies increase product quality, as well as the competitiveness of the industry chain as a whole. Finally, a numerical example is presented to show how to approach this method and its efficacy.

Minimum leakage current optimization on 22 nm SOI NMOS device with HfO2/WSix/Graphene gate structure using Taguchi method.

To acquire the optimal value of the performance parameter, a bilayer graphene with silicon on insulator (SOI) was enhanced and analyzed on 22 nm NMOS device. The device is made of Hafnium Dioxide (HfO2) as a high-k material whereas Tungsten Silicide (WSix) as a metal gate. The Silvaco software ATHENA and ATLAS modules were applied to simulate the fabrication process of virtual devices and to verify the device’s electrical properties accordingly. The Taguchi L9 orthogonal array method was then used to enhance the device process parameters minimum leakage current (ILEAK) according to the International Technology Roadmap Semiconductor (ITRS) specification of 100nA/μm maximum range. The result from smaller-the-better (STB) for ILEAK is then reviewed by the percentage affecting the process parameter. The simulation result shows that the halo tilting angle is the most dominant factor for ILEAK optimization process. The optimized results indicate excellent device performance with ILEAK = 9.29746 nA/µm which is far lower than the prediction.

Robust Co-Design for Energy Saving of Plug-in Hybrid Electric Bus With Existing Components

The energy saving of Plug-in hybrid electric bus (PHEB) can be maximized by co-design method (integrated design of topology, component sizing and energy management). In many cases, the components have been manufactured, so it is a shortcut to realize the co-design with existing components. Motivated by this, a Taguchi robust design (TRD) method is proposed for the robust co-design of the PHEB. The main innovation is that the noises of driving cycles and stochastic vehicle mass are considered in the TRD, and the TRD is formulated as a smaller-the-better (STB) problem. Moreover, the signal-to-noise ratio (SNR) is taken as the analysis index, where the fuel economy together with its robustness can be simultaneously enhanced. In specific, the dynamic programming (DP) is firstly taking as the fuel consumption calculation module of the TRD. Then, a series of historical driving cycles and the stochastic vehicle mass are designed as noise factors; the components are designed as control factors. Finally, a receding horizon control (RHC) strategy is deployed to realize adaptive energy management control using the robust component match and the same DP. The TRD results demonstrate that the proposed co-design method is applicable and reasonable; the simulation results show that the RHC strategy can realize adaptive control, and averagely improve the fuel economy by 10.85% compared to a rule-based control strategy.

Two-phase selection framework that considers production costs of suppliers and quality requirements of buyers

Buyers are faced with selecting the optimal supplier, while suppliers are left to consider production costs. In this study, we developed a two-phase selection framework that allows buyers to evaluate the performance of suppliers while taking production costs into account for value maximisation. This scheme is a win-win solution capable of promoting long-term relationships between buyers and suppliers. Under the assumption of normality, the first phase involves constructing a new Six Sigma quality capability analysis chart (SSQCAC) which takes production costs into account. The objective is to evaluate all potential suppliers using the 100 × (1–α)% upper confidence limit (UCL) of an integrated Six Sigma quality index (SSQI) QPIh when dealing with products with smaller-the-better (STB), larger-the-better (LTB), or nominal-the-best (NTB) quality characteristics. According to interval estimation theory, this method can have a significant impact on the consumption of resources; i.e. the production costs of the supplier can be decreased by reducing the production quality to below that required by the buyer. The proposed method also filters out unsuitable suppliers in order to simplify the decision problem and reduce computational demands and operational risks/costs without compromising the quality of the final product. In the second phase, a detailed analysis is conducted using Euclidean distance measure to select the optimal supplier from among the remaining candidates. We conducted a real-world case study to evaluate the efficacy of the proposed method. We also conducted comparisons with existing methods to demonstrate the advantages of the proposed method and its managerial implications. Suggestions for future study are also provided.

Quality evaluation of internal cylindrical grinding process with multiple quality characteristics for gear products

Gears are among the most crucial components in the transmission systems of machine tools. Gear manufacturing includes a number of processing procedures. The grinding process is an important procedure involving high precision and fairly small grinding surfaces. For this reason, this study aimed at developing a quality assessment model for the internal cylindrical grinding process of gears. The Six Sigma quality indices (SSQIs) were used to directly assess the quality of the internal cylindrical grinding process due to their ability to directly reflect quality level and process yield. Since the process may include nominal-the-best (NTB), larger-the-better (LTB) and smaller-the-better (STB) quality characteristics, so we used the variable transformation method to normalise the specifications of each quality characteristic for the convenient and effective management and analysis of process performance for multiple quality characteristics. We then constructed a multi-characteristic process quality analysis chart (MPQAC) to simultaneously assess the quality levels of various quality characteristics. Furthermore, the MPQAC can provide references for process improvement. This ensures the quality of internal cylindrical grinding and enhances the quality of gear and machine tool products. Finally, a real-world application and numerical experiments demonstrate the effectiveness and practical applicability of the proposed method.

APPLICATION OF TAGUCHI’S PARAMETER DESIGN FOR WEBSITE COMPATIBILITY TESTING

Testing the product just before its release to the customer is very important as it marks the success of that product. In software development, testing of the software is conducted at the last stage of the development cycle. During software testing, there will a large number of variables and their possible values. For this if conventional testing process becomes cumbersome and hence a more efficient testing strategy has to be applied. This paper discusses the application of Orthogonal Array based Software Testing (OATS) for minimizing the number of bugs in the software. In this paper, Taguchi’s Orthogonal Array (OA) is applied for compatibility testing of a website, by considering five control factors and one interaction between the factors. Experiments have been conducted using L18 orthogonal array; experimental results are analyzed using Smaller-The-Better (STB) type of Signal-toNoise (S/N) ratio and optimal levels for the control factors are obtained. With these optimal levels it is found that the number of bugs has been considerably reduced.

Optimisation of Process Parameters for Lower Leakage Current in 22 nm n-type MOSFET Device using Taguchi Method

In this article, Taguchi orthogonal array method was used to optimize the process parameters during the design of a 22 nm n-type Metal Oxide Semiconductor Field Effect Transistor (MOSFET) in order to decrease the leakage current (ILEAK) of the device. Titanium dioxide (TiO2) was used as the dielectric layer to replace the traditional silicon dioxide SiO2 and tungsten silicide (WSix) was used as a metal gate to replace polysilicon. The device’s fabrication and electrical characterization were executed using ATHENA and ATLAS modules from Silvaco International. Taguchi’s Power of Three Series L9 orthogonal array was used to optimize the device process parameters and to finally predict the best process parameter combination to obtain the minimum leakage current (ILEAK) using Smaller-the-Better (STB) signal-to-noise ratio (SNR). The optimization resulted in the attainment of the lowest ILEAK mean value of 0.25759 nA/µm which is in accordance to the predicted value given in the International Technology Roadmap for Semiconductors (ITRS) 2011.

Optimisation of Process Parameters for Lower Leakage Current in 22 nm n-type MOSFET Device using Taguchi Method

In this article, Taguchi orthogonal array method was used to optimize the process parameters during the design of a 22 nm n-type Metal Oxide Semiconductor Field Effect Transistor (MOSFET) in order to decrease the leakage current (I LEAK ) of the device. Titanium dioxide (TiO 2 ) was used as the dielectric layer to replace the traditional silicon dioxide SiO 2 and tungsten silicide (WSi x ) was used as a metal gate to replace polysilicon. The device’s fabrication and electrical characterization were executed using ATHENA and ATLAS modules from Silvaco International. Taguchi’s Power of Three Series L9 orthogonal array was used to optimize the device process parameters and to finally predict the best process parameter combination to obtain the minimum leakage current (I LEAK ) using Smaller-the-Better (STB) signal-to-noise ratio (SNR). The optimization resulted in the attainment of the lowest I LEAK mean value of 0.25759 nA/µm which is in accordance to the predicted value given in the International Technology Roadmap for Semiconductors (ITRS) 2011.

A neuro-data envelopment analysis approach for optimization of uncorrelated multiple response problems with smaller the better type controllable factors

In this paper, a new method is proposed to optimize a multi-response optimization problem based on the Taguchi method for the processes where controllable factors are the smaller-the-better (STB)-type variables and the analyzer desires to find an optimal solution with smaller amount of controllable factors. In such processes, the overall output quality of the product should be maximized while the usage of the process inputs, the controllable factors, should be minimized. Since all possible combinations of factors’ levels, are not considered in the Taguchi method, the response values of the possible unpracticed treatments are estimated using the artificial neural network (ANN). The neural network is tuned by the central composite design (CCD) and the genetic algorithm (GA). Then data envelopment analysis (DEA) is applied for determining the efficiency of each treatment. Although the important issue for implementation of DEA is its philosophy, which is maximization of outputs versus minimization of inputs, this important issue has been neglected in previous similar studies in multi-response problems. Finally, the most efficient treatment is determined using the maximin weight model approach. The performance of the proposed method is verified in a plastic molding process. Moreover a sensitivity analysis has been done by an efficiency estimator neural network. The results show efficiency of the proposed approach.

Modeling Present Worth of Product Quality Loss of STB Characteristic Based on Service Life Distribution

The product smaller-the-better (STB) quality characteristics are continually changing and out of specification limits because of the constant stress, wear and others after the product is put into use, which will cause loss because of the product rejected and scrapped. On the basis of the quality viewpoint that product quality loss is present worth of a loss caused as a result of its quality characteristics because its quality characteristic is out of specification and lead to product scrap after the product is put into service, the paper establishes the present worth model of quality loss of STB characteristic based on service life distribution, and proposes the calculation method on the probability density function (PDF) of the product service life based on the technical specifications of STB quality characteristic. It takes the concentricity between the inner cylindrical surface and the outer cylindrical surface of the link bushing as an example to analysis the various factors that impact on the present worth of concentricity quality loss in the new model, and contrast with Taguchi quality loss model. The results show that the new model describes an actual loss that a product imparts to society after the product is put into service, and can reflect the quality loss of STB characteristic in the product service process, and is more realistic than Taguchi quality loss model of STB. The new model extends tolerance design of STB characteristic from the manufacturing stage to the service stage.

A comparative study between smaller-the-better and normal-the-best quality characteristics when lapping ceramic blocks

In traditional study, minimum surface roughness is an objective function, so the smaller-the-better (STB) quality characteristic is selected. This paper proposes three models of the normal-the-best (NTB) quality characteristic for surface roughness. A comparative study employing three indices for normal-the-best and one index for smaller-the-better for surface roughness is presented when lapping ceramic blocks. The results show that the dominating lapping parameter for surface roughness is the abrasive size, and the smaller-the-better can be replaced by the normal-the-best quality characteristic. Model 3 is better than Models 1 and 2 at the normal-the-best quality characteristics.

The alpha risk of the Taguchi method for STB type quality characteristic

One of the basic assumptions of experimental design is that the error variances are equal for all treatment combinations. On the contrary, one of the basic assumptions of Taguchi’s parameter design is that the error variances are not equal for the treatment combinations. Thus, the significant parameter levels are found by maximising the signal-to-noise ratio of the quality characteristic. In the analysis of variance (ANOVA) of the signal-to-noise ratio, the combination of column effects to better estimate error variance is referred to as pooling. Taguchi has suggested the strategy of “pooling-up”. When using the pooling-up strategy, there will be the tendency to make the alpha mistake more often. If the assumption of the former is true, then there is an alpha risk that judges some factor being significant when in fact it is not. The purpose of this paper is to investigate the alpha risk of the Taguchi method for the smaller-the-better (STB) type problem by simulation. The results show that the alpha risk is very high for several orthogonal arrays.

Comparing Multi‐response Design Methods with Mixed Responses

AbstractThe multi‐response optimization process is commonly applied to engineering design problems involving more than one quality characteristic of interest. Define quality characteristics as output responses that fall into three general categories: larger‐the‐better (LTB), smaller‐the‐better (STB), and nominal‐the‐best (NTB). In the multi‐response optimization process, the objective is to define a set of input factors that, when combined, provide the optimal overall response. This paper investigates the relationship between response types when they are mixed (i.e. LTB, and/or STB, and/or NTB) and the choice of approach. The paper demonstrates that the mix of response types impacts the choice of final input parameters and response levels. In addition, the choice of an additive versus a multiplicative approach may adversely impact the response relationship. That is, it may produce two optimal combinations of factor settings or drive responses away from their target values and toward their extreme values. Copyright © 2004 John Wiley & Sons, Ltd.

Quadratic quality loss functions and signal-to-noise ratios for a trivariate response

This paper extends Taguchi's quadratic quality loss function (QQLF) and signal-to-noise (S/N) ratios to a trivariate case by considering correlations between all pairs of quality characteristics. Single static quality characteristics (QCHs) are classified as: (1) smaller the better (STB), (2) larger the better (LTB), and (3) nominal the best (NTB). Initially, Taguchi studied single-response models. Later Chang (1993), Maghsoodloo and Chang (2001), and Maghsoodloo and Huang (2001) obtained relationships for the bivariate response cases. Chang (1993) and Maghsoodloo and Chang (2001) developed relationships for cost coefficients of the bivariate QQLF and S/N ratios for the cases of (NTB, NTB), (STB, STB), and (LTB, LTB). Later Maghsoodloo and Huang (2001) developed relationships for the remaining cases, which are (STB, LTB), (STB, NTB), and (LTB, NTB). This paper extends the number of variates from two to three, which are correlated, and obtains relationships between cost coefficients to ensure that the cost matrix is positive definite (pd). Also, S/N ratios are developed for all combinations of trivariate responses.

Quadratic loss functions and signal-to-noise ratios for a bivariate response

Abstract In this paper, the quadratic quality loss functions and signal-to-noise (S/N) ratios for a bivariate response are developed. Quality characteristics by variables are divided into three types: (1) Smaller the better (STB), (2) Larger the better (LTB), and (3) Nominal the best (NTB). The focus is on the bivariate quality characteristic response combinations (NTB, NTB), (STB, STB), and (LTB, LTB) cases. The treatment of mixed bivariate (STB, LTB), (STB, NTB), and (LTB, NTB) response cases will be forthcoming as a sequel to this paper in the next issue of this journal (Vol. 20, No. 2, 2001). The relationships among quality loss constants are also discussed in each case. An example of a robust parameter design experiment using simulated data is provided to illustrate the use of signal-to-noise ratios, which were developed to identify the optimal factor settings. The design matrix used in the example was an L 8 (2 7 ) Taguchi orthogonal array (OA) as a one-half fraction of a 2 4 full factorial experiment.

Quality evaluation of domestic airline industry using modified Taguchi loss function with different weights and target values

The Taguchi loss function and its modification are used to evaluate service quality of a domestic airline industry. Service quality is classified into three categories: the nominal-the-better, the smaller-the-better and the larger-the-better characteristic. Different target values for the smaller the-better and the larger-the-better characteristic are discussed. The application of weight to the modified Taguchi loss function is also considered. Different weights used for the smaller-the-better characteristic are described. When the performance of a domestic airline is evaluated by cost loss, action is taken when the loss is greater than the competitors.

Design of material flow networks in manufacturing facilities : J.W. Herrmann, G. Ioannou, I. Minis, R. Nagi, J.M. Proth, pp. 277–289

This paper extends Taguchi's quadratic quality loss function (QQLF) and signal-to-noise (S/N) ratios to a trivariate case by considering correlations between all pairs of quality characteristics. Single static quality characteristics (QCHs) are classified as: (1) smaller the better (STB), (2) larger the better (LTB), and (3) nominal the best (NTB). Initially, Taguchi studied single-response models. Later Chang (1993), Maghsoodloo and Chang (2001), and Maghsoodloo and Huang (2001) obtained relationships for the bivariate response cases. Chang (1993) and Maghsoodloo and Chang (2001) developed relationships for cost coefficients of the bivariate QQLF and S/N ratios for the cases of (NTB, NTB), (STB, STB), and (LTB, LTB). Later Maghsoodloo and Huang (2001) developed relationships for the remaining cases, which are (STB, LTB), (STB, NTB), and (LTB, NTB).This paper extends the number of variates from two to three, which are correlated, and obtains relationships between cost coefficients to ensure that the cost matrix is positive definite (pd). Also, S/N ratios are developed for all combinations of trivariate responses.