Unification of robust design and goal programming for multiresponse optimization—a case study

Fixing the levels of input process parameters to meet a required specification of output is a common process quality control problem. Especially when the output has many quality characteristics, and each of these quality characteristics has to satisfy a given specification, difficulties may arise. One such problem was encountered in an injection moulding process. This process was optimized using Taguchi's Robust Design methodology. Details of the process, problems encountered and outcome of optimization are presented in this paper. The optimization study using Taguchi's methodology revealed that the optimum conditions obtained for one response are not completely compatible with those of other responses. So trade-offs were made in selection of levels for factors using engineering judgement. This increases the uncertainty in the decision making process. In this paper, an approach is presented to optimize multiresponses simultaneously using goal programming in conjunction with Taguchi's methodology. Details of modelling, analysis and inferences obtained with relevance to the case are presented. This study revealed that the optimum conditions obtained using goal programming in conjuction with Taguchi's methodology have better goal attainment properties compared to Robust design. To understand goal attainment behaviour of output characteristics for various process conditions, a detailed sensitivity analysis was also conducted. The outcome of this analysis is also discussed in this paper. © 1997 John Wiley & Sons, Ltd.     

Multi‐response optimization in industrial experiments using Taguchi's quality loss function and principal component analysis

Many industrial experiments based on Taguchi's parameter design (PD) methodology deal with the optimization of a single performance quality characteristic. Studies have shown that the optimal factor settings for one performance characteristic are not necessarily compatible with those of other performance characteristics. Multi‐response problems have received very little attention among industrial engineers and Taguchi practitioners. Many Taguchi practitioners have employed engineering judgement for determining the final optimal condition when several responses are to be optimized. However, this approach always brings some level of uncertainty to the decision‐making process and is very subjective in nature. In order to rectify this problem, the author proposes an alternative approach using a powerful multivariate statistical method called principal component analysis (PCA). The paper also presents a case study in order to demonstrate the potential of this approach. Copyright © 2000 John Wiley & Sons, Ltd.     

Robust design for multiple dynamic quality characteristics using data envelopment analysis

The Taguchi method is extensively adopted in various industries to continuously improve product design in response to customer requirements. The dynamic system of the Taguchi method is frequently implemented to design products with flexible applications. However, Taguchi's dynamic system can be employed only for individual quality characteristic, and the relationship between the quality characteristic and the signal factor is assumed to be linear. Because of these restrictions, Taguchi's dynamic system is ineffective for multiple quality characteristics or when the quality characteristic has a nonlinear relationship with the signal factor. This study describes a novel procedure for optimizing a dynamic system based on data envelopment analysis. The proposed procedure overcomes the limitations of Taguchi's dynamic system. Two cases are analyzed to demonstrate the effectiveness of the proposed procedure. The results show that the proposed procedure can enhance multiple dynamic quality characteristics. Copyright © 2008 John Wiley & Sons, Ltd.     

Quality of v-process moulds through the taguchi technique

The global consciousness for quality has motivated designers and manufacturing engineers to be engaged constantly in product and process development. The approach, quality by design, developed by Taguchi has produced a unique and powerful quality improvement discipline that differs from traditional practices. In the present paper, Taguchi's technique has been applied to obtain an optimal setting of V-process parameters. The results indicate that the sand grain fineness number and amplitude of vibration are the control factors. These factors affect both the mean and the variation of the bulk density of the V-process mould. The signal factor, that is the factor that affects only the mean value, is time of vibration. The insignificant factor is the degree of vacuum imposed. The optimum value of bulk density (1–588 gm/cm³) at the optimal setting of these parameters has been obtained and confirmed by further experiments.     

Off-line quality control for V-process castings

In the present work Taguchi's approach has been applied to the V-process castings of Al-11 per cent Si alloy to acertain the most influential control factors which will provide better and consistent surface finish to the castings regardless of the noise factors present. The control factors of the V-process that may affect the quality of the castings are the molding sand, vibration frequency, vibrating time, degree of vacuum imposed, and pouring temperature. In order to understand how these factors affect the surface roughness of the V-process castings, response surface methodology has been applied, and to obtain the optimal setting of the control factors Taguchi's method has been used. It is found that the pouring temperature has a significant effect on the surface roughness of Al-11 per cent Si alloy castings made by a V-process. Thus the pouring temperature must be kept at the lower level. All other factors are insignificant. Therefore, any setting of the insignificant factors/variables that give the minimum cost can be used.     

Designing the optimal process target levels for multiple quality characteristics

The selection of the optimal process target has become an important research area in which the focus is to increase productivity and improve product quality. Although the quality engineering literature related to this issue contains a vast collection of work, some questions still remain unanswered. First, most previous studies have viewed this issue from a manufacturer's perspective. When designing the optimal process target in the early stage, the customer's perception of product quality needs to be incorporated. Secondly, many researchers have carried out their studies based on a single quality characteristic. From the customer's viewpoint, however, products are often judged based on more than one characteristic. To address these questions, this paper first studies a multivariate quality loss function to capture customer dissatisfaction with product quality, and then proposes an optimization scheme to determine the most economical process target levels for multiple quality characteristics. The optimization procedures are demonstrated in a numerical example, and the effects of process parameters are examined by conducting a sensitivity analysis.     

Robust Parameter Design: A Review

Parameter design is an engineering methodology intended as a cost‐effective approach for improving the quality of products and processes. The assumption is that there are both controllable factors (control variables) and uncontrollable/difficult to control factors (noise variables) that operate on the quality characteristic of a process. The goal of parameter design is to choose the levels of the control variables that optimize a defined quality characteristic while minimizing the variation imposed on the process via the noise variables. Parameter design was popularized in the mid 1980s by Japanese quality consultant Genichi Taguchi. A panel discussion edited by Nair summarized important responses to Taguchi's ideas and methodology. In the last decade, there have been many applications and new developments in this important area. This review paper focuses largely on the work done since 1992, but a historical perspective of parameter design is also given. Copyright © 2003 John Wiley & Sons, Ltd.     

Confirmation testing of the Taguchi methods by artificial neural-networks simulation

In Taguchi's methods of parameter design, a confirmation test is usually necessary to remove concerns about the choice of control parameters, experimental design, or assumptions about responses. This paper investigated the use of artificial neural-networks simulation to validate the set of control parameters identified as significant through Taguchi's methods, and to verify that the recommended settings for the control parameters are indeed optimal or near-optimal. Using the experimental layout and measured responses from a Taguchi parameter-design experiment, we applied cross-validate training to ascertain that the trained neural-network can reproduce acceptable results on unseen experimental layouts. We then used the trained neural-network to simulate and search for the global optimal settings for the control parameters, and the results compared with the recommended settings from the Taguchi parameter-design experiment.     

The Taguchi's Performance Statistic to Optimize Theophylline Beads Production in a High-Speed Granulator

An original process using a simple procedure is developed to produce theophylline active pellets. In order to improve this process, an optimization approach is applied. But rather than only trying to bring the process to the target optimal values, attempt is made to find operating conditions leading also to stable and non-sensitive pellets characteristics. In this purpose, the classic experimental design approach and response surface methodology are completed by using Taguchi's philosophy.     

Economic considerations on parameter design

A simultaneous consideration of process mean and variance in product design stages has been considered one of the most significant of Taguchi's contributions. Among his quality improvement methods, parameter design has drawn a great deal of particular attention from researchers. The ultimate objective of Taguchi's parameter design is to find control factor settings to achieve an on‐target process mean with a minimum variance. There is no doubt regarding the virtue of the minimum variance. However, considering a variety of economic aspects related to product specifications as well as a quality loss, the on‐target process mean may not necessarily be economical. This paper investigates the parameter design problem from an economic point of view and proposes an alternative procedure to achieve the most economical process mean as well as the minimum variance by taking product specifications and an asymmetric quality loss into consideration. It is shown through an illustrative example that a significant cost saving can be accrued from the proposed procedure. Copyright © 2000 John Wiley & Sons, Ltd.     

Optimal levels of process parameters for products with multiple characteristics

The purpose of off-line quality control is to design robust products using robust manufacturing processes before the actual manufacturing of the product. Most of the research work has focused on determining the optimal level settings of process parameters for products with a single quality characteristic. In this paper, we employ the loss function approach to determine the optimal level settings of the process parameters of the production processes for products with multiple characteristics.     

Parametric optimization of surface roughness castings produced by Evaporative Pattern Casting process

In the present paper Taguchi's approach has been applied to the Evaporative Pattern Casting (EPC) process of Al–7%Si alloy to determine the most influential control factors which will provide better and consistent surface roughness to the castings regardless of the noise factors present. In order to evaluate the effect of process parameters such as grain fineness number, time of vibration, degree of vacuum and pouring temperature on surface roughness of EPC process castings, the Taguchi parameter design and optimization approach is used. Through the Taguchi's parameter design approach, optimal levels of process parameters have been determined. The results indicated that the grain fineness number, time of vibration, degree of vacuum were the significant parameters in deciding the surface roughness of Al–7%Si alloy castings. Pouring temperature was the insignificant parameter. The predicted optimal value of surface roughness of Al–7%Si alloy castings produced by EPC process was 2.31 μm. The results were confirmed by further experiments.     

Sequential optimization of parameter and tolerance design for multiple dynamic quality characteristics

System design, parameter design and tolerance design are the three stages of design process as presented by G. Taguchi. Systems design identifies the basic elements of the design to provide new or improved products to customers. Parameter design determines the optimal parameter settings, which will minimize variation from the target performance of the product. Tolerance design finally identifies the components of the design, which are sensitive in terms of affecting the quality of the product, and establishes tolerance limits that will give the required level of variation in the design. Most studies have focused primarily on optimizing the parameter design or tolerance design for multiple static quality characteristics. In this paper, a mathematical formula corresponding to the model is derived from Taguchi's quadratic quality loss function to minimize the expected total cost for the parameter design of multiple dynamic quality characteristics. When the optimal parameter design is not sufficient to reduce the output variation, the first-order Taylor series expansion is then used to analyse the variations of noise factors for optimizing the tolerance design. It concludes with an example demonstrating this approach.     

Process-targeting model for a product with two dependent quality characteristics using acceptance sampling plans

The purpose of this paper is to develop a process-targeting model for a product with two quality characteristics produced by two processes in series. The first quality characteristic is determined by the setting of the first process, whereas the second quality characteristic depends on the setting of the two processes. The quality of the product is controlled by a single sample inspection plan where inspection is assumed to be error free. The objective of the model is to determine the optimal target for both processes that maximises the profit. A realistic case study is used to demonstrate the utilisation of the model. The results of applying the model indicated that the plant could improve its profit by using optimal process setting and better inspection plans parameters. In addition, sensitivity analysis was performed to study the effect of different parameters on the expected profit and optimal processes means.     

Reliability analysis for mechanical parts considering hidden cost via the modified quality loss model

The improvement of mechanical parts inherent reliability has an impact on the reputation and performance of the company. To estimate the inherent reliability of products more conveniently and economically, a hidden quality cost-production cost (HQC-PC) reliability prediction model is put forward. To estimate the hidden quality cost (HQC) of products more accurately, a quadratic exponential quality loss function model is established, which is different from Taguchi's quadratic quality loss function (QLF) and the modified QLFs. In the new quality loss model, the growth rate of quality loss on both sides of the target value is considered. Under the condition that the quality characteristic value obeys normal distribution, the general estimation formulas of HQC in the tolerance range is obtained considering sampling error and the numerical model of inherent reliability is established. The effect of different parameters on the inherent reliability of products is discussed with practical case, such as design and production parameters. Then, the appropriate process capability index (PCI) is selected according to different production processes. The relationship between the HQC-PC reliability prediction model and PCI is derived by a numerical model of inherent reliability. A new analysis method of inherent reliability is proposed.     

Optimization of hot extrusion process for AZ61 magnesium alloy carriers

This study applies fuzzy-base Taguchi method to investigate the optimal process parameters of the multiple performance characteristics index (MPCI) for the hot extrusion process of AZ61 magnesium alloy products. Flattening strength, fracture strength and extrusion load are taken as the input data of MPCI. Since the optimal combination of process parameters for Taguchi method varies with individual quality characteristic, the optimal combination of parameters for different quality characteristics may be contradictory to each other. In order to consider the larger-the-better quality characteristic of flattening strength and T-slot fracture strength values as well as the smaller-the-better quality characteristic of extrusion load, the fuzzy-base Taguchi method is used to analyze and to obtain the optimal combination of process parameters for the MPCI. First of all, orthogonal array is applied to arrange the experimental combination of extrusion process. The signal-to-noise (S/N) ratios of the three quality characteristics of flattening strength, T-slot fracture strength and extrusion load for the products acquired from experiments are calculated. The S/N ratio serves as the input variable of fuzzy control unit, whereas MPCI serves as a single output variable. The acquired MPCI is employed to analyze the optimal process parameters. In this study, an optimal combination of process parameters of AZ61 carrier for MPCI is obtained, and the verification experiments are conducted to prove the accuracy. Moreover, mechanical properties of AZ31 and AZ61 magnesium alloy carriers are tested for further comparison.     

Solving the Multidisciplinary Robust Parameter Design Problem for Mixed Type Quality Characteristics under Asymmetric Conditions

Quality practitioners often identify robust parameter design (RPD) as one of the most important and effective methods for process and quality improvement. Within this framework, identifying the optimal factor settings that achieve desired process targets with minimum variance is critical and can translate to significant reductions in product waste and processing costs. In solving this problem, most traditional RPD models consider only a single quality characteristic of interest. However, products are often judged by multiple quality characteristics, which often have conflicting objectives. Conventional RPD models that address the multi‐response problem typically only examine like‐type cases, and those that consider mixed types of quality characteristics often overlook any asymmetry that is likely to exist in certain types. In contrast, this article proposes a multidisciplinary RPD methodology that provides an enhanced approach for modeling multiple, mixed type quality characteristics; uses the skew normal distribution to allow for a fuller and more accurate representation of asymmetric system properties and to facilitate simultaneous modeling of both symmetric and asymmetric conditions; and implements a priority‐based optimization scheme that affords engineers' and decision makers' flexibility in establishing and modifying optimization priorities. A numerical example is used to demonstrate the proposed methodology, and the results are compared traditional approaches to illustrate potential improvements. Copyright © 2013 John Wiley & Sons, Ltd.     

Analysis of tribological behaviour of aluminum-titanium carbide-basalt metal matrix composite

In the recent years, particulate reinforced aluminum based matrix composites are playing an important role in automobile and aerospace applications due to their enhanced properties. In this work, an attempt has been made to optimize the tribological behaviour of aluminum 7075 matrix reinforced with titanium carbide (3 percent weight) and basalt particles (2 percent weight) using Taguchi based grey relational analysis. Composites are fabricated according to american society for testing materials standard using stir casting method dry sliding wear tests were carried out using pin on disc apparatus as per Taguchi's L9 orthogonal array. Grey relational analysis was used to obtain the optimum process parameters for multiple quality characteristics such as wear rate and coefficient of friction. Then significant contribution of wear parameters was determined by analysis of variance. A confirmatory test was carried out to validate the test result. Finally, the micro structural investigation on the worn surfaces was performed by scanning electron microscope.     

Optimization of the Deposition Parameters of DLC Coatings with the IC-PECVD Method

Amorphous carbon film, also known as diamond-like carbon (DLC) film, is a promising material for tribological application. It is noted that properties relevant to tribological application change significantly depending on the method of preparation of these films. These properties are also altered by the composition of the films. In view of this, the purpose of the present study was to determine the optimal values of selected deposition parameters of hydrogenated DLC films on high-speed steel tool substrates with the inductively coupled plasma enhanced chemical vapor deposition (IC-PECVD) method. To optimize the deposition parameters for hydrogenated DLC films, Taguchi's method was used. Deposition parameters (bias voltage, bias frequency, deposition pressure, and gas composition) were optimized with consideration to hardness of the film. Based on the experimental results, the optimal parameter setting are ?50 V, 500 Hz, 4 µbar, and 90:10 for achieving maximum value of hardness. It was found that bias voltage has greater influence on hardness. At the optimum conditions, the conformance run resulted in a hardness value of 1580 KHN. Atomic force microscopy images showed that the DLC films are smooth with an average roughness (Ra) of 1.24 nm on silicon substrate.     

Continuous Taguchi—a model-based approach to Taguchi's ‘quality by design’ with arbitrary distributions

Statistical experimental design has been used in ‘off-line’ quality control to determine the optimal settings for a system even when the mathematical model is known. Taguchi demonstrated how signal-to-noise ratios could be used to improve the performance of a system through variance minimization. However, these statistical methods often do not use the full distribution information that may be available. Proposed in this paper is an extension and complement to Taguchi's use of experimental design and signal-to-noise ratios for known system models. The use of a probability transformation method with the mathematical system model will allow designers to perform parameter and tolerance design simultaneously using a method of ‘fast integration’. The result is a new method in the field of ‘quality by design’, which we call continuous Taguchi, that can handle both linear and non-linear systems, with components of any distribution type, with or without correlation of the variables. In addition, an interpretation of Taguchi's classification of factors is given in the context of our full distribution method. © 1998 John Wiley & Sons, Ltd.