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Multi-characteristics parameter design: A desirability function approach based on process capability indices
Abstract
A PCI (Process Capability Index)-based desirability function approach for multi-characteristics parameter design problems is presented. Three types of PCI's, including the one newly developed for the-nominal-the-best characteristic, are employed depending on the type of performance characteristics, and a new desirability function (i.e. a logistic function) is proposed for the PCI's. The weighted geometric mean of the desirabilities for PCI's is then used as an aggregated performance measure for compromising the conflicts among the levels of a design parameter. Using PCI's and a logistic desirability function for solving a multi-characteristics parameter design problem is relatively simple and easy to implement. In addition, the proposed approach yields dispersion-sensitive results regardless of the type of performance characteristics. The developed approach is illustrated with an example from a drawing process of optical fiber, and compared with the existing desirability function approaches.
... Its maximum speed could reach 12 Mach at the endo-atmosphere. The difference between scramjet and ramjet is that scramjet decreases the incoming airspeed to subsonic while the combustion process occurs at supersonic velocity [7]. Scramjet generally uses hydrogen as fuel and is aerodynamically complicated. ...
... Researchers are studying how to improve fuel efficiency and engine reliability, reducing greenhouse gas and particle emissions and decreasing noise. Trivedi et al. claimed that the greenhouse gas emissions could be reduced by 60-80% when mixing microalgae biofuels with conventional jet fuel [7,8]. ...
... In terms of military jet engines. efficiency of engine research and development could be improved by variable cycle engine (VCE), which is a kind of aircraft jet engine designed to operate efficiently under subsonic, transonic and supersonic mixed flight conditions [7]. And this leads to the attractiveness of the variable cycle engine. ...
The development status of aero-engines is a sign of a country's technological development level and comprehensive national strength. Jet engines undergone a rapid development since being invented and are widely applied in both commercial and military aircraft nowadays. The objective of jet engines is to provide thrust for aircraft and maintain high performance in different flight segments. Engine design choice must be compromised to balance different selection criteria. This article reviews the development history of jet engines and reviews the development paths of jet engines in various technical fields in detail. It also summarizes the current state and development of jet engines from the civil and military fields and finally looks forward to the future development of jet engines. The discussion of several publications shows that considerable attention has been paid in reducing emissions, increasing fuel efficiency and reducing noise. Advanced manufacturing technologies and materials could improve engine performance. Establish new operations could be another future direction while it has limitations. Bio-fuel could be a promising solution in reducing emissions while its feasibility in meeting real operating conditions still need to be investigated.
... Its maximum speed could reach 12 Mach at the endo-atmosphere. The difference between scramjet and ramjet is that scramjet decreases the incoming airspeed to subsonic while the combustion process occurs at supersonic velocity [7]. Scramjet generally uses hydrogen as fuel and is aerodynamically complicated. ...
... claimed that the greenhouse gas emissions could be reduced by 60-80% when mixing micro-algae biofuels with conventional jet fuel [7,8]. ...
... In terms of military jet engines. efficiency of engine research and development could be improved by variable cycle engine (VCE), which is a kind of aircraft jet engine designed to operate efficiently under subsonic, transonic and supersonic mixed flight conditions [7]. And this leads to the attractiveness of the variable cycle engine. ...
The development status of aero-engines is a sign of a country's technological development level and comprehensive national strength. Jet engines undergone a rapid development since being invented and are widely applied in both commercial and military aircraft nowadays. The objective of jet engines is to provide thrust for aircraft and maintain high performance in different flight segments. Engine design choices must be compromised to balance different selection criteria. This article reviews the development history of jet engines and reviews the development paths of jet engines in various technical fields in detail. It also summarizes the current state and development of jet engines in the civil and military fields and finally looks forward to the future development of jet engines. The discussion of several publications shows that considerable attention has been paid to reducing emissions, increasing fuel efficiency, and reducing noise. Advanced manufacturing technologies and materials could improve engine performance. Establishing new operations could be another future direction while it has limitations. Bio-fuel could be a promising solution in reducing emissions while its feasibility in meeting real operating conditions still needs to be investigated.
... In the case of machining bore diameters, the performance characteristic of machine tool is the-nominal-the-best (NB) type. 25 The index of process capability describes the actual capability of a process to generate a specific quality characteristic consistently within specifications. Process capability ratio (PCR) or process capability index (PCI) compares the spread of the process with the width of the tolerance. ...
... Process capability ratio (PCR) or process capability index (PCI) compares the spread of the process with the width of the tolerance. 25,31 Among the five PCI's (C p , C pk , k, C pu , C pl ), the NB type PCI assumes the following form: 25 ...
... 31 The downside of C p is that it only considers the variability of the process and does not consider the location of the process mean, which means that the performance of the process degenerates rapidly as the process mean deviates from the nominal value. 25 C pk , on the other hand, is the one-sided C p that considers the process centering, represented in the form of 25,31 : ...
A dynamic, globalized and customer-driven market brings opportunities and threats to companies, depending on the response speed and production strategies. One strategy is Concurrent Engineering (CE) that focuses on improving the product development process, by considering various factors associated with the life cycle of the product from the early stages of the product design. Design for Manufacturing (DFM) has proven to be an effective approach to implement CE concept. Recently, an important DFM concept in machining (i.e. a real-time inspection) has drawn much attention from both academia and industry. This is because intense domestic and international competition has put more emphasis on the part quality to achieve a shorter inspection time, improved part accuracies, and reduced scrap. The current methodology, using a machine mounted touch probe, suffers from the fact that the measurement accuracy is affected by the individual machine tool's positional accuracy and positioning system. To address this concern, the cutting experiments were conducted to collect touch probe measurement data. The data were analyzed to verify whether using a touch probe is suitable for real-time inspection. The analysis results show the touch probe has the higher capability index numbers and consistencies than the coordinate measuring machine (CMM), suggesting that the touch probe can be integrated into DFM as a means of real-time quality inspection.
... Previously, Wu and Hamada (2000) and Chiao and Hamada (2001) considered optimizing probability of defectives in a multiple response setting based on experimental designs and responses that follow a multivariate normal distribution. Plante (2001), Lee and Yum (2003), and Jayaram and Ibrahim (1999) sought to maximize some function of the process capability indices of responses that are approximately normally distributed. Peterson (2004), , and applied the probability that a response is within specification using Bayesian methods. ...
... Del Castillo et al. (1996) modified the desirability functions so that they are differentiable and allow assignment of different priorities among the response variables. Lee and Yum (2003) used logistic desirability functions in conjunction with capability indices. Khuri and Conlon (1981) simultaneously optimized several response functions by finding the point with minimum distance to individually optimized responses. ...
A process output has multiple performance measures (response variables) that are related to multiple input variables (both controllable and noise variables). The input variables are modeled as random variables and the relationships are modeled by transfer functions that may be known functional relationships or response surfaces that have been estimated from experimental data. The performance measures have specification limits. The goal is to select the target (or mean) values for the controllable input variables to minimize the weighted probabilities that the response variables will have values outside their specification limits without making distributional assumptions on the response variables. A single set of simulation replications is used to efficiently estimate derivatives of the weighted probability of defectives with respect to the parameters of the probability distributions of each input variable. These derivative estimates are used in a gradient-based optimization algorithm to select the mean values for the controllable input variables. The problem is motivated by and the algorithm is applied to the design and production of a resin to be used in the manufacture of an infant car seat.
... The Taguchi process capability index can be considered an extension of the mean square error. The optimal level combination of each response value to the target is obtained in the case where the response variance is small; this approach is preferred for situations with target values and upper and lower tolerance lines [25][26][27]. Therefore, the evaluation index of the physical and mechanical properties of the cold roll-beating spline surface is constructed using the Taguchi process capability index to construct the optimization function, as shown in ...
The aim of this work is to control the physical and mechanical properties of a spline surface and achieve a reasonable choice of high-speed cold roll-beating processing parameters. The surface residual stress and surface work hardening at the indexing circle serve as the main evaluation indices of the physical and mechanical properties of the spline surface. The influence degree of the processing parameters on each evaluation index is analyzed using Taguchi theory. An optimized model for improving the Taguchi process capability index that combines Taguchi theory with entropy theory is established, and the integral process capacity index is optimized via the generalized price reduction gradient method. The results of the optimization and the verification test are implemented in a high-speed cold roll forming test for comparison. The results show that the influence of processing parameters on the physical and mechanical properties of the splash surface of the cold roll can be ordered as follows: feed rate > roll round radius > cold roll-beating speed. In addition, the spline surface physical and mechanical properties of the optimal processing parameters were obtained for the combination of a cold rolling speed of 1581 r/mm, feed rate of 42 mm/min, and roll round radius of 2 mm.
... The desirability function, which is based on the sigmoid function, can reflect multiple cKPI criteria in service level agreements (SLA). Further, unlike existing desirability functions, the sigmoid based desirability function can transform different scales of cKPIs into values between 0 and 1 without requiring maximum or minimum values (Lee and Yum, 2003). The weighted values of two-folded desirability functions for all cKPIs are summed to determine the synthetic performance of a collaboration, which can be compared with prior performance or partners' performance. ...
Effective performance measures must be developed in order to effectively maintain successful collaboration. This paper presents a methodology of collaborative performance measures to evaluate the overall performance of a collaboration process between multiple manufacturing partners. The partners first define collaborative key performance indicators (cKPI), and they then measure the cKPIs and calculate the synthetic performance from the cKPI values to evaluate the result of the collaboration case. To measure different scales of cKPI, we develop a two-folded desirability function based on the logistic sigmoid functions. The proposed methodology provides a quantitative way to measure collaborative performance in order to effectively manage collaboration among partners, continuously improving collaboration performance.
... The lower and upper technical limits of the jth controllable factor are shown by LR j and UR j , respectively. Lee and Yum [33] applied process capability analysis in a multi response problem, while the responses were assumed to be uncorrelated and normally distributed. In their method, the process capability value of each response in each treatment is computed and then they are converted into desirability values using Eq. ...
Most of the researches developed for single response and multi response optimization problems are based on the normality assumption of responses, while this assumption does not necessarily hold in real situations. In the real world processes, each product can contain correlated responses which follow different distributions. For instance, multivariate non-normal responses, multi-attribute responses or in some cases mixed continuous-discrete responses. In this paper a new approach is presented based on multivariate process capability index and NORTA inverse transformation for multi response optimization problem with mixed continuous-discrete responses. In the proposed approach, assuming distribution function of the responses is known in advance based on historical data; first we transform the multivariate mixed continuous-discrete responses using NORTA inverse transformation to obtain multivariate normal distributed responses. Then the multivariate process capability index is computed in each treatment. Finally, for determining the optimum treatment, the geometric mean value of multivariate Process Capability Index (PCI) is computed for each factor level and the most capable levels are selected as the optimum setting. The performance of the proposed method is verified through a real case study in a plastic molding process as well as simulation studies with numerical examples.
Multistage production processes are becoming more important in the industry to ensure levels of flexibility, efficiency and modularity. Thus, the way in which companies define optimal production parameters related to production costs and quality must be adapted to this reality. In this paper we introduce a multi-response optimization (MRO) model for a two stage production process. The model gives first stage quality specification limits which minimize the rework costs caused by the nonconforming parts of the whole process. The proposed model is applied to an example based on a production process of the automotive industry. The benefits of the model are evaluated by comparing the capability and the rework costs of the multistage production process before and after the optimization.
Desirability function method is the most popular approach for multi-response optimization, however, the variation, correlation and the uncertainty of parameter estimation of the responses are ignored in this approach. Thus improved desirability function method is presented. The proposed method applies variance-covariance structure of the responses and predicted variance to desirability function. The implementation and effectiveness of the proposed method are illustrated by an example from the literature. The result shows that, compared with traditional desirability function approach, the variance and predicted variance of responses obtained by improved desirability function method reduce 5.6% and 6.2% respectively, and the variance of desirability function decreases 7%. As a result, the proposed method, which is robust to predicted quality and variation of responses, yields better results than traditional desirability function method.
During the past several decades, the Taguchi robust design method has been widely used in various fields successfully. On the other hand, some researchers and practitioners have criticized the method with respect to the way of utilizing orthogonal arrays, the signal-to-noise ratio as a performance measure, data analysis methods, etc., and proposed alternative approaches to robust design. This paper introduces the Taguchi method first, evaluates the validity of the criticisms, and discusses advantages and disadvantages of each alternative. Finally, research issues to be addressed for effective robust design are presented.
As Augmented Reality Navigation systems receive increasing attention as the next generation navigation systems, the importance
of the layout of the elements and searching for the appropriate level of information cannot be overstated. Due to this, a
series of experiments of usability tests had been designed. According to the experiments, the results for the screen arrangement
showed that the MBN screen displayed on the left and the ARN screen on the right was preferred the most while the results
for changing lanes showed that displaying information directly on the road and highlighting the path was the best method.
As for switching direction, using the upper icons and displaying information directly on the road was preferred. The adequate
amount of information was found out to be an average of 3 POI with 20pt font sizes for ARN displays and 10 POI with 18pt font
sizes for MBN displays. Lastly, the Eye-tracking experiments showed that the ARN screen was viewed more often with a ratio
of 7:3.
This paper contains a bibliography of approximately 530 journal papers and books on process capability indices for the period 2000–2009. The related literature is classified into four major categories, namely, books, review/overview papers, theory- and method-related papers, and special applications. Theory- and method-related papers are further classified into univariate and multivariate cases, and special applications include acceptance sampling plans, supplier selection, and tolerance design and other optimizations. Copyright © 2010 John Wiley & Sons, Ltd.
A new measure of the process capability (Cpm) is proposed that takes into account the proximity to the target value as well as the process variation when assessing process performance. The sampling distribution for an estimate of Cpm (Ĉpm) and some of its properties have been examined and an example of its application is included. The new index is easy to compute and, with the aid of the included tables, easy to analyze. Ĉpm has some more desirable statistical properties than Ĉp and Ĉpk,the estimates of the Cp and Cpk indices, respectivel
In this paper we survey and critically comment on some basic concepts and notions relevant to the methodology dealing with process capability indices (PCI's). The emphasis is on distributional and inferential aspects. The intent is to contribute to the understanding and interpretation of these indices, if one is (unfortunately) required to use them. We regard them primarily as indicators of the expected proportion of nonconforming items, and not as having some relationship to arbitrary loss functions, as is currently the more fashionable viewpoint. New PCI's, related to the expected proportion of nonconforming items, are suggested.
Taguchi parameter design is used extensively in industry to determine the optimal set of process parameters necessary to produce a product that meets or exceeds customer expectations of performance while minimizing performance variation. The majority of research in Taguchi parameter design has concentrated on approaches to optimize process parameters based on experimental observation of a single quality characteristic. This paper develops a statistical method, the DMT method, to evaluate and optimize multiple quality characteristic problems. The method incorporates desirability functions, a performance statistic based on the mean squared error, and data-driven transformations to provide a systematic approach that is adjustable to a variety of situations and easy for nonexperts to apply. This paper presents the DMT method in a step-by-step format and applies the method to two examples to illustrate its applicability to a variety of parameter design problems.
Over the years, Japanese managers, engineers, and workers have been very successful in reducing manufacturing costs by adopting more enlightened quality thinking and by applying more technical quality methods. Since 1980, US automotive companies and their suppliers have made dramatic improvements in quality. Much of this improvement has been due to more intensive application of traditional quality methods. Although statistical methods are uniform throughout the world, they are applied very differently in the East and West. Of foremost importance is the new definition of 'manufacturing' quality as product uniformity around the target rather than conformance to specification limits. This difference in thinking results in totally different operational and engineering approaches to quality and productivity. This article explores the distinctions in terms of process variations, capability index, relationships between cost and quality, and related subjects.
Robust design is an important method for improving product or manufacturing process design by making the output response insensitive (robust) to difficult-to control variations (noise). Most research in robust design has focused on problems with a single characteristic or response. This paper concerns the application of a robust design method to problems with multiple characteristics. We extend the multivariate loss considered by Pignatiello to include the smaller- and largerthe-better type characteristics. Under various assumptions, we develop appropriate two-step procedures that minimize the average multivariate loss. Similar to the advantages in the single characteristic problem, the proposed two-step procedures substantially reduce the dimension of the design optimization problem and allow for future changes of response target values without re-optimization. We illustrate the proposed procedures with a polysilicon deposition example.
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.
A problem facing the product development community is the selection of a set of conditions which will result in a product with a desirable combination of properties. This essentially is a problem involving the simultaneous optimization of several response variables (the desirable combination of properties) which depend upon a number of independent variables or sets of conditions. Harrington, among others, has addressed this problem and has presented a desirability function approach. This paper will modify his approach and illustrate how several response variables can be transformed into a desirability function, which can be optimized by univariate techniques. Its usage will be illustrated in the development of a rubber compound for tire treads.
Abstract Most previous Taguchi method applications have only addressed a single-response problem. However, more than one correlated response normally occurs in a manufactured product. The multi-response problem has received only limited attention. In this work, we propose an effective procedure on the basis of principal component analysis (PCA) to optimize the multi-response problems in the Taguchi method. With the PCA, a set of original responses can be transformed into a set of uncorrelated components. Therefore, the conflict for determining the optimal settings of the design parameters for the multi-response problems can be reduced. Two case studies are evaluated, indicating that the proposed procedure yields a satisfactory result.
This paper focuses on studies where the goal is to optimize the key quality characteristics of a specific product or process. In order to do that, the process parameters must be adjusted in such a way that deviations from target are minimized while robustness to noise and to process parameter fluctuations are maximized. Since this is a multi-response, multi-objective problem, the optimum solution is a compromise. In this paper we present a gradient loss function which captures all the desired objectives, and propose a general methodology to perform the optimization analysis. This methodology is then carried out experimentally on a cosmetic product and the results are discussed.
Multi-response quality design techniques are used to identify settings of process parameters that make a product's performance close to a target value in the presence of multiple quality characteristics. In many situations, these quality characteristics, and thus their functional relations, are imprecise to some degree due to tolerances, nonspecificity, measuring errors, incomplete knowledge, vagueness of definitions, and so on. Here, possibility distributions and possibilistic regressions are used to model these imprecise natures and induced imprecise functional relationships. We first integrate and extend existing possibilistic regression methods to obtain unified measures of predictive quality characteristics or responses. The unified possibility distributions are also practical for many forecasting problems. We then propose a multiple objective programming model to obtain an appropriate combination of process parameter settings based on the unified possibility distributions of imprecise predictive responses. We not only optimize the most possible responses values, but also minimize imprecision or deviations from the most possible values. Through a die casting example, we show how to use our approach to reach an appropriate machine setting which simultaneously optimizes both porosity and temperature difference on die surfaces.
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.
Virtually every manufactured product has more than one characteristic by which its overall quality is determined. Since those quality characteristics may be correlated, some changes in the levels of the controllable product design and process design variables may improve one of the quality characteristics while adversely affecting one or more of the other quality characteristics. In this paper we define a quadratic loss function for use with multiple quality characteristics. We discuss several strategies that could be employed for robust quality engineering of products and processes when there is more than one quality characteristic of interest.
For controlling quality of products, there are two things we have to consider; how to measure the quality and how to improve it. The former is discussed in section 2 by introducing the difference in quality levels between Japan and USA. After briefly introducing all countermeasures for improving quality of products, an on-line quality control system design is proposed as the one which is more economical than removing defec- tives after manufacturing by conducting inspection. It has been ma?y Japanese companies' policy to keep pro- cess conditions at best in order to produce uniform products as far as possible. This paper discusses the optimum feed-back process control system design by checking either quality characteristics or process pa- rameters after introducing overall quality countermea- sures starting with product design.
One of the conventional approaches used in off-line quality control is the Taguchi method. However, most previous Taguchi method applications have only dealt with a single-response problem and the multi-response problem has received only limited attention. The theoretical analysis in this study reveals that Taguchi's quadratic loss function and the indifference curve in the TOPSIS (Technique for order preference by similarity to ideal solution) method have similar features. The Taguchi method deals with a one-dimensional problem and TOPSIS handles multi-dimensional problems. As a result, the relative closeness computed in TOPSIS can be used as a performance measurement index for optimizing multi-response problems in the Taguchi method. Next, an effective procedure is proposed by applying fuzzy set theory to multiple attribute decision making (MADM). The procedure can reduce the uncertainty for determining a weight of each response and it is a universal approach which can simultaneously deal with continuous and discrete data. Finally, the effectiveness of the proposed procedure is verified with an example of analysing a plasma enhanced chemical vapour deposition (PECVD) process experiment. © 1997 by John Wiley & Sons, Ltd.
In this paper we demonstrate the ability of the Taguchi technique accurately to characterize and successfully to optimize complicated multi‐response processes with the minimum of experiments, provided one uses simple statistical techniques which can ensure valid, and definitive results. We point out the usefulness of suitable data‐transformations, and we suggest a systematic procedure for establishing the optimal operating conditions and for carrying out confirmatory experiments.
For the particular case detailed in this paper (which is typical of multi‐response processes) the Taguchi technique achieved an improvement in uniformity of a factor of 2, together with optimized process control.
Multiresponse optimization techniques are used to identify settings of process parameters that make the product's performance close to target values in the presence of multiple quality characteristics. In this study, a fuzzy multiresponse optimization procedure is proposed to search an appropriate combination of process parameter settings based on multiple quality characteristics or responses. Fuzzy regression models are first used to model the relations between process parameters and responses. The possibility distributions of the prediction responses are then obtained. The problem is reduced to a multiobjective optimization problem with fuzzy objectives. A strategy of optimizing the most possible response values and minimizing the deviations from the most possible values is proposed. We consider not only the most possible value, but also the imprecision of the prediction responses. Through a die casting example, we show how to use our approach to reach an appropriate machine setting which simultaneously optimize both casting quality and die life.
Taguchi methods: Research and development
- G Taguchi
G. Taguchi, "Taguchi methods: Research and development," Quality Engineering Series 1 (ASI Press, Dearborn, 1992).
The desirability function
- E C Harrington
- Jr
E. C. Harrington, Jr., "The desirability function," Industrial Quality Control 21 (1965), pp. 494–498.
A balancing act: Optimizing a product's properties
- G C Derringer
G. C. Derringer, "A balancing act: Optimizing a product's properties," Quality Progress 27 (1994), pp. 51–58.
Robust parameter design for multiple performance characteristics
- S K Seo
- J D Choi
S. K. Seo and J. D. Choi, "Robust parameter design for multiple performance characteristics," Journal of Korean Society for Quality Management (in Korean) 22 (1994), pp. 34–53.
A new measure of process capability: Cpm36 WSPC/122-IJRQSE 00126 Multi-Characteristics Parameter Design 461 22Distributional and inferential properties of process capability indices
- L K Chan
- S W Cheng
- F A Spiring
L. K. Chan, S. W. Cheng, F. A. Spiring, "A new measure of process capability: Cpm," Journal of Quality Technology 20 (1988), pp. 162–175. November 14, 2003 10:36 WSPC/122-IJRQSE 00126 Multi-Characteristics Parameter Design 461 22. W. L. Pearn, S. Kotz, and N. L. Johnson, "Distributional and inferential properties of process capability indices," Journal of Quality Technology 24 (1992), pp. 216–231.
An objective function of multiple quality character-istics for parameter optimization experiments
- J L Ribeiro
- S L Albin
J. L. Ribeiro and S. L. Albin, " An objective function of multiple quality character-istics for parameter optimization experiments ", IE Working Paper 93 111, Rutgers University.
- M S Phadke
M. S. Phadke, Quality Engineering Using Robust Design (Prentice Hall, Englewood
Cliffs, 1989).