Quality Loss Function Research Articles

Concurrent optimization of the design and manufacturing stages of product development

The problem of concurrent optimization of the design and the process planning stages when a new product is developed is addressed. The paper advocates for a simultaneous approach rather than the traditional sequential one. A mathematical representation of this approach is given for these two stages. A mathematical programming technique is used to find the optimal values of the design and the process characteristics. The objective function is a quality loss function. The constraints are the customer requirements, the product's specification limits, the parts’ dimensional limits and the process capability. The traditional sequential approach of concurrent engineering is compared with the proposed simultaneous approach. A parametric analysis of the objective function is performed by applying an interactive multi-objective goal programming technique. A numerical example of a low-pass electrical circuit is given. It is shown that the proposed approach leads to better efficient solutions than the sequential approach. The decision-maker interacts with the optimization process and can choose the efficient solution that best satisfies the company's needs.

Evaluating the quality level of a product with multiple quality characterisitcs

Most of the studies of quality systems or product assessment deal with a single quality characteristic to determine the quality loss. From the customer’s point of view, however, products are often judged by more than one quality characteristic. For this reason, a multivariate quality loss function is required as an extension to the Taguchi loss function to capture the overall losses caused by bad quality when multiple quality characteristics are present. A numerical example is illustrated showing that using inappropriate univariate loss functions will give an underestimated quality loss or even ignored the loss incurred because of the poor quality.

An improved multivariate loss function approach to optimization

The basic purpose of a quality loss function is to evaluate a loss to customers in a quantitative manner. Although there are several multivariate loss functions that have been proposed and studied in the literature, it has room for improvement. A good multivariate loss function should represent an appropriate compromise in terms of both process economics and the correlation structure among various responses. More important, it should be easily understood and implemented in practice. According to this criterion, we first introduce a pragmatic dimensionless multivariate loss function proposed by Artiles-Leon, then we improve the multivariate loss function in two respects: one is making it suitable for all three types of quality characteristics; the other is considering correlation structure among the various responses, which makes the improved multivariate loss function more adequate in the real world. On the bases of these, an example from industrial practice is provided to compare our improved method with other methods, and last, some reviews are presented in conclusion.

Determining the Optimum Process Mean of a One-sided Specification Limit with the Linear Quality Loss Function of Product

Wen & Mergen (1999) proposed a method for setting the optimal process mean when a process was not capable of meeting specifications in the short term. However, they neglected to consider the quality loss for a product within specifications in the model. Chen & Chou (2002) presented a modified Wen & Mergen's (1999) model, including the quadratic quality loss function for a one-sided specification limit. In this paper, we propose the modified Wen & Mergen (1999) cost model including the linear quality loss function of a product for determining the optimal process mean of a one-sided specification limit.

Evaluating the product quality level under multiple L-type quality characteristics

One of the most critical issues encountered in the area of quality engineering is the selection of an appropriate quality loss function to relate key quality characteristics of a product to its quality performance. The loss function can be used to evaluate the quality loss in terms of monetary units that enables managers to quantify unobservable costs. It aids manufacturers to evaluate quality improvement projects more rigorously, hence, the choice of paths for quality enrichment depends on the type of loss function. Although several multivariate quality loss functions have been proposed, these models only considered the-nominal-the-best (N-type) quality characteristics. The effect of other types of quality characteristics was not addressed. In this paper, a cost model is proposed to evaluate the quality level of a product with multiple the-larger-the-better (L-type) quality characteristics. An example with two quality characteristics is given to illustrate the application.

Quality evaluation model using loss function for multiple S-type quality characteristics

Most of the studies of quality system or product-quality assessment deal with a single quality characteristic to determine the quality loss. Products are often assessed on more than one quality characteristic. For this reason, different multivariate quality loss functions have been proposed. However, these loss functions only consider the nominal-the-best quality characteristics (N-type); they do not consider the condition when the quality characteristics are of the smaller-the-better (S-type). In this article, we present a quality evaluation model using loss function for multiple S-type quality characteristics. A numerical example is illustrated showing that using inappropriate loss functions will lead to inaccurate results that give either an underestimate or overestimate of the expected quality costs.

Quality Loss Functions for Nonnegative Variables and Their Applications

Loss functions play a fundamental role in every quality engineering method. A new set of loss functions is proposed based on Taguchi's societal loss concept. Its applications to robust parameter design are discussed in detail. The loss functions are shown to posses some interesting properties and lead to theoretical results that cannot be handled with other loss functions.

Set the Optimum Process Parameters Based on Asymmetric Quality Loss Function

Recently, Huang has presented a trade-off problem of determining the optimumprocess parameters for the product quality and process adjustment cost. Aboutproduct quality, Huang adopts the symmetric quadratic quality loss function formeasuring the loss of profit. However, he has neglected other types of qualityloss function in the model. In this paper, we will further propose the modifiedHuang's cost model with the linear and quadratic asymmetric quality loss function of product for determining the optimum process parameters.

Strengths and limitations of taguchi's contributions to quality, manufacturing, and process engineering

This paper reviews Genichi Taguchi's contributions to the field of quality and manufacturing engineering from both a statistical and an engineering viewpoint. His major contributions are first listed and then described in a systematic and analytical manner. The concepts underlying Taguchi's univariate quality loss functions (QLFs), his orthogonal arrays (OAs), robust designs, signal-to-noise (S/N) ratios, and their corresponding applications to quality and process engineering are examined and described in great detail. Some of Taguchi's OAs are related to the classical (fractional) factorial designs (a field that was started by Sir Ronald A. Fisher in the early 1920s). The applications of Taguchi's robust (parameter and tolerance) designs to manufacturing engineering are illustrated through designed experiments.

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

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

Optimization of TQFP molding process using neuro-fuzzy-GA approach

Abstract This paper focuses on an integrated optimization problem that involves multiple qualitative and quantitative responses in the thin quad flat pack (TQFP) molding process. A fuzzy quality loss function (FQLF) is first applied to the qualitative responses, since the molding defects cannot be simply represented by the relationship between molding conditions and mathematical models. Neural network is then used to provide a nonlinear relationship between process parameters and responses. A genetic algorithm together with exponential desirability function is employed to determine the optimal parameter setting for TQFP encapsulation. The proposed method was implemented in a semiconductor assembly factory in Taiwan. The results from this study have proved the feasibility of the proposed approach.

Applying Quality Loss Function in the Design of Economic Specification Limits for Triangular Distribution

In 1987, Kapur and Wang presented that the inspection in an on-line quality control system may be conducted as a short term approach to reduce variance of the items shipped to the customers. They used Taguchi's quality loss function for designing the optimal specification limits. The normal and log-normal quality characteristics are used in their model. In this paper, we further extend Kapur and Wang's model for the triangular quality characteristic. For this modified Kapur and Wang's model, the managerial implication is that by using the triangular distribution we determine the optimum inspection policy for product assembly including two or more parts follow uniform distribution, control the nonconforming items prevented to be shipped to the customer, and decrease the total loss to the society.

Joint Design of Continuous Sampling Plans and Specification Limits

This paper explores the problem of integrating a Type I continuous sampling plan (CSP-1 plan) and the design of specification limits based on Taguchi's quality loss function. By adopting the minimax-regret principle, we can obtain the economic specification limits and the optimal inspection policy. This study is an extension of Kapur and Wang's work.

Quality Loss Functions for the Measurement of Service Quality

Service industries are growing at an explosive rate, particularly in comparison with manufacturing. Numerous service industries concentrate on service quality to enhance their competitive power. Customer satisfaction is a growing concern to many leading companies throughout the world Improving service quality is considered an essential strategy for success and survival in today's competitive situation. In order to meet the actual needs of customers, it is important to quantify service quality. However, using Taguchi's quality loss function is not adequate for portraying the real situation in the service sector. In this paper, two modified quality loss functions are provided to measure service quality. The properties of these quality loss function parameters are discussed. The expected quality losses for the modified loss functions are also compared to that of Taguchi's loss function. The results show that these modified quality loss functions are much more suitable for measuring service quality.

Modular product family design: Agent-based Pareto-optimization and quality loss function-based post-optimal analysis

The advent of mass customization and increased manufacturing competition has necessitated that many companies offer platform-oriented multiple product variants. Various design strategies such as Design for Variety and product family design have become critical in this respect. This paper provides a two-step approach to tackle the modular product family design problem. The first step performs a multi-objective optimization using a multi-agent framework to determine the Pareto-design solutions for a given module set. The proposed multi-agent framework is new and has built in flexibility to handle various constraints such as module compatibility during the optimization process. The second step performs post-optimization analysis that includes a novel application of the quality loss function to determine the optimal platform level for a related set of product families and their variants. The proposed method is applied to a product family design example to demonstrate its validity and effectiveness.

Economic-Statistical Design of Multivariate Control Charts Using Quality Loss Function

_2_nL is used to develop this procedure and the cost model is established based on the cost function developed by Montgomery and Klatt and the multivariate quality loss function presented by Kapur and Cho. A numerical example is provided to illustrate the solution procedure of the design and then the effects of cost parameters on the optimal design are studied.

Minimum-loss design of x-bar charts for correlated data

Abstract When the x-bar chart is used to monitor a production process, three parameters should be determined: the sample size, the sampling interval between successive samples, and the control limits for the chart. In 1956, Duncan presented a cost model to determine the three parameters, which is called the economic design of x-bar charts. In 1995, Alexander et al. combined Duncan’s cost model with the Taguchi’s quality loss function to present a loss model for determining the three parameters. When designing an x-bar chart, one usually assumes that the measurements within a sample are independent; however, this assumption may not be true for some processes. In this paper, we develop the minimum-loss design of x-bar charts for correlated measurements within a sample by incorporating the Taguchi’s quality loss function. An example of orange juice production process is presented to illustrate the solution procedure. From the results of sensitivity analysis, we find that as the measurements in the sample are positively correlated, highly correlated data result in a smaller sample size and a frequent sampling interval; however, as the measurements in the sample are negatively correlated, highly correlated data yield a smaller sample size and a narrower control limits.

Determining the Optimum Process Mean Under Quality Loss Function

Kapur et al. and Wen and Mergen have addressed the problems of products having specification limits but the manufacturing process not being capable of meeting the specifications in the short term. Kapur et al. report that inspection in an on-line quality control system is carried out as a short-term approach to reduce variance of the items shipped to the customers. Wen and Mergen balance the costs of products being out-of-specification by setting the optimal process mean in the short term. In this paper, we propose a modified Wen and Mergen's cost model with a linear and quadratic asymmetrical for the measurement of the quality loss of products which are within specification, for determining the optimum process mean.

Optimum Process Target for Two Quality Characteristics Using Regression Analysis

The selection of the optimum process target has become one of the key research areas for increasing productivity and improving product quality. Although the quality engineering literature contains a vast collection of work related to this issue, several questions still remain unanswered. First, a quality loss function approach using conventional quality loss functions, such as step loss and quadratic loss functions, has been extensively used to determine the optimum process target largely due to mathematical convenience. When historical data concerning customer loss associated with product performance are available, a quality loss function using a well-established statistical method, such as regression analysis, might be a more practical alternative procedure. Second, 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. In this article, we consider two quality characteristics and develop a bivariate empirical loss function based on the historical data associated with the product performance and its associated customer loss. We then propose an optimization scheme for the most economical process target.