Loss Function Approach Research Articles

Simultaneous optimization of multiple performance characteristics of carbonitrided pellets: a case study

The performance of a product is generally characterized by more than one response variable. Hence, the management often faces the problem of simultaneous optimization of many response variables. In recent years, a lot of literature has been published on various methodologies for tackling the multi-response optimization problems. Among them, the approach based on Taguchi’s quality loss function is very popular. This paper discusses a case study on multiple response optimization in carbonitriding process. The surface hardness, case depth, and dimensional variation of carbonitrided pellets were simultaneously optimized using quality loss function methodology. The optimum obtained through loss function approach was found to be superior to the ones obtained through optimizing the response variables separately. The result obtained through the implementation of the solution is also presented in the study.

How Well Do Multiple Testing Methods Scale Up when Both n and k Increase?

With increasingly massive data sets in biopharmaceutical research, particularly in genomic and related applications, there is concern about how well multiple comparisons methods “scale up” with increasing number of tests (k). Familywise error rate-controlling methods do not scale up well, and false discovery rate-controlling methods do scale up well with increasing k. But neither method scales up well with increasing sample size (n) when testing point nulls. We develop a loss function approach to investigate scale-up properties of various methods; we find that while Efron's recent proposal scales up best when both sample size n and number of tests k increase, but its performance otherwise can be erratic.

Multiresponse Optimization: A Literature Review and Research Opportunities

A common problem encountered in product or process design is the selection of optimal parameter levels which involves simultaneous consideration of multiple response variables. This is called a multiresponse problem. A multiresponse problem is solved through three major stages: data collection, model building, and optimization. Up to date, various methods have been proposed for the optimization, including the desirability function approach and loss function approach. In this paper, the existing studies in multiresponse optimization are reviewed and a future research direction is then proposed.

The Late Pretest Problem in Randomized Control Trials of Education Interventions

Pretest–posttest experimental designs often are used in randomized control trials (RCTs) in the education field to improve the precision of the estimated treatment effects. For logistic reasons, however, pretest data often are collected after random assignment, so that including them in the analysis could bias the posttest impact estimates. Thus, the issue of whether to collect and use late pretest data in RCTs involves a variance-bias trade-off. This article addresses this issue both theoretically and empirically for several commonly used impact estimators using a loss function approach that is grounded in the causal inference literature. The key finding is that for RCTs of interventions that aim to improve student test scores, estimators that include late pretests will typically be preferred to estimators that exclude them or that instead include uncontaminated baseline test score data from other sources. This result holds as long as the growth in test score impacts do not grow very quickly early in the school year.

Mean Square Error Criteria to Multiple Quality Characteristics Robust Design by the Weighted Tchebycheff Method

Robust design has been widely applied in quality improvement. For most products, quality is multidimensional. Little attention has been paid to multiple quality characteristics robust design (MQCRD). MQCRD mainly faces two problems: measurement model and multiple objectives optimization. In order to give an appropriate measurement criterion and generate better Pareto solutions, a MQCRD model by the Weighted Tchebycheff method based on the mean square error (MSE) criterion is proposed. Firstly the MSE estimations for each quality characteristic are obtained by response surface method (RSM) and a MQCRD model based on the MSE criteria is given. Then a MQCRD model by the Weighted Tchebycheff method is present, which minimizes the distance between objective functions and the idea point based on the weighted infinite norm. The proposed approach could find very efficient Pareto solutions. Illustrative example shows the model can generate more efficient and robust solutions than the weighted-sum approach. Furthermore it has better results than the generalized reduced gradient (GRG) and quadratic loss function approach.

Inverse modeling of vadose zone flow processes using squared ε-insensitivity loss function

An accurate representation of reality in numerical variably-saturated flow models requires reliable estimates of necessary model parameters. Inverse modeling seeks to estimate parameters such as the saturated and residual water contents, the saturated hydraulic conductivity, the shape parameters of the soil hydraulic functions, using easily attainable observations of actual or cumulative water fluxes, pressure heads, water contents, and concentrations. The inverse procedure usually combines the nonlinear least-squares-based (SSQ) parameter optimization method with a numerical solution of the variably-saturated flow and transport equations. The SSQ-based inverse method is however sensitive to outliers. A novel Squared e-Insensitive Loss Function (SILF) approach is introduced in this study. The SILF approach is inspired by the e-insensitive loss function proposed by Vapnik (1995). The objective function used in the SILF approach is similar to the least-squares objective function, except that it penalizes only for errors greater than a certain predefined acceptable error term e. The SILF approach shows an improved performance over the SSQ approach in estimating the soil hydraulic parameters. Apart from providing robust estimates of the soil hydraulic parameters, the SILF approach also gives an approximation of the relative measurement error during sampling.

Calculation of Total Cost, Tolerance Based on Taguchi’s, AsymmetricQuality Loss Function Approach

Problem statement: Current world market force the manufacturing sectors to develop high quality product and process design with minimum possible cost. About 80% of problems in production units may be attributed to 20% of design tolerance causes. While design typically represents the smallest actual cost elements in products (around 5%), it leverages the largest cost influence (around 70%). So design engineers continuously stumble upon problem of design for high quality performance with lower cost. Objectives of this study where to: (i) simultaneous selection of design and manufacturing tolerance (ii) minimization of total cost (sum of the manufacturing cost and Taguchi’s asymmetric quality cost) (iii) minimum cost and its machining tolerance. Approach: Rotor key base assembly was considered as case study to optimize the minimization of assembly total cost and machining tolerance. New global nonlinear optimization techniques called pattern search algorithm had been implemented to find optimal tolerance allocation and total cost. Results: In this study minimum cost arrived was 45.15 Cr and its corresponding tolerances for machining process turning, drilling, face milling, face milling and drilling where 0.063, 0.0508, 0.2127, 0.2127, 0.2540 mm respectively at worst case conditions. Conclusion: Results indicated that optimization by integer programming, sequential quadratic programming and exhaustive search, nonlinear programming, genetic algorithm, simulated annealing, fuzzy logic, number set theory and Monte Carlo simulation did not give much least total cost and also predicted that pattern search algorithm was robust method. Second the method, generally termed as concurrent tolerance synthesis was well suited for engineering environment, where high quality products with low total cost were designed and manufactured.

Quantifying the Predictive Performance of Prognostic Models for Censored Survival Data with Time‐Dependent Covariates

Prognostic models in survival analysis typically aim to describe the association between patient covariates and future outcomes. More recently, efforts have been made to include covariate information that is updated over time. However, there exists as yet no standard approach to assess the predictive accuracy of such updated predictions. In this article, proposals from the literature are discussed and a conditional loss function approach is suggested, illustrated by a publicly available data set.

Prediction and Minimization of Delamination in Drilling of Medium-Density Fiberboard (MDF) Using Response Surface Methodology and Taguchi Design

In this article, an attempt has been made to predict and minimize the delamination in drilling of medium density fiberboard (MDF). The experiments are carried out on LAMIPAN PB panel based on orthogonal array with feed rate and cutting speed as process parameters. The second order delamination factor models at entry and exit of the holes have been developed using response surface methodology. The parametric analysis has been carried out to study the interaction effects of the machining parameters. Taguchi's quality loss function approach has been employed to simultaneously minimize the delamination factor at entry and exit of the holes. From the analysis of means and analysis of variance, the optimal combination level and the significant parameters on delamination factor are obtained. The optimization results showed that the combination of low feed rate with high cutting speed is necessary to minimize delamination in drilling of MDF.

Evaluating value-at-risk measures in the presence of long memory conditional volatility

This work analyze different approaches in the evaluation of Value-atRisk measures when returns show long memory patterns in conditional variance. In a Montecarlo study we follow the approaches of Kupiec (1995), Christoffersen (1998), Christoffersen, Hahn and Inoue (2001) and Lopez (1998) using the suggested test and loss functions in choosing the best model among a group of alternatives (GARCH, IGARCH, the true FIGARCH DGP and the EWMA). Our Montecarlo analysis shows that the test of Kupiec and the loss function approach lead to the choice of a misspecified model, while the test of Christoffersen et al. (2001) correctly identify long memory. We apply then all the previous tests and measures in the comparison of different models for the Value-at-Risk of the returns of the FIB30, the future on the italian stock market index.

Using analytic hierarchy process to determine process economics in multivariate loss functions

Performance of a product usually depends on several responses (quality characteristics) which must meet all of the specifications simultaneously. This could be achieved by applying of (the) robust design methodology to problems with multiple characteristics. In the literature, several works have been published concerning multi-response optimization methods, which aim to achieve the best possible robustness. One of the approaches for multi-response optimization is Loss Function Approach which allows the practitioner to include variance–covariance structure of the responses, prediction quality and the economic importance of the responses relevant to the product or process. In this paper, we propose utilizing Analytic Hierarchy Process, a multi-criteria decision making tool, to determine the economic importance matrix in the multivariate loss function. An example of the suggested method is presented on a study conducted for a company producing water proof polymer roofing materials.

Taguchi Approach for Achieving Better Machinability in Unreinforced and Reinforced Polyamides

Polyamide composites find wide applications in engineering fields due to favorable properties and hence replaced many traditional metallic materials. In order to increase the properties, the glass fibers are added to unreinforced polyamides. Even though polyamides are produced as near net shapes, machining is required to get the finished products. Thus, the selection of tool and cutting conditions is important in the machining of unreinforced and reinforced polyamides. This article presents the application of Taguchi's quality loss function approach, a multi-response optimization method, for achieving better machinability during turning of both unreinforced polyamide (PA6) and reinforced polyamide with 30% of glass fibers (PA66 GF30). The analysis of means (ANOM) and analysis of variance (ANOVA) on multi-response signal to noise (S/N) ratio are employed to determine the optimal parameter levels and to identify the level of importance of the parameters. The ANOVA results showed that the cutting speed is the most significant factor affecting machinability. Taguchi optimization results suggest that the optimal value of feed rate and cutting speed should be kept at a low level, whereas a polycrystalline diamond (PCD) tool is beneficial over cemented carbide (K10) for machining of both PA6 and PA66 GF30 polyamides to achieve better machinability.

A Bayesian Procedure for Assessing Process Performance Based on Expected Relative Loss with Asymmetric Tolerances

Taguchi has introduced the loss function approach to quality improvement by focusing on the reduction of variation around the target value. This concept pays attention to the product designer’s original intent; that is, values of a critical characteristic at a target lead to maximum product performance. To address this concept, Johnson (1992) proposed the concept of expected relative squared error loss L e for symmetric cases, by approaching capability in terms of loss functions. Unfortunately, the index L e inconsistently measures process capability for processes with asymmetric tolerances, and thus reflects process potential and performance inaccurately. To remedy this, Pearn et al. (2006) proposed a modification of expected loss index, which is referred to as , to handle processes with both symmetric and asymmetric tolerances. The majority of the researches for assessing process performance based on the process loss indices are investigated using the traditional frequentist approach. However, the sampling distribution of the estimated is intractable, this makes establishing the exact confidence interval and testing process performance difficult. In the paper, we consider an alternative Bayesian approach to assess process performance based on the loss index for processes with asymmetric tolerances. Based on the derived posterior probability, a simple but practical procedure is proposed for practitioners to assess process performance on their shop floor, whether the manufacturing tolerance is symmetric or asymmetric.

A loss function approach to group preference aggregation in the AHP

The Analytic Hierarchy Process is a useful method in aggregating group preference. However, judgments are frequently inconsistent, and, in reality, pairwise comparison matrices rarely satisfy the inconsistency criterion. In this situation, we suggest a new method, called a loss function approach, that uses inconsistency ratio as the group evaluation quality. For this method in detail, we introduce Taguchi's loss function. We also develop an evaluation reliability function to derive group weight. Finally, we provide a step-by-step numerical example of a loss function approach.

Selecting Optimal Specification Limits

This paper presents a new approach to optimal specification limit selection based on using economic and process modeling to maximize profitability. The profit maximization approach is compared with Dr. Taguchi’s loss function approach to specification selection and the results indicate that the new methodology provides significantly different results.

Decision-Theoretic Views on Simultaneous Testing of Superiority and Noninferiority

ABSTRACT In a simultaneous testing of noninferiority and superiority in clinical trials, there is no multiplicity penalty. Ng (2003), however, argues that even though there is no inflation of the Type I error rate, this type of simultaneous testing is problematic because it may lead to loss of power in the subsequent confirmatory trial. And he recommends to conduct only one test chosen on the basis of the sponsor's preliminary assessment. We view the question of whether one should simultaneously test for noninferiority and superiority from a decision-theoretic view point. We develop the loss function approach implicit in Ng's research and compare his recommendation to simultaneous testing procedures indexed by a variety of design parameters. We find that the simultaneous testing procedure generally provides smaller loss than Ng's method, except when the prior distribution allocates a large probability to equivalence of the two treatments.

A Loss function approach to identifying environmental exceedances

A frequent problem in environmental science is the prediction of extrema and exceedances. It is well known that Bayesian and empirical-Bayesian predictors based on integrated squared error loss (ISEL) tend to overshrink predictions of extrema toward the mean. In this paper, we consider a geostatistical extension of the weighted rank squared error loss function (WRSEL) of Wright et al. (2003), which we call the integrated weighted quantile squared error loss (IWQSEL), as the basis for prediction of exceedances and their spatial location. The loss function is based on an ordering of the underlying spatial process using a spatially averaged cumulative distribution function. We illustrate this methodology with a Bayesian analysis of surface-nitrogen concentrations in the Chesapeake Bay and compare the new IWQSEL predictor with a standard ISEL predictor. We also give a comparison to predicted extrema obtained from a “plug-in” goestatistical analysis.

Evaluating Design Choices in Economic Capital Modeling: A Loss Function Approach

This paper considers issues relating to the segmentation or grouping of credit exposures and the potential impact upon economic capital allocation and attribution. When discussing capital allocation, we refer to the assessment of total capital at the portfolio level, while our discussion of capital attribution focuses on getting capital assigned appropriately at the bucket level. We emphasize that a loss or value function must be specified so as to quantify the gains and losses from choosing a more or less granular asset segmentation scheme. Our chosen loss function considers the trade-off between the decrease in sampling variance obtained by combining data to increase sample size and the bias resulting from characterizing unlike assets with the same default probability. The implications are illustrated with several numerical examples that consider accuracy in the estimation of both portfolio-level and asset-level capital requirements. The suggested technique can be used to quantify whether a loss in accuracy from grouping or segmentation is outweighed by the decrease in variance of estimated capital. That is, the loss from grouping is small when the evaluation criterion is the accuracy of estimation of the required total capital; grouping is of more concern when we are interested in getting capital attributed correctly at the bucket level.

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.

Integration of Taguchi's loss function approach in the economic design of x¯‐chart

In this paper we incorporate Taguchi's loss function in the economic design of the control chart. This is done by redefining the in‐control and out‐of‐control costs using Taguchi's loss function. The new model brings Taguchi's off‐line concepts to the classical SPC approach and continues to have the advantages of the economic design model by taking into consideration the cost consequences of the design. Sensitivity analysis with respect to important model parameters is discussed.