Quadratic Quality Loss Function Research Articles

Design a Continuous Sampling Plan Based on Quadratic Quality Loss Function

In this paper, we present the problem of determining the cost-optimal Type I continuous sampling plan (CSP-1 plan) under Taguchi's quality loss function. Assume that the quality fluctuates between two levels according to a two-slate time homogeneous Markov chain. This article proposes the heuristic method for obtaining the optimal inspection policy.

Process improvement in the presence of qualitative response by combining fuzzy sets and neural networks

Improving quality is essential work for manufacturing organizations competing in the global marketplace. Parameter optimization is an efficient technique to achieve process improvement. Most parameter optimization studies primarily focus on the quantitative quality response. Only a few studies address parameter optimization of the qualitative (or linguistic) response. The fuzzy set is a well‐known approach for dealing with the uncertainties of the linguistic description. Additionally, Taguchi’s quadratic quality loss function is an efficient technique to evaluate quality of a product or an operational process. A concept of loss function, fuzzy‐quality‐loss‐function (FQLF), developed in the proposed approach can be viewed as a feasible evaluation index for including the subjective estimation from engineers. Artificial neural networks (ANN) have been successfully employed to model the complexity structure of a system including linear or non‐linear relationships. A novel approach combining fuzzy sets and ANN is proposed in this study to deal with the quality improvement problem of the quality response with a linguistic category. By employing the proposed approach, the information of subjective estimation can be considered, and the optimum continuous settings of control factors can be determined. An illustrative case involving a downset process from a lead frame manufacturer in Taiwan’s Science‐Based Park demonstrates the effectiveness of the proposed approach.

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

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

Optimal asymmetric tolerance design

An asymmetric tolerance design occurs when deviation (from the ideal target) of a quality characteristic in one direction is more harmful than in the opposite direction. Asymmetric tolerances are common in many manufacturing processes. Traditionally, the designer of a manufactured component either would choose the smaller tolerance as the tolerance for both sides of the ideal target, or would set a process mean at the middle of the tolerances. Both methods fail to minimize the expected value of Taguchi's societal quality losses when the quality loss function is asymmetric. Linear and quadratic quality loss functions are considered to determine the optimal value of a process mean that minimizes the expected value of the quality loss function. Also, a quality loss model involving a pokayoke defect prevention procedure is investigated.

Identification and Extensions of Quasiconvex Quality Loss Functions

This paper presents a set of related quasiconvex quality loss functions. Characteristics of quasiconvex functions that are desirable for modeling quality loss are noted. Three frequently used univariate quasiconvex quality loss functions are discussed. Bivariate and multivariate quasiconvex quality loss functions are developed. A set of necessary and sufficient conditions is established for the quasiconvexity of multivariate quality loss functions. An industrial product example is used to illustrate the development of a bivariate quadratic quality loss function.

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

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