Taguchi's Quality Loss Function Research Articles

THE OPTIMUM SELECTION OF IMPERFECT QUALITY ECONOMIC MANUFACTURING QUANTITY AND PROCESS MEAN BY CONSIDERING QUADRATIC QUALITY LOSS FUNCTION

ABSTRACT In this paper, we present a modified economic manufacturing quantity (EMQ) model under the imperfect product quality. Taguchi's quadratic quality loss function is adopted for measuring the product quality. The modified EMQ model denotes the total loss to the society which includes the producer's loss and the customer's loss. The total inventory cost of the modified EMQ model includes the set-up cost, the holding cost, and the product cost. The perfect and imperfect reworks of product are considered in the modified EMQ model, respectively. By solving the modified EMQ model, we can obtain both the optimum combination of EMQ and process mean in order to have the minimum total loss of society.

A Robust Tolerance Design Method Based on Fuzzy Quality Loss

The traditional tolerance design model ignores the impact of noise factor, so that the design may be infeasible due to variations in design constraints. Based on the analysis of fuzzy factors in tolerance design and the limitations of the traditional Taguchi squared quality loss function, a fuzzy quality loss function model utilizing fuzzy theory was introduced. Concepts on fuzzy quality loss and fuzzy quality loss cost were proposed in the model. The characteristics of the new model and the advantages over the traditional Taguchi quality loss function were analyzed. A robust tolerance design model using a fuzzy quality loss function was proposed. An example was given to illustrate the proposed model. Results and comparisons show that the method is suitable and reliable, and makes the conclusions more objective and reasonable.

Concurrent optimisation of a computer vision system’s multiple responses

Computer vision systems can effectively be used to inspect parts/products in unmanned manufacturing cells. Proper development and deployment of a computer vision system for product inspection looks for evaluation of its capability, which is based upon a number of responses such as accuracy and repeatability of the system. However, the performance of a vision system also depends on several factors, e.g. the type of the back-illumination system, colour of the background, distance between the vision camera and the object, angle between the optical axis of the camera and object, processing speed of the developed software etc. Since several factors can be controlled in a vision system’s setting, a number of combinations of the factor levels can be obtained. In this paper, Taguchi methods are used to determine the optimal levels of the controllable factors for the vision system. However, different settings are observed to be optimal for accuracy and repeatability responses. Hence, Harrington’s desirability function, total loss function and Taguchi quality loss function methods are simultaneously applied for multi-response optimisation analysis. The experimental results show that with concurrent optimisation of the vision system’s multiple responses, its performance can be effectively improved.

The economic feasibility of adoption of a new in-pond mechanical grader for food-sized channel catfish ( Ictalurus punctatus)

An economic analysis of an in-pond horizontal floating bar grader for food-sized channel catfish was performed. Data from previously reported field trials were used to determine whether farmer adoption of this grader is economically feasible. Scenarios for four farm sizes (65, 130, 259, and 478 ha) were evaluated. Partial budget, payback period, net present value, internal rate of return, and Taguchi quality loss function analyses were used to quantify and compare economic losses due to deviation from the target fish size. Partial budget results indicated positive net revenue for all farm sizes. Net revenue increased with farm size, market price, and increased dockage penalties. Payback periods ranged from 0.1 to 2.0 years depending on the scenario. Net present values were positive and increased with increasing farm size. Estimated internal rates of return were higher than the current opportunity cost of capital and increased with increasing farm size. The value of the gain in quality from reducing size variation from use of the UAPB grader was estimated to range from $770 to $5575/year, depending on farm size. Producer adoption of the UAPB grader is economically feasible for the scenarios analyzed.

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.

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.

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.

Simultaneous Optimisation of Multiple Quality Characteristics in Manufacturing Processes Using Taguchi's Quality Loss Function

Taguchi methods have proved to be successful over the last fifteen years or so for the improvement of product quality and process performance. Most Taguchi experiments are concerned with the optimisation of a single quality characteristic. Optimisation of multiple quality characteristics in manufacturing processes is not common and has received very little attention among the Taguchi practitioners. Many engineers using Taguchi methods have employed pure engineering judgement when dealing with multiple quality characteristics in manufacturing process optimisation. This approach is very subjective and therefore always brings an element of uncertainty to the decision-making process. This paper presents an alternative approach for tackling such optimisation problems using Taguchi quality loss function analysis, the paper also presents a case study to illustrate the potential of the proposed methodology.

SOLVING MULTI-RESPONSE PROBLEMS THROUGH NEURAL NETWORKS AND PRINCIPAL COMPONENT ANALYSIS

ABSTRACT In this study, we propose a four-phased procedure based on neural networks and principal component analysis to resolve the parameter design problems with multiple responses. The quality characteristics of a product are first evaluated through Taguchi's quality loss function. A backpropagation neural model is then trained to map out the functional relationship between control factors and responses' quality loss. The functional relationship is then fed into the principal component analysis procedure to transfer a set of responses into a set of uncorrelated principal components. A feasible combination of control factors can be obtained through the recalling function of a backpropagation neural model. Therefore, the conflict for determining the optimal combination of control factors in a multi-response problem can be greatly reduced. The proposed procedure is illustrated with a case study of a fused optical fiber coupling process. The confirmation experiment also yields a satisfactory result. The proposed procedure is relatively simple and could be implemented easily by using ready-made neural and statistical software.

Choosing a lower specification limit for an exponential process with ‘the larger the better’ tolerance: A simple, exact solution

Chen (1999) proposed an economic design, using Taguchi's quality loss function, for choosing a producer's lower specification limit eta for a product with a quality characteristic that has an exponential distribution with mean θ and 'the larger the better' tolerance. Chen (1999) developed an approximate solution that is applicable when 0.5 r m /θ r 0.7 and that requires numerical minimization. We derive a simple, exact solution that is applicable for all values of m /θ and does not require numerical minimization.

Dynamic management of cutting tools for flexible and quality machining

Traditional economic tool-life models assume a homogeneous cutting environment, where a tool's continued service is irrespective of its condition. It is wellknown that the quality of a machining process is significantly impacted by a tool's wear-and-tear. To ensure good machining quality, tool assignment should consider the wear level of the tool as well as the type of machining job to be performed. This paper presents a dynamic management model for cutting tools that emphasizes the cost of machining quality. The model describes a heterogeneous environment typical of computerized manufacturing systems, where a tool carries out variable machining assignments during its life. The formulation is a stochastic dynamic programme, which determines optimal preventive actions based on a periodic evaluation of the tool's operating conditions. Tool deterioration is described as movement to different operating states (increasing levels of tool wear) and job assignment of tools is state-dependent. A tool's optimal economic life is also determined within the context of variable machining. The cost of quality-deviation is assessed using Taguchi's quality-loss function.

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.

Specification limit under a quality loss function

The purpose of this paper is to present the problem of selecting a lower specification limit under Taguchi's quality loss function. Considering that the product quality characteristic obeys an exponential distribution, we propose a modification of the method of Kapur and Wang for the economic design of the specification limit.

Calculating derivatives in statistical tolerance analysis

Current statistical tolerance analysis techniques rely on Monte Carlo estimation. The typical Monte Carlo analysis does not provide derivative information however, so it is poorly suited to tolerance synthesis where derivatives are important in determining the next set of tolerances to analyze. Skowronski and Turner (Skowronski V.J. and Turner J.U., Using Monte Carlo variance reduction in statistical tolerance synthesis, Computer-Aided Design, 1997, 29, (1), 63–69) 1 proposed a method for estimating the derivatives of the Taguchi Quality Loss function with respect to tolerance values. This paper extends that derivative estimation technique to tolerance analysis problems that use the acceptance fraction criterion. The application of two variance reduction techniques to derivative estimation is also described. Finally, the accuracy of the techniques in this paper are compared to the finite difference calculation. It is concluded that the derivative estimation of Skowronski and Turner 1 provides equivalent or better accuracy than finite difference, and has the added advantage that the derivative of more than one tolerance can be calculated without a new analysis for each derivative.

分解的アプローチによる品質設計法 (第1報)

This paper presents a new method of designing a product in consideration of its quality, or solving the design-for-quality problem of the product, with decornpositional approach, assuming that the product is decomposed into plural parts in parallel. At the stage of product design, product quality is evaluated with Taguchi's quality loss function, which can be regarded as a measure of the generalized quality cost of the product, and its expected value is often estimated through statistically designed experiments. The proposed method derives the solution of the design-for-quality problem from performing plural small groups of experiments, which are concerned with each part of the product respectively, instead of conducting a huge group of experiments about the whole of the product, so that the scale, complexity and difficulty of the experiments are reduced. Further, the effectiveness of the method is investigated through an example.

解析的アプローチによる品質設計法

This paper presents an analytical approach to the problem of designing a product in consideration of its quality, i.e. the design-for-quality problem. At the stage of product design, product's quality is evaluated with Taguchi's quality loss function, which can be regarded as a measure of the generalized quality cost of the product. In the concept of the generalized quality cost, not only the traditional quality cost, which is defined as the manufacturer's cost of quality, but also the user's cost of quality and the social cost of quality are included. At first, the design-for-quality problem is formulated as a problem to minimize the expected sum of the fundamental manufacturing cost and the generalized quality cost of a product. Then, an analytical approach to this problem is proposed, assuming that the relation among quality characteristics, design parameters and noize parameters is available. In this approach, the solution of this problem is derived without performing experiments. Further, the effectiveness of this approach is investigated through an example.

ON‐LINE QUALITY MANAGEMENT: INTEGRATION OF PRODUCT INSPECTION AND PROCESS CONTROL

A growing recognition that quality management is an important factor in defining a firm's competitive position has led to renewed attention to this function and has resulted in implementation of elaborate systems for on‐line quality control comprising product inspection and process control. Traditionally, these functions have been treated independently, with very little interaction. In this paper we examine, in detail, a scheme that integrates the two functions, and we demonstrate that such an approach can result in significant cost savings. The motivation for this work comes from our experience in a wafer fabrication facility that suggested that exchange of quality information between different stages of production could result in significant performance improvements. To illustrate this approach, we consider a specific environment characterized by a single‐stage continuous production process whose status is monitored by an X̄ control chart. We assume that quality‐related costs may be described as a function of the process output. This is analogous to Taguchi's quality loss function and may be interpreted as a generalization of conventional classification of process output as either acceptable or defective units. The integrative scheme essentially relies on utilization of the process status information (based on process control) in making product inspection decisions. For this system we derive a cost model and develop a solution procedure to determine optimal decision parameters. Limited computational results indicate that the scheme has significant potential for reducing quality‐related costs.

Optimization of mechanical assembly tolerances by incorporating Taguchi's quality loss function

In an end-to-end mechanical assembly, optimization of tolerance allocation is a critical issue. Many papers have concentrated on minimum cost-tolerance allocation without considering the quality of the final assembly. The objective is to examine the optimal tolerance allocation by considering both tolerance cost and quality loss so that the total assembly cost is minimized. In this paper, a sensitivity analysis is also conducted to determine the effects of shifts in a component's mean and variance. We find that if a component's mean varies, only the quality loss associated with that component will be changed. If a component's variance shifts, the optimal allowance, tolerance costs, and quality losses associated with each component will be affected.