Taguchi Loss Research Articles

Dynamic Pricing Model for Batch-Specific Tolerance Allocation in Collaborative Production Networks

In high-tech production, non-conforming products can result from an unfavorable combination of components, even if the individual components are within specification. Quality control strategies aiming to prevent said combinations such as selective assembly, adaptive manufacturing, or tolerance allocation haven't been applied across company borders yet due to the lack of incentives to share data and adapt parameters. The article presents a pricing model to incentivize batch-specific tolerancing of supplier parts. We use Taguchi's loss function to quantify the expected quality costs based on the resulting distribution of the product's predicted functional deviation after assembling varying batches of matching components.

Optimization of Fractal Dimension of Turned AISI 1040 Steel Surface Considering Different Cutting Conditions

The present work examines the effect of turning process parameters, namely depth of cut and feed rate on the fractal dimension of AISI 1040 steel. Machined surfaces have been characterized using fractal dimensions. Apart from the aforesaid conventional turning parameters, cutting condition has been also considered as a design variable. Three cutting conditions have been considered, e.g. dry, water lubricated, and commercially available water-soluble emulsion lubricated condition. The depth of cut and feed rate has been also been varied at three levels. Experiments were performed following Taguchi's L9 orthogonal array. The optimal setting of process parameters has been achieved through the use of Taguchi's quality loss function represented by a signal-to-noise ratio. The optimal condition predicted from Taguchi's analysis is a 0.4 mm depth of cut, a 0.07 mm/rev feed rate and a water-based emulsion cutting environment. The results obtained for fractal dimensions has been also compared with the more conventional roughness parameter centre line average roughness which is dependent on instrument resolution.

Effects of quality characteristic distributions on the integrated model of Taguchi's loss function and economic statistical design of -control charts by modifying the Banerjee and Rahim economic model

ABSTRACTAlthough the normality is a usual assumption for quality measurements, it may be erroneous and misleading in many industrial applications of quality control online models. In addition, incorporating Taguchi's loss function to these inspection activities leads the management to better decisions. In this paper, the integrated model of Taguchi's loss function and the economic statistical design of -control charts are investigated under both normal and non normal quality data. This purpose has been achieved by modifying the cost model of Banerjee and Rahim (1988) in which a non uniform sampling scheme is utilized for systems with increasing failure rate and Weibull shock model. For the same values of time and cost quantities and Weibull distribution parameters, the effects of three most popular quality characteristic distributions (Normal, Burr, and Johnson) that are fitted on a case study data in Rahim (1993) are studied and compared. The optimal parameters of both economic and economic statistical designs reveal that there is an insignificant difference between Normal and Burr distributions, whereas a relative difference can be observed in the case of Johnson distribution.

Simultaneous settings of order quantity, wholesale price, production run length, process mean, and warranty period

In this article, the authors propose a modified version of S.L. Chen and Liu's model with a two-stage production system. Assume that the retailer's order quantity is concerned with the manufacturer's selling price and the warranty period of product. The used cost of the customer is measured under the Taguchi's quadratic quality loss function and concluded in the retailer's profit function. The quality of the lot for the manufacturer is determined by adopting a two-stage single sampling rectifying inspection plan. The modified economic manufacturing quantity (EMQ) model is addressed in formulating the manufacturer's expected profit. The retailer's order quantity, manufacturer's wholesale price, production run length, process mean, and warranty period of product will be jointly determined by maximizing the total expected profit of the supply chain system including the manufacturer and the retailer. Finally, the quality investment policy is introduced to illustrate the profit improvement for the supply chain system.

Simultaneous determination of manufacturer's process mean and production run length, and retailer's order quantity

In Chen and Liu's optimum profit model with a traditional production system, they did not consider the effect of product quality on the customer's demand order quantity, and also ignored the used cost of customers for product. In fact, the customer's demand quantity is always seriously related to product quality. Hence, in the present paper, we modify Chen and Liu's model to address the determination of the optimal process parameters by employing the idea of quality loss and single sampling rectifying inspection plan. Assuming that the quality characteristic of the product is normally distributed, Taguchi's symmetric quadratic quality loss function is applied in evaluating the product quality. Three decision variables, i.e., the mean of the process characteristic, the production run length of the product and the retailer's order quantity, are jointly determined in our modified model to maximize the expected total profit of society, which includes both the manufacturer and the retailer. A heuristic solution procedure is developed for this optimization problem, and a numerical example is provided for illustration. From the numerical results, it can be seen that both the sale price per unit and the intercept of the mean demand of the customer are two major (or significant) parameters in the model and should be more accurately estimated in practice. Finally, the quality investment policy is provided to compare its effect on the optimum profit model with quality improvement.

Modified Imperfect Economic Manufacturing Quantity Model with Limited Investment Capital

Traditional economic manufacturing quantity model assumes that the perfect product for production. Recently, Teng proposes an imperfect production process with limited investment capital for determining the optimal investment cost and production run time. Teng assumes that the percentage of process defectives with uniform distribution is a decreasing function of the investment cost. However, Teng's model does not include the customer's used cost for the conforming product. In this study, the authors adopt another investment cost function, i.e., the exponential reduction of process mean and standard deviation as the function of quality investment cost, for formulating the modified Teng's model. Taguchi's quadratic quality loss will be used for measuring the product quality. Finally, the numerical example and sensitivity analysis of parameters are provided for illustration.

Modelling in selective assembly with symmetrical interval-based Taguchi loss function for minimising assembly loss and clearance variation

The functional performance of an assembled product depends upon its component tolerance and assembly clearance. For producing components with tight tolerance, advanced machining process may be required but it will increase the product cost. In any manufacturing process, final step is assembly and plays a vital role in determining the product quality. The selective assembly is a method of assembly that provides an effective way for producing high precision product from low precision components. The conventional Taguchi's loss function targets on a single value but in real situations an interval of values will be essential. To overcome this issue, a symmetrical interval-based Taguchi (SIT) loss function is proposed in this paper and it is applied into the selective assembly method to evaluate the assembly loss. Also, an improved sheep flock heredity (ISFH) algorithm is proposed to obtain the best combination of selective group with minimum clearance variation and least assembly loss value.

Assessment of Cpm in the presence of measurement errors

With the advent of Taguchi's loss function, the concept of target and sticking to the target to achieve better process performance has become widely accepted. In practice, while estimating process performance, the gauge measurement error is not taken into consideration. In the real world scenario this hardly happens since measurement errors cannot be avoided in most of the manufacturing processes. Ignoring this measurement error while estimating the process capability may often lead to unreliable/wrong decision about the capability of the process under study. Therefore, in this work we apply the method of Generalized Confidence Interval (GCI) to measure the process capability index ܥ ௣௠ in presence of measurement errors. In this study, an exhaustive set of simulation has been conducted to assess the performance of the GCI method in terms of expected value of generalized lower confidence limit (ܮ ௣௠) and Coverage Probability (CP). The efficacy of dealing with the measurement error has been found satisfactory in this model. Finally it can be concluded that GCI method seems to be quite satisfactory for measuring process capability when the measurement errors are present; as well as when measurement error is negligible.

Minimising assembly loss for a complex assembly using Taguchi's concept in selective assembly

The component tolerance and assembly variation determines the quality of any product. For producing high precision product it requires high accuracy operations both in machining and assembly. Advanced machining process can be used to produce high precision product but it will increase the manufacturing cost as well as cost of the product. In such cases, selective assembly provides an effective way for producing high precision product from relatively low precision components. According to Taguchi's concept, manufacturing a product within the specification may not be sufficient and it must be manufactured to the target dimension. In this article, artificial immune system (AIS) algorithm is developed to obtain the best combination of selective group with minimum clearance variation and least assembly loss value within the specification range. The concept of Taguchi's loss function is applied into the selective assembly method to evaluate the deviation from the mean.

A Proposal for a Management-Oriented Process Capability Index

During the past three decades, PCIs – process capability indices – have inspired hundreds of pages of scientific research. The trade-off between simplicity and precision in reproducing an overall process quality prediction is both the reason behind the criticism for Cp and Cpk and the motive for their widespread use. Indeed, their strength in simplifying the assessment of a process control status compensates for some of the statistical shortcomings largely recognized in the literature, amongst which is the normality assumption. Hence, this article aims at overcoming the main statistical problems of Cp and Cpk indices by proposing a new indicator, still compliant with the traditional PCIs approach, but applicable for cases of non-normal processes while being simple to implement and easy to interpret. The proposed indicator is composed of three sub-indices, each related to a specific process characteristic: how the process is repeatable, how much the data distribution is skewed about the mean value and how much the process data comfortably lies between the specifications limits. On top of this, a specific parameter allows designers or quality engineers to modify the index value range in order to finetune the effect of the cost of Taguchi's loss function. The article presents the theoretical structure of the new indicator and an extensive numerical test on several different processes with different distributions upon multiple specification limit combinations, along with a comparison to the Cpk index, in order to demonstrate how the new index provides a clearer indication of the process criticalities.

A Statistical Solution to Mitigate Functional Requirements Coupling Generated from Process (Manufacturing) Variables Integration-part I

Utilizing the Axiomatic Design (AD) principles to develop a perfect product, design of a manufacturing system with minimal complexity is required. For the purpose of reducing the manufacturing system complexity, theoretically, it is preferred to integrate multiple Process Variables (PVs) of the product into a single process unit. However, due to significant presence of some active noise factors, this integration practice may result in failing to maintain the independence among some of Functional Requirements (FRs) of the product. This event is the result of statistical causal relationships unintentionally developed among a subset of the integrated PVs. In such a condition, the AD's Independence Axiom cannot be successfully satisfied and reaching a system with minimal complexity is inconceivable, even though an uncoupled or decoupled system design is apparently presented. To mitigate this kind of FRs coupling generated from the PVs integration, this study proposes partial & semi-partial correlation analysis as a statistical solution to identify the most appropriate integration choices where integrating a subset of the PVs is inevitable. Furthermore, based on the Taguchi's loss function, a quantitative criterion is established to fairly compare any two non-ideal manufacturing system designs and choose the one with relatively lower loss. The proposed approach explained in this study is verified based on hypothetical data.

Economic-Statistical Design of EWMA Control Charts Based on Taguchi's Loss Function

This paper proposes an economic-statistical design of the EWMA chart with time-varying control limits in which the Taguchi's quadratic loss function is incorporated into the economic-statistical design based on Lorenzen and Vance's economical model. A nonlinear programming with statistical performance constraints is developed and solved to minimize the expected total quality cost per unit time. This model, which is divided into three parts, depends on whether production continues during the period when the assignable cause is being searched for and/or repaired. Through a computational procedure, the optimal decision variables, including the sample size, the sampling interval, the control limit width, and the smoothing constant, can be solved for by each model. It is showed that the optimal economic-statistical design solution can be found from the set of optimal solutions obtained from the statistical design, and both the optimal sample size and sampling interval always decrease as the magnitude of shift increases.

Modified optimum profit model with single supplier and multi-retailers under the consignment policy

In this study, the authors propose a modification of the consignment policy model presented by Chen and Liu in 2007, with imperfect product quality, a single supplier and multiple retailers. A 100% inspection of the product is considered. Conforming product from the supplier is sold to the customer and non-conforming product is scrapped and sold at a lower price. Taguchi's quadratic quality loss function is used for measuring product quality. The optimum supplier's process mean, per-unit commission, fixed commission fee, and production run length and each retailer's economic order quantity will be jointly determined under the maximum expected total profit including the single supplier and multiple retailers. Numerical results show that the selling price per unit and the mean of the customer demand have major effects on the expected profit of the supply chain system.

Quantitative evaluation of quality loss for fraction defective case using Taguchi's quality loss function

The conventional perception about the quality of the product was concentrated only around the specification limits. If the product characteristic was within the specifications, it was found to be good and accepted for use. If it did not meet the specifications, the product was rejected, or reworked and used. This is the concept of step function. Taguchi’s quality loss function, which is quadratic in nature, evaluates the quality even when the product characteristic is within the specification. This paper discusses the application of Taguchi’s quality loss function to evaluate the quality loss during spline hobbing operation of a shaft manufacturing process. The quality characteristic considered here is fraction defective type. The fraction defective data has been collected from five industries manufacturing the same kind of shaft; Taguchi’s loss function has been applied and average quality loss has been calculated for each of the industries. The loss function graphs are constructed for these industries for the purpose of comparison. Using the loss function, the industries having a comparatively larger quality loss are identified and necessary action has been suggested to improve their product quality.

Considering Taguchi loss function on statistically constrained economic sum of squares exponentially weighted moving average charts

In this paper, Duncan's cost model combined Taguchi's quadratic loss function is applied to develop the economic-statistical design of the sum of squares exponentially weighted moving average (SS-EWMA) chart. The genetic algorithm is applied to search for the optimal decision variables of SS-EWMA chart such that the expected cost is minimized. Sensitivity analysis reveals that the optimal sample size and sampling interval decrease; optimal smoothing constant and control limit increase as the mean and/or variance increases. Moreover, the combination of optimal parameter levels in orthogonal array experiment plays an important guideline for monitoring the process mean and/or variance.

An integrated EPQ model based on a control chart for an imperfect production process

The notion of quality control is introduced into the classic economic production quantity (EPQ) model. Based on previous research, this paper contributes to an integrated EPQ model combining the concepts of statistical process control and maintenance. An imperfect production process involving three different conditions is considered. A control chart is adopted to monitor the whole process with Taguchi's loss function estimating the quality cost of each condition. A corresponding maintenance policy is planned for the machine depending on what condition it runs in. Thus the proposed EPQ model takes quality-related costs and maintenance-related costs into account other than storage costs and ordering costs already considered in the classic model. The objective of this model is to minimise the total expected production cost per production cycle while simultaneously determining the optimal parameters of control chart design, the interval between sampling, the sample size and the maintenance decision policy. The pattern search method is used to solve the problem using the MATLAB toolbox. In addition, a case study, sensitivity analysis and comparison analysis are presented to demonstrate the application of the model.

An integrative supplier selection model using Taguchi loss function, TOPSIS and multi criteria goal programming

Some of the key factors affecting the selection of supplier are price, quality, delivery, satisfaction, and warranty degree. The present paper is an extension of previous related work to select the appropriate supplier. This paper deals with an integrative approach considering Taguchi's loss function, Technique for Order preference by similarity to ideal solution (TOPSIS) and Multi criteria goal programming. The model is split up into three phases. In the first phase, the quality losses are identified using Taguchi's loss function. In the second phase, suitable factors are identified with different weights from TOPSIS and in the third phase, a goal programming model is developed to identify the best performing supplier with the weights and the loss associates. The purpose of this paper is to integrate different criteria levels to select relatively better performing supplier. A case is also presented and finally a comparison with data envelopment analysis (DEA) is discussed.

Concurrent Tolerance Design System Based on Manufacturing Context

This paper introduces a computer-aided concurrent tolerance design system based on real manufacturing resources (CATFM), which can ensure the optimal robust tolerance and consider real manufacturing resource owned by the factory. Firstly, the concurrent tolerance design model which can get balance between quality and cost utilizing Taguchi's quality loss function is proposed. Then the principle of concurrent tolerancing is concisely depicted through analyzing the overall structure of the system, and the design method is described in detail. Finally, an example is adopted to illustrate the proposed system.

Optimum profit model considering production, quality and sale problem

Chen and Liu [‘Procurement Strategies in the Presence of the Spot Market-an Analytical Framework’, Production Planning and Control, 18, 297–309] presented the optimum profit model between the producers and the purchasers for the supply chain system with a pure procurement policy. However, their model with a simple manufacturing cost did not consider the used cost of the customer. In this study, the modified Chen and Liu's model will be addressed for determining the optimum product and process parameters. The authors propose a modified Chen and Liu's model under the two-stage screening procedure. The surrogate variable having a high correlation with the measurable quality characteristic will be directly measured in the first stage. The measurable quality characteristic will be directly measured in the second stage when the product decision cannot be determined in the first stage. The used cost of the customer will be measured by adopting Taguchi's quadratic quality loss function. The optimum purchaser's order quantity, the producer's product price and the process quality level will be jointly determined by maximising the expected profit between them.

Capability index of a complex-product machining process

A complex product often requires a high machining precision. This is often achieved by a close-loop machining process to be carried out in several stages, and the measurements, fixture adjustments, and feedback or feed-forward control are inserted after each of these stages. The Complex Product Machining Process (CPMP) Capability Index (CPMPCI) is affected by the control and adjustments in a CPMP, and hence the calculation results of CPMPCI can be used as references to select a proper CPMP. In this paper, we present a novel calculation method of CPMPCI as quality control and improvement technology in a CPMP. A linear model is proposed for describing the variation propagation effect throughout all stages in a CPMP, and an observation model with the pre-specified control and adjustment strategy is employed to calculate the process mean and variation during a CPMP. Finally, through application of Taguchi's quality loss function, the CPMPCI calculation method is derived. The feasibility and effectiveness of this method are validated by a case study on a three-stage CPMP.