Taguchi's Quality Loss Function Research Articles

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.

Economic production order quantity and quality

The purpose of this study is to integrate a conventional production-inventory management approach and a process-quality design approach so as to promote quality and reduce costs. Because the integration of these two approaches into a single system is conducted under the influence of a deterioration process, estimated costs of production must be modified. Only then can these various costs be presented as a total cost for the present integrated system. This total cost includes: a setup cost for production reordering and process resetting, quality-related costs stemming from the loss of product quality along with a tolerance-related production process cost and a failure cost for product defects, backorder costs for production shortage, carrying costs generated by the storing and handling of inventory, and material costs for determining the process mean. The Taguchi quality loss function is introduced to assess quality loss in the system. The decision variables include the initial setting (process mean), process tolerance, and production order quantity. These variables need to be determined simultaneously to minimise the average total cost for a cycle time. An example is presented to demonstrate the proposed approach.

Bionic Fan Optimization Based on Taguchi Method

In this research, the multi-response optimization of mass flow rate and A-weighted SPL using Taguchi quality loss function has been done for bionic fan performance. The factors of the geometric parameters selected in this investigation are blade number, boss ratio, and blade stagger angle. The contribution of each parameter factor to the performance of bionic fan has been determined. The blade stagger angle has been found as the most effective factor and its contribution is 52.58% on multiple quality characteristics. The verification test has also been performed based on the optimum conditions predicted. The values of the mass flow rate and the A-weighted SPL at the optimum levels of the fan parameters are 0.4518 kg/s and 61.47 dB(A), respectively against the initial fan of 0.3438 kg/s and 70.50 dB(A). The mass flow rate and the A-weighted SPL have been increased by 0.1080 kg/s and decreased by 9.03 dB(A), respectively. The optimization results demonstrate considerable improvement in both mass flow rate and A-weighted SPL with the multiple response optimization combination, as compared with those of the initial fan.

Optimization of Multi-Response Problems Using Taguchi's Quality Loss Function Based on Grey Relational Grade

This article presents an approach which first combines grey relational grade and weighted quality loss function to convert the values of multiple responses obtained from each of the Taguchi orthogonal designed experiments into a single performance evaluation value. Then the analysis of variance (ANOVA) and the SN ratio based Taguchi analysis are conducted to find out respectively the relative importance of the process parameters and a set of near optimal parameter settings. A validation experiment is then conducted to confirm the finding. A case of multi-response turning process optimization is used to illustrate the proposed approach. Two sets of weights for the total quality loss were applied and the results were compared. The effectiveness of this approach was demonstrated by the improvement of turning performance in the both weight settings.

Multi-response optimization of oil agglomeration with multiple performance characteristics

In this paper, the multi-response optimization of grade and recovery simultaneously using Taguchi quality loss function has been done for Zonguldak/Turkey bituminous coal by oil agglomeration. The controllable factors selected in this investigation are solid content, amount of oil, agitation time and agitation rate. The percentage contribution of each controllable factor has been determined on the performance of oil agglomeration. The amount of oil has been found as the most effective factor and its contribution is 65.42% on multiple quality characteristics. The confirmation experiment has also been carried out according to the optimum conditions predicted. The grade and recovery have been increased up to 0.565% and 93.04%, respectively against the initial value of grade and recovery as 0.436% and 75.08%, respectively. The results show considerable improvement in both the quality characteristics such as grade and recovery with the multi-response optimization used, as compared the initial value of grade and recovery.

Applying Taguchi method to determine the target values in goal programming

Setting the right target is of utmost importance in goal programming. An erroneous or an unreasonable target can lead to inferior solutions, resulting in misallocation of resources. This paper, using Taguchi's quality loss function proposes a systematic approach for setting an appropriate achievement level for goals in goal programming. The application of the proposed model is illustrated through a case study.

Multi-objective optimization of some process parameters of a multi-gravity separator for chromite concentration

The multi-gravity separator (MGS) is one of the fine particle mineral concentration machines based on gravity separation. Concentration performance, indicators such as grade and recovery, depends on appropriate selection of process parameters. Maximum concentrate grade and maximum recovery is of today’s demand with MGS concentration as it is with many concentration processes. To date, no experimental study on MGS has been done for grade and recovery simultaneously. In this paper, the multi-objective optimization of grade and recovery using the Taguchi quality loss function has been carried out for chromite concentration with MGS. The input process parameters considered are drum speed, tilt angle, wash water flow rate, and shake amplitude. The results show considerable improvement in both the quality characteristics such as grade and recovery with multi-objective optimization, compared to the initial value of grade and recovery.

Optimal settings for vision camera calibration

As machine vision system has significant applications in computerized inspection systems, the precise calibration of it is essential to enhance its application potential. The parameters, namely, illumination intensity, length of extender tube, number of control points, and region of interest influence the accuracy and repeatability of calibration. The objective of this study is to determine the optimal settings of the parameters in the operating environment that will maximize the performance of the machine vision system. This paper considers the above-mentioned four factors as the influencing parameters on accuracy and repeatability of calibration and distorted image plane error (DIPE) as a measure of its performance. The Taguchi method-based orthogonal array is applied to evolve the independent optimal settings and the percentage contributions of various parameters on accuracy and repeatability. In addition to the independent optimization, the settings for simultaneous optimization of accuracy and repeatability are evolved with desirability function, total loss function, and Taguchi quality loss function. The optimal settings under independent and simultaneous cases are analyzed and reported.

The Application of Analytic Hierarchy Process to Determine Proportionality Constant of the Taguchi Quality Loss Function

Taguchi's philosophy of quality improvement is quite unique and challenging. Traditionally, quality management focused on conformance to specifications within a given range. In Taguchi's philosophy, the aim of quality management should be achieving a specific target value. Any deviation from the predetermined target value results in a loss (e.g., due to customer dissatisfaction). Taguchi measures this loss with a quadratic function called quality loss function (QLF). An important component of QLF is the proportionality constant ( ). An inaccurate or erroneous value for can result in misallocation of the organizational resources and can easily lead to chaos in quality management efforts. Thus, an accurate estimate for is of utmost importance. This paper proposes a new methodology for calculating the proportionality constant . To this end, the analytical hierarchy process is used to estimate the value of the proportionality constant in QLF. It is argued that the proposed methodology takes into account the relative importance of various quality characteristics and captures different levels of sensitivity along the loss function. Both symmetric and asymmetric loss functions are considered.

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.

Multi-Objective Optimization of Setting of Resistance Spot Welding Machine using Taguchi's Quality Loss Function

Multi-Objective Optimization of Setting of Resistance Spot Welding Machine using Taguchi's Quality Loss Function

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.

Optimization of kerf quality during pulsed laser cutting of aluminium alloy sheet

In laser beam cutting (LBC) process, the cut quality is of great importance. The quality of laser cut kerf mainly depends on appropriate selection of process parameters. Uniform kerf with minimum kerf width is of today's demand. It has been found that the kerf width during LBC is not uniform along the length of cut and the unevenness is more in case of pulsed mode of LBC. Till date, no experimental study has been done for kerf unevenness or kerf deviation along the length of cut. In present paper, two kerf qualities such as kerf deviation and kerf width have been optimized simultaneously using Taguchi quality loss function during pulsed Nd:YAG laser beam cutting of aluminium alloy sheet (0.9 mm-thick) which is very difficult to cut material by LBC process. A considerable improvement in kerf quality has been achieved.

Multi-objective optimisation of laser beam cutting process

This paper presents a hybrid Taguchi method and response surface method (TMRSM) for the multi-response optimisation of a laser beam cutting process. The approach first uses the Taguchi quality loss function to find the optimum level of input cutting parameters such as assist gas pressure, pulse width, pulse frequency and cutting speed. The optimum input parameter values are further used as the central values in the response surface method to develop and optimise the second-order response model. The two quality characteristics Kerf width (KW), and material removal rate (MRR), that are of different nature (KW is of the smaller-the-better type, while MRR is of the higher the better type), have been selected for simultaneous optimisation. The results show considerable improvement in both the quality characteristics when the hybrid approach is used, as compared the results of a single approach.

Robust parameter design and multi-objective optimization of laser beam cutting for aluminium alloy sheet

The application of laser beam for precise cutting of sheet metals, in general, and reflective sheet metals, like aluminium, in particular, has become of interest in the recent past. The optimum choice of the cutting parameters is essential for the economic and efficient cutting of difficult to cut materials with laser beams. In this paper, a robust design and quality optimization tool called the Taguchi methodology has been applied to find the optimal cutting parameters for cutting of a reflective sheet made of aluminium alloy with a Nd:YAG laser beam. All the steps of the Taguchi method, such as a selection of orthogonal array, computation of signal-to-noise ratio, decision of optimum setting of parameters, and the analysis of variance (ANOVA), have been done by a self-developed software called computer aided robust parameter design (CARPD). A considerable improvement in the kerf taper (KT) and material removal rate (MRR) has been found by using Taguchi method-based predicted results. Confirmatory experimental results have shown good agreement with predicted results. Further, the Taguchi quality loss function has also been used for multi-objective optimization of laser beam cutting of Al-alloy sheet. The results of multi-objective optimization are compared with the single-objective optimization and it has been found that the kerf taper was increased by 1.60% in multi-objective optimization while the MRR was same in both cases.

Sequential optimization of parameter and tolerance design for multiple dynamic quality characteristics

System design, parameter design and tolerance design are the three stages of design process as presented by G. Taguchi. Systems design identifies the basic elements of the design to provide new or improved products to customers. Parameter design determines the optimal parameter settings, which will minimize variation from the target performance of the product. Tolerance design finally identifies the components of the design, which are sensitive in terms of affecting the quality of the product, and establishes tolerance limits that will give the required level of variation in the design. Most studies have focused primarily on optimizing the parameter design or tolerance design for multiple static quality characteristics. In this paper, a mathematical formula corresponding to the model is derived from Taguchi's quadratic quality loss function to minimize the expected total cost for the parameter design of multiple dynamic quality characteristics. When the optimal parameter design is not sufficient to reduce the output variation, the first-order Taylor series expansion is then used to analyse the variations of noise factors for optimizing the tolerance design. It concludes with an example demonstrating this approach.

Multi-Response Optimization of CFAAFM Process Through Taguchi Method and Utility Concept

Centrifugal force assisted abrasive flow machining (CFAAFM) process has recently been tried as a hybrid machining process with the aim towards the performance improvement of AFM process by applying centrifugal force on the abrasive laden media with a rotating centrifugal force generating (CFG) rod introduced in the work piece passage. For optimization of process parameters, an approach based on a Utility theory and Taguchi quality loss function (TQLF) has been applied to CFAAFM for simultaneous optimization of more than one response characteristics. Three potential response parameters i.e., material removal, % improvement of surface finish and scatter of surface roughness over the fine finished surface of a sleeve type work piece of brass are examined. Utility values based upon these response parameters have been analyzed for optimization by using Taguchi approach.

The Modified Pulak and Al-Sultan's Model for Determining the Optimum Process Parameters

Economic selection of process parameters has been an important topic in modern statistical process control. The optimum process parameters setting have a major effect on the expected profit/cost per item. There are some concerns on the problem of setting process parameters. Boucher and Jafari (1991) first considered the attribute single sampling plan applied in the selection of process target. Pulak and Al-Sultan (1996) extended Boucher and Jafari's model and presented the rectifying inspection plan for determining the optimum process mean. In this article, we further propose a modified Pulak and Al-Sultan model for determining the optimum process mean and standard deviation under the rectifying inspection plan with the average outgoing quality limit (AOQL) protection. Taguchi's (1986) symmetric quadratic quality loss function is adopted for evaluating the product quality. By solving the modified model, we can obtain the optimum process parameters with the maximum expected profit per item and the specified quality level can be reached.