Quality Cost Function Research Articles

Quality cost-based allocation of training hours using learning-forgetting curves

The training of suppliers and inbound quality inspectors is a common strategy to increase the quality performance of the supply chain but, under budget constraints, these actors compete for a limited amount of training hours. The proposed model aims to allocate the available training hours so as to minimise a total quality cost function composed of prevention, appraisal, and failure costs; it also sets the inspection rates defining the inspection policies assigned to suppliers. The relationship between decision variables and costs is expressed through organisational and individual learning-forgetting curves, for suppliers and quality inspectors respectively, and the effect of the training hours on quality improvement is measured in terms of failure rates. To the best of our knowledge, a total quality cost model with such decision variables is new in the related literature, as it is a model including both organisational and individual learning-forgetting phenomena.A nonlinear optimisation approach was adopted to solve this complex problem. The experimental section includes a decision trees analysis of simplified scenarios in order to interpret the model functioning, as well as a complex numerical example to extrapolate managerial insights.

Hidden quality cost function of a product based on the cubic approximation of the Taylor expansion

The-Nominal-The-Best (N-type) loss function is established based on the Taylor expansion. Results become more accurate as more Taylor expansion items are retained. N-type loss function neglects terms with powers higher than two, which inevitably leads to a certain deviation between the calculated result and the true value. In this paper, Taylor expansion is retained to the third-order, and the quality loss function is extended to three items. The quality loss coefficients of each item are determined, and the asymmetric piecewise cubic quality loss function is established. The deviation between the cubic and quadratic functions is evaluated. The formula for calculating the hidden quality cost of a product is derived by choosing an appropriate density distribution function and using process capability. Two cases are utilised to analyse and discuss the quality loss and hidden quality cost of a product using the cubic quality loss and quadratic quality loss functions. This paper provides a more accurate approach for the study of product quality management.

The Optimal Allocation Combination for the One-Sided Sequential Screening Procedure Based on the Individual Misclassification Error

In this article, the expected total costs of three kinds of quality cost functions for the one-sided sequential screening procedure based on the individual misclassification error are obtained, where the expected total cost is the sum of the expected cost of inspection, the expected cost of rejection, and the expected cost of quality. The computational formulas for three kinds of expected total costs are derived when k screening variables are allocated into r stages. The optimal allocation combination is determined based on the criterion of minimum expected total cost. At last, we give one example to illustrate the selection of the optimal allocation combination for the sequential screening procedure.

The optimal allocation combination for the two-sided sequential screening procedure based on the individual misclassification error

In this paper, the expected total costs (ETCs) of three kinds of quality cost functions for the two-sided sequential screening procedure (SQSP) based on the individual misclassification error are obtained, where the ETC is the sum of the expected cost of inspection, the expected cost of rejection and the expected cost of quality. The general formulas for all the desired probabilities and three ETCs when k screening variables are allocated into r-stages are derived. The optimal allocation combination for each ETC is determined based on the criterion of minimum ETC. Finally, we give two examples to illustrate the selection of the optimal allocation combination for the SQSP.

A Simulation-Based Optimization Approach for Water Quality Management of Xiangxihe River Under Uncertainty

A simulation-based interval quadratic programming (IQP) method was developed for river water quality management, where uncertainties associated with water quality parameters, cost functions, and environmental requirements were described as interval values. IQP was applied to a real-case study of the Xiangxihe River, China. A multisegment simulation model of one river with one tributary was used to generate water-quality transformation matrices and vectors, which were used to establish the river water quality constraints; in addition, the cost function of wastewater treatment were expressed as quadratic form. System cost, wastewater treatment efficiencies, and river pollution situations were analyzed under two scenarios and three criteria. A number of cost-effective schemes were generated by adjusting different combinations of decision variables within their solution intervals. Results can help decision makers generate alternatives between wastewater treatment cost and stream water quality requirement under uncertainty.

Environmental performance measures for supply chains

Purpose – The paper seeks to develop an analytical decision model that is used to investigate the performance of a supply chain when product, process, and environmental quality characteristics are considered.Design/methodology/approach – Environmental performance measures and methods to quantify quality are reviewed and then used to develop a method to measure environmental quality and its associated costs. This was translated into a two‐level supply chain coordination model that captures most aspects of green supply chains. Numerical examples are provided and solved using Excel Solver enhanced with VBA codes.Findings – The results confirmed some findings in the literature that investing to reduce environmental costs improves environmental performance and increases total profits.Research limitations/implications – The environmental quality cost function that was used was of a form that guarantees a global optimal solution. A limitation is that the function may take more complex forms where different analy...

A hybrid ant colony, Markov chain, and experimental design approach for statistically constrained economic design of MEWMA control charts

The multivariate exponentially weighted moving average, MEWMA, control chart is an effective statistical tool for detecting small shifts in process mean vectors. On the one hand, the economic design process of a MEWMA control chart involves determining the main parameters of the chart, namely, the sample size n, the sampling interval h, the smoothing constant r, and the control limit L such that a quality cost function is minimized. On the other hand, the statistically constrained economic design of MEWMA chart is to determine the chart parameters such that a cost function is minimized while the statistical performance of the chart is maintained at a desire level. In this paper, the statistically constrained economic design model of the MEWMA control chart is first extended by the Taguchi loss function to improve its effectiveness. Next, an ant-colony optimization algorithm is proposed to solve the model in which a Markov chain approach is developed to calculate the average run lengths, ARLs. Then, the main parameters of the employed ant colony algorithm are tuned by means of a response surface methodology, RSM, approach. Finally, a sensitivity analysis on the main parameters of both the cost function and the control chart is performed using experimental design approach. The results show that augmenting a proper statistical nonlinear constraint to the model will improve the effectiveness of the model without a significant increase in the cost.

On the Effects of Selective Below-Cost Pricing in a Vertical Differentiation Model

Abstract We analyse the effects of predation in a vertical differentiation model, where the high-quality incumbent is able to price discriminate while the low-quality entrant sets a uniform price. The incumbent may act as a predator, that is, it may price below its marginal costs on a subset of consumers to induce the rival’s exit. We show that the entrant may adopt an aggressive attitude to make predation unprofitable for the incumbent. In this case predation does not occur and the equilibrium prices are lower than the equilibrium prices which would emerge in a contest of explicitly forbidden predation. Moreover, we show that when the incumbent may choose whether to price discriminate or not before the game starts, if the quality cost function is sufficiently convex, there always exists a parameter space on which the incumbent prefers to commit not to price discriminate.

An Interval-Parameter Waste-Load-Allocation Model for River Water Quality Management Under Uncertainty

A simulation-based interval quadratic waste load allocation (IQWLA) model was developed for supporting river water quality management. A multi-segment simulation model was developed to generate water-quality transformation matrices and vectors under steady-state river flow conditions. The established matrices and vectors were then used to establish the water-quality constraints that were included in a water quality management model. Uncertainties associated with water quality parameters, cost functions, and environmental guidelines were described as intervals. The cost functions of wastewater treatment units were expressed in quadratic forms. A water-quality planning problem in the Changsha section of Xiangjiang River in China was used as a study case to demonstrate applicability of the proposed method. The study results demonstrated that IQWLA model could effectively communicate the interval-format uncertainties into optimization process, and generate inexact solutions that contain a spectrum of potential wastewater treatment options. Decision alternatives can be generated by adjusting different combinations of the decision variables within their solution intervals. The results are valuable for supporting local decision makers in generating cost-effective water quality management strategies.

On the Effects of Selective Below-Cost Pricing in a Vertical Differentiation Model

We analyse the effects of predation in a vertical differentiation model, where the highquality incumbent is able to price discriminate while the low-quality entrant sets a uniform price. The incumbent may act as a predator, that is, it may price below its marginal costs on a subset of consumers to induce the rival's exit. We show that the entrant may adopt an aggressive attitude to make predation unprofitable for the incumbent. In this case predation does not occur and the equilibrium prices are lower than the equilibrium prices which would emerge in a contest of explicitly forbidden predation. Moreover, we show that when the incumbent may choose whether to price discriminate or not before the game starts, if the quality cost function is sufficiently convex, there always exists a parameter space on which the incumbent prefers to commit not to price discriminate.

A Model to Determine the Optimal Sampling Schedule of Diet Components

Various recommendations have been issued regarding the sampling schedule of diet components, especially forages. Their basis is unclear and none are justified from an economic standpoint. The objective of this research was to derive a general method for determining the optimal sampling design for forages. The process of forage removal from storage can be conceptualized as a quality control issue that can be monitored using a Shewhart X-bar chart. This procedure requires 3 control parameters: number of samples (n), sampling interval (h), and control limits (L). A quality cost function made of 4 parts is proposed: cost per cycle while the process is in-control (I); cost per cycle while the process is out-of-control (O); cost per cycle for sampling and analyses (A); and expected duration of a cycle (D). Thirteen inputs enter the cost function: the mean time that process is in control, the number of animals in the herd, the unit price of milk, the milk production loss due to white noise, the milk production loss from an abrupt change in forage composition, the time to sample and analyze one item, the expected time to discover the assignable cause, the expected time to fix the diet, the cost per false alarm, the cost to fix the diet, the fixed cost of sampling at each sampling time, the cost for each unit sampled, and the number of standard deviation slips when forage changes. The total quality cost per day C = (I + O + A)/D. The C function can be optimized with respect to n, h, and L to yield an optimal sampling schedule. Because n and h are discrete variables in a highly nonlinear function, parametric optimization algorithms cannot be used to optimize the function. A genetic algorithm was used for the minimization of C. Results showed that the optimal sampling designs are close to current practices in small herds of 50 cows, but very different in large herds of 1,000 cows, resulting in reduced total quality costs of $250/d. Total sensitivity of C was greatest for the number of cows in the herd, the shift in milk production when forage changes, the mean time that the process is in control, the price of milk, and the time to sample and analyze one item. Total sensitivities of n, h, and L were greatest for the mean time that the process is in control, the extent of the change in composition when there is a change in forage composition, the number of cows in the herd, the shift in milk production when forage changes, and the cost per unit sampled.

ECONOMIC SELECTION OF MEAN VALUE FOR A FILLING PROCESS UNDER QUADRATIC QUALITY LOSS

Consider a filling process where containers are filled with an important ingredient in a character. All containers are inspected, and the containers satisfying to meet the predetermined specification limits are sold in a regular market for a fixed price, and failing to meet them are emptied and refilled by the same filling process after some reprocessing. We assume that reprocessing cost is proportional to the quantity of the ingredients in a container that is not changed after reprocessing. An economic model is constructed on the basis of the selling price and the costs of production, inspection, reprocessing, and quality. We assume that the quality cost function is a quadratic function of the deviation from target and the quantity of the ingredients in a container is normally distributed with a known variance. Method for finding the optimum process mean is presented and a numerical example is given.

Technical and qualitative information sharing between fabric finishing and garment manufacturer

This paper presents an integrated information system proposed for the textile/apparel industries. The main idea is to propose a common communication platform between fabric producer and garment manufacture in order to standardise technical and qualitative fabric definition. The heart of the system is the fabric technical and qualitative chart as well as the quality-cost function formulation procedure that seriously affects trade relationships. The innovative contribution of this system is represented by the fact that the technical and qualitative chart of the piece will now be created by the fabric producer on the basis of the requirements of the Garment Manufacturer so that it can be used directly by the latter's computer system.

Economic complete inspection plans with multi-decision alternatives

In situations where there are several markets with different price/cost structures, economic complete inspection plans are developed for determining the best market for each product. Two complete inspection plans are considered; an inspection based on a performance variable of interest, and an inspection based on a screening variable which is highly correlated with the performance variable. Profit models for linear and quadratic quality cost functions are constructed which include selling price, cost incurred by imperfect quality, and quality inspection cost. Methods of finding the optimal inspection plan and a numerical example are presented.

Economic designs of two-sided single and double screening procedures

Economic designs of single and double screening procedures for improving outgoing product quality based on two screening variables are presented for the case of two-sided specification limits. Two screening variables are observed simultaneously in the single screening procedure. In the double screening procedure, one variable is used first to make one of three decisions — accept, reject, or undecided — and after the first screening, the second variable is employed to screen the undecided items. It is assumed that the performance and the two screening variables are jointly normally distributed, and the deviation of the performance variable from the ‘ideal’ value causes dissatisfication to the consumers. Two quality cost functions — constant and quadratic — are considered. Cost models are constructed which involve screening inspection cost, and costs of accepted and rejected item. Methods of finding the optimal cutoff values are presented and a numerical example is given.

Economic designs of single and double screening procedures

Economic designs of single and double screening procedures for improving outgoing product quality based on two screening variables are presented for the case of one-sided specification limit. Two screening variables are observed simultaneously in single screening procedure and are observed sequentially in double screening procedure. It is assumed that the performance variable and the two screening variables are jointly normally distributed. Three quality cost functions — constant, linear, and quadratic — are considered. Cost models are constructed which involve screening inspection cost, and costs of accepted and rejected item. Methods of finding the optimal cutoff values are presented and a numerical example is given.

A quality and risk-adjusted cost function for banks: Evidence on the ?too-big-to-fail? doctrine

We estimate a multiproduct cost function model incorporating measures of bank output quality and the probability of failure. We model a bank's uninsured deposit price as an endogenous variable depending on the bank's output level, output quality, financial capital level, and risk measures. Accounting for these aspects in the cost model significantly affects measures of scale and scope economies. We find evidence that the “too-big-to-fail” doctrine significantly affects the price a bank pays for its uninsured deposits. For large banks, an increase in size, holding default risk and asset quality constant, significantly lowers the uninsured deposit price.