Economic Specification Limits Research Articles

The integrated quality control model with product inspection and process improvement

ABSTRACT Sampling inspection is one of preventive quality methods for decreasing waste of time and cost, but should be along with other quality control approaches to effectively enhance product quality. Determination of optimum process mean tends to reduce the bias of the central tendency of process characteristic from its target, and has been an important topic in quality system design. Pulak and Al-Sultan developed a single sampling rectifying inspection model to determine the optimum process mean, based on maximization of the expected total profit per item. Since setting the economic specification limits for process characteristic is considered a short-term approach for quality assurance and, on the other hand, quality investment is a long-term approach for process improvement, in the present paper, a modified product inspection model, which is modified from Pulak and Al-Sultan’s work, is firstly presented to simultaneously determine the optimum process mean and economic specification limits, based on maximization of the expected total profit per item. Then, quality investment is integrated into this modified model to obtain the optimum quality investment level.

The integrated study for process improvement with economic specification limits, process means setting and quality investment: an extension of the model in Abdul-Kader et al. (2010)

ABSTRACT In the present paper, the model in Abdul-Kader et al is modified by incorporating the capability index Cpm to assure the capability of production process and to obtain the process mean, economic specification limits, and quality investment level with minimization of the expected total cost per item. Three modified models are presented and discussed, where Model I firstly determines the optimal process mean and economic specification limits, and then by applying this optimal mean and specification limits, the optimal quality investment level is subsequently obtained, Model II firstly determines the optimal process mean and quality investment level and then, by applying this optimal mean and quality investment level, the economic specification limits are obtained afterwards, and Model III simultaneously determines the optimal process mean, economic specification limits and the optimal quality investment level. Solution procedure for each modified model is provided and a numerical example is given for illustration. Based on the results of sensitivity analysis, Model II is generally superior to the other two modified models under consideration of cost.

Economic specification limits and process mean settings by considering unequal target value and specification center

In this paper, the author proposes a modified Kapur and Wang’s model with unequal target value and specification center. The economic specification limits and process mean are determined by minimizing the expected total quality loss per unit product under the specified process capability index value. The process capability indices Cpm and Cpmk correlated with Taguchi’s quadratic quality loss function are considered. The 100% inspection is executed before the product shipped to the customer. Taguchi’s asymmetric quadratic quality loss function is applied in evaluating the product quality. The numerical results show that the modified model with specified Cpm value has smaller specification tolerance, larger process mean, and smaller expected total cost per unit product than those of the modified model with specified Cpmk value.

Production quantity and specification limits settings by considering specified process capability value

In the present paper, we propose a modified Kouikoglou and Phillis’s produce-to-stock system with a the specified process capability index value under the partly loss sales or complete backlogging. The economic specification limits, specified process capability value, output quantity, and incoming order are jointly determined by maximizing the expected total profit of product. Hundred percent inspection is executed before the products are shipped to the customer. The finite output buffer (production quantity) and rejection of incoming order are also considered in our model. Assuming that the target value of product characteristic is equal to its specification center, the Taguchi’s asymmetric quadratic quality loss function is applied to evaluate the product quality. From the above numerical examples and sensitivity analysis of parameters, the results suggest that one can adopt the modified Kouikoglou and Phillis’s produce-to-stock system under the complete backlogging. If the produce-to-stock system under the partly loss sales, then one should use the original Kouikoglou and Phillis’s model for obtaining the larger expected total profit of product than that of modified one.

Optimization of engineering tolerance design using revised loss functions

Engineering tolerance design plays an important role in modern manufacturing. Both symmetric and asymmetric tolerances are common in many manufacturing processes. Recently, various revised loss functions have been proposed for overcoming the drawbacks of Taguchi's loss function. In this article, Kapur's economic tolerance design model is modified and the economic specification limits for both symmetric and asymmetric losses are established. Three different loss functions are compared in the optimal symmetric and asymmetric tolerance design: a revised Taguchi quadratic loss function, an inverted normal loss function and a revised inverted normal loss function. The relationships among the three loss functions and process capability indices are established. A numerical example is given to compare the economic specification limits established by using the three loss functions. The results suggest that the revised inverted normal loss function be used in determining economic specification limits.

JOINT DETERMINATION OF OPTIMUM PROCESS MEAN AND ECONOMIC SPECIFICATION LIMITS FOR RECTIFYING INSPECTION PLAN WITH INSPECTION ERROR

In 2006, Chen presented a modified Pulak and Al-Sultan's model with quadratic quality loss function of product within the specification limits for determining the optimum process parameters. However, he did not consider the problem of inspection error. In this paper, the authors propose an integrated model for obtaining the optimum process mean and economic specification limits based on the modified Chen's model with inspection error. Finally, the numerical results and sensitivity analyses of the modified Chen's model with inspection error and those of Chen's model without inspection error are further provided for illustration.

JOINT DETERMINATION OF OPTIMUM PROCESS MEAN AND ECONOMIC SPECIFICATION LIMITS FOR RECTIFYING INSPECTION PLAN WITH INSPECTION ERROR

ABSTRACT In 2006, Chen presented a modified Pulak and Al-Sultan's model with quadratic quality loss function of product within the specification limits for determining the optimum process parameters. However, he did not consider the problem of inspection error. In this paper, the authors propose an integrated model for obtaining the optimum process mean and economic specification limits based on the modified Chen's model with inspection error. Finally, the numerical results and sensitivity analyses of the modified Chen's model with inspection error and those of Chen's model without inspection error are further provided for illustration.

Economic manufacturing quantity, optimum process mean, and economic specification limits setting under the rectifying inspection plan

Economic manufacturing quantity, process mean, and specification limits setting are three important methods for the inventory and quality control problems. In the imperfect production system, we usually consider the manufacturing quantity for reducing the inventory cost, determine the process level for reducing the production cost, and select the specification limits for screening the products. In this paper, we propose the above integrated model based on the application of rectifying inspection plan for obtaining maximum expected total profit of product. The asymmetric quadratic quality loss function is adopted for measuring the product quality. The sensitivity analyses of parameters are provided for illustration.

A Note on the Appropriateness of Taguchi's Loss Function

Taguchi defined product quality in a universal way by adopting a quadratic quality loss function. In 1987, Kapur and Wang addressed the problem of setting economic specification limits for processes being not capable to meet given tolerances and, therefore, product quality has to be improved by inspection. Kapur and Wang selected for their investigations Taguchi's quadratic loss function. In this paper, we assume a asymmetrical linear quality loss function and show that the obtained optimal values differ greatly from those obtained by Kapur and Wang.

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.

ECONOMIC SPECIFICATION LIMITS UNDER THE INSPECTION ERROR

ABSTRACT Kapur and Wang [2] have presented that the inspection in an on-line quality control system conducts as a short term approach to reduce variance of the items shipped to the customers. However, they have neglected to consider the inspection error in the model. In this article, we further propose the modified Kapur and Wang's [2] model with inspection error for determining the economic specification limits. Finally, the sensitivity analysis of the parameters is provided.

Joint Design of Economic Manufacturing Quantity, Sampling Plan and Specification Limits

In this paper we propose an extension of the problem to determine the economic design of a Type I continuous sampling plan (CSP-1 plan) and the economic manufacturing quantity (EMQ) under imperfect quality investigated in Chen et al. (Economic Quality Control 15: 137-146, 2000), where the economic objective equals the total inventory cost including the set-up cost, the holding cost and the expected quality loss. The extension refers to the economic specification limits. The problem can be formulated as a non-linear mixed-integer minimization problem. By solving it, the required level of product quality is obtained at minimum total inventory cost. A numerical example is given to illustrate the solution procedure.

Economic Design of the Specification for Geometrical Quality Characteristic

The economic design of specification limits must be determined on an economic basis where we minimize total loss to society, which consists of both the producer and the consumer. Economic specification limits have been developed based on the assumption that the quality characteristic is normally distributed. Unfortunately, the assumption is not to meet some practical cases. In this paper, some non‐normal distributions are considered for quality characteristic with geometrical features. An economic model for selecting the optimum specification limits on the basis of minimizing total cost is introduced. A case study is presented to illustrate the application in practice.

An Integrated Approach for Designing a Sampling Plan and Fixing Specifications

In 1986 Taguchi presented the quadratic function for describing the loss of quality due to deviation from the production value. The objective then is to improve quality by minimizing the quadratic loss function which reflects the loss of both, the producer and the consumer. Subsequently, Kapur et al. (Wang, Economic design of specifications based on Taguchi's concept of quality loss function.: 23-36, 1987, Quality Engineering 1:63-77, 1988, Cho, Quality Engineering 6: 401-417, 1994) addressed the problem of deriving a loss function to be applied for determining the design of specification limits. This article further explores the problem of determining an integrated design of a Type I continuous sampling plan ( CSP -1) and the specification limits. By modifying Kapur and Wang's (Economic design of specifications based on Taguchi's concept of quality loss function.: 23-36, 1987) model, we not only obtain economic specification limits, but also obtaib an optimal CSP -1 plan for inspection.

Economic design of the specification region for multiple quality characteristics

Economic specification limits have typically been developed on the basis of a single quality characteristic. From the viewpoint of the customer, products are often evaluated based on multiple quality characteristics. The specification region for multiple quality characteristics must be determined on an economic basis where we minimize the total loss to both the producer and the customer and thus to the whole society. In this paper a multivariate normal distribution is considered for the quality characteristics. The specification region is given by truncating the multivariate normal distribution. We present the optimization model to develop the specification region for multiple quality characteristics based on the framework of multivariate quality loss function.

Models for determining the optimal in-process inspection specification limits in multistage production systems

A multistage production system is characterized by items being processed through a sequence of production operations. In general, it may be desirable to have inspection operations performed between some production operations for the purpose of detecting a defective item prior to the final inspection. Furthermore, it may even be more economically desirable to consider tightening the specifications—that is. rejecting a manufacturing unit having defects less than the maximum number to be tolerated. Thus, the hypothesis examined in this paper is that there could exist a method for determination of economically optimal specifications for in-process inspection of a multistage production system. Two production environments considered are: (a) a manufacturer producing to satisfy a fixed production goal, so that any defective item must be replaced by reprocessing a substitute; (b) a manufacturer producing until be exhausts fixed levels of resource availability, so that a rejected item results in a loss in revenue. An economic dynamic programming model is formulated for each of the two production environments. Illustrative examples are presented. Indications are that the concept of specification tightening should be considered for utilization, and that the dynamic programming approach can be used to determine the most economic specification limits for a given inspection program.