Rectifying Inspection Plan Research Articles

The integrated application of acceptance sampling in the quality control of manufacturing process and quality assurance of shipment product

In this work, the authors propose the integrated application of CSP-1 plan and Dodge-Romig rectifying inspection plan with expected inspection cost, expected replacement cost, expected warranty cost, expected quality loss for conforming product, and expected quality loss for non-conforming product per item. The quality characteristics of product is considered as the normal distribution with nominal-the-best and symmetric quadratic quality loss function. The CSP-1 plan is firstly applied in the process control. The optimal combination of parameters is obtained from the minimum expected total cost per item produced under the specified average outgoing quality limit (AOQL) protection. One needs to have the optimal clearance number, sampling frequency, and specification limit coefficient. Then Dodge-Romig rectifying inspection plan is applied in the product improvement. The optimal sample size, clearance number, and quality investment are obtained by minimizing the expected total cost per lot under the specified consumer’s risk.

The asymmetric specification limit and quality investment settings for rectifying inspection plan

In this work, the authors propose the asymmetric specification limit and quality investment settings for the Dodge-Romig rectifying inspection plan with quality loss and product cost. This method can be used for product improvement. The optimal combination of parameters of Dodge-Romig plan with the specified consumer’s risk protection, the asymmetric specification limit coefficients of product, and quality investment are obtained by minimizing the expected total cost per unit.

Quality control for production and shipment process of product

In this article, the authors propose the integrated application of type I continuous sampling plan (CSP-1 plan) and Dodge-Romig rectifying inspection plan with quality loss and product cost. The normal quality characteristic, nominal-the-best, and asymmetric quadratic quality loss function of product are considered. The CSP-1 plan is firstly applied in the process control. Then Dodge-Romig rectifying inspection plan is applied in the product improvement. The optimal combination of parameters of CSP-1 plan and asymmetric specification limit coefficients are obtained under the specified average outgoing quality limit (AOQL) protection. The optimal combination of parameters of Dodge-Romig rectifying inspection plan and quality investment are determined under the specified consumer’s risk. Finally, the sensitivity analysis of numerical example will be provided for illustration.

Optimum profit model based on the average outgoing quality limit protection

The optimal setting of process mean is an important issue in operations management and a variable sampling inspection plan is an acceptance sampling technique for quality assurance. In the present study, the newsvendor problem (i.e., the mixed procurement system) is modified by applying a variable sampling inspection plan with specified average outgoing quality limit (AOQL) with maximization of the expected total profit including the manufacturer and the retailer. The optimal retailer’s order quantity and manufacturer’s process mean and the parameters of sampling plan are jointly determined by maximizing the expected total profit. In the model, the single sampling rectifying inspection plan is adopted to determine the quality of lot product and the used cost of customer for product is measured by Taguchi’s quadratic loss function. A numerical example is given and the sensitivity analysis of model parameters are provided for illustration. Based on the results of sensitivity analysis, it may be seen that a higher processing cost per unit generally leads to a lower expected profit. In the meantime, a higher retailer’s selling price always results in a higher expected profit.

Practical application of product and process parameters under the specified process capability value

In 2018, Chen and Chou proposed a jointly design model with manufacturing quantity, specification limits, process mean, and the parameters of X-bar control chart based on the specified process capability index Cpm or Cpmk value. This integrated model is a generalization of economic manufacturing quantity (EMQ) model with statistical quality control chart. In this study, the author presents the practical application of Chen and Chou’s model for the manufacturer. The manufacturer can apply these parameters in the design of a variable single rectifying inspection plan for the output product before shipping to the customer and the determination of the stock quantity for shipment to the customer in the newsvendor problem.

Optimal process mean and standard deviation settings for rectifying sampling inspection plan with quality investment

In this paper, the rectifying sampling inspection plan with quality investment for the product lot is used in the determination of optimal process mean and standard deviation. Consider the quality characteristic of product is normally distributed with both unknown process mean and unknown standard deviation. The product lot is sold to the different markets according to the defective numbers of sample. Assume that the declining exponential reduction of process mean and standard deviation is the function of quality investment. For a given rectifying inspection plan, one can obtain the optimal quality investment and corresponding improved process mean and standard deviation based on the maximum expected total profit of product lot per unit.

Optimum process mean setting under the rectifying inspection plan

In this paper, the rectifying inspection plan with multiple decisions for the product lot is used in the determination of optimal process mean. Consider the quality characteristic of product is normally distributed with known standard deviation and unknown mean. The product lot is soled to the different markets according to the defective numbers of sample. For a given rectifying inspection plan, one can obtain the optimal process mean based on the maximum expected total profit of product lot per unit.

Optimum process mean setting based on variable sampling plan with producer’s and consumer’s risks

In this paper, the author applies a variable sampling inspection plan with the producer’s and consumer’s risks on the operational characteristic curve for setting the optimum process mean. Assume that the quality characteristic of a one-sided lower specification limit product is normally distributed. The process standard deviation is known but the process mean is unknown. The rectifying inspection plan is adopted when the lot of product is rejected. The optimum process mean and the parameters of single variable sampling inspection plan are simultaneously determined by maximizing the expected total profit per unit under the specified producer’s and consumer’s risks. The numerical results show that (1) the unit price of product for the accepted lot, the production cost per unit, and the specification limit have a major effect on the expected total profit per unit; (2) the process standard deviation and the lot tolerance percent defective have a moderate effect on the expected total profit per unit

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.

The Modified Economic Manufacturing Quantity Model Based on Inspection Error, Quality Loss, and Shortage

AbsractIn 1996, Pulak and Al-Sultan presented the problem of determining the optimum process mean for a product with the one-sided specification limit under the rectifying inspection plan. However, they didn't consider the quality loss within the specification limit. The inspection is perfect and the non-conforming items of the accepted lot aren't eliminated or replaced by the conforming ones in their model. Traditional economic manufacturing quantity (EMQ) model addressed that the perfect production for product. However, there possibly exists the defective product in the manufacturing process. Hence, it is necessary to consider the quality loss of product in the modified EMQ model. In this study, the author integrates the modified Pulak and Al-Sultan's model with inspection error and quality loss into the Cardenas-Barron's production lot model with shortage for determining the economic manufacturing quantity, shortage and optimum process mean.

Economic Order Quantity, Process Quality Level, Warranty Period, and Production Run Length Settings

In the present paper, a modified optimal profit model with settings of production and process parameters is proposed, where the larger-the-better product characteristic with the one-sided lower specification limit is considered. The product characteristic is assumed to be normally distributed with unknown mean and known standard deviation. The selling price of product is assumed to be linearly proportional to its warranty period. We also assume that the retailer’s order quantity is negatively correlated with the wholesale selling price and is positively correlated with the warranty period. The single sampling rectifying inspection plan is adopted for determining the quality of product lot. The Taguchi’s quadratic quality loss function is addressed for measuring the used cost of customer for product. The optimal manufacturer’s process quality level, production run length, warranty period, and retailer’s order quantity can then be simultaneously determined by maximizing the expected total profit of society including both the manufacturer and the retailer. Numerical results show that the longer warranty period and the higher product quality level will lead to the larger expected total profit of society.

Optimum process mean setting based on variable sampling plans with specified consumer’s risk

In the present paper, a new economic design with variable single sampling inspection plan for determining the optimal process mean is presented. The quality characteristic with the one-sided lower specification limit is assumed to be normally distributed with unknown mean and known standard deviation. The 100% rectifying inspection plan is adopted when the product lot is rejected. The optimum process mean and the parameters of sampling inspection plan are simultaneously determined by maximizing the expected total profit per unit and meeting the requirement of the specified consumer’s risk. Two numerical examples and sensitivity analyzes of parameters are provided for illustration. The numerical results show that, among the model parameters, the price of product for accepted lot, the processing cost per unit, and the lower specification limit significantly affect the expected total profit per unit.

English

In this article, the author proposes a modification of Dodge-Romig single rectifying inspection plan with average outgoing quality limit (AOQL) protection. The quality investment and inspection error are considered in the modified model.  The optimal parameters of sampling inspection plan and quality investment level are simultaneously determined by minimizing the expected total cost of product under the specified AOQL value. Finally, the comparison of solution between the modified model with/without inspection error will be provided for illustration.   Key words: Dodge-Romig Single Rectifying Inspection Pan, average outgoing quality limit (AOQL), quality investment, inspection error.

Fuzzy optimum design of Dodge–Romig sampling rectifying inspection plan under quality investment

Design of sampling plan always plays a key role in statistical quality control. Dodge–Romig provided the rectifying single sampling plans (SSP) for attributing with the protection of lot tolerance percent defective (LTPD) or the average outgoing quality limit. The on-line 100% rectifying inspection can be applied as a short-term method for controlling the product quality, while the quality investment is an available method for improving the process parameters in the long run. In the present paper, the economic selection of quality investment for designing a Dodge–Romig SSP with LTPD protection is proposed. Both the mean and standard deviation of process characteristic are measured as the exponential function of quality investment. The optimal sampling plan and quality investment level are jointly determined by minimizing the expected total cost of product for a specified consumer’s risk. The Dodge–Romig LTPD SSP with quality investment under fuzzy environment that satisfies the consumer’s risk is also developed. Numerical examples are provided for illustration. Based on the results of analysis, it can be seen that the quality investment level and the expected total cost of product are significantly influenced by the known process standard deviation and the exponential reduction coefficient of process standard deviation for quality improvement.

A note on some modified Pulak and Al-Sultan's model

Pulak and Al-Sultan presented a rectifying inspection plan applying in the determination of optimum process mean. However, they did not point out whether the non-conforming items in the sample of accepted lot are replaced or eliminated from the lot and neglected the quality loss within specification limits. In this paper, we further propose the modified Pulak and Al-Sultan model with quadratic quality loss function. There are four cases considered in the modified model: (1) the non-conforming items in the sample of accepted lot are neither replaced nor eliminated from the lot; (2) the non-conforming items in the sample of accepted lot are not replaced but are eliminated from the lot; (3) the non-conforming items in the sample of accepted lot are replaced by conforming ones; (4) the non-conforming items in the sample of accepted lot are replaced by non-inspected items. The numerical results and sensitivity analysis of parameters show that their solutions are slightly different.

Optimum process mean and manufacturing quantity settings for serial production system under the quality loss and rectifying inspection plan

In 1994, Al-Sultan presented a single sampling plan applied in determining the optimum process mean for two machines in a serial production system. However, Al-Sultan did not consider the quality cost for the product within the specification limits, pointed out that the non-conforming items in the sample of accepted lot is replaced or eliminated from the lot, and proposed an integrated model with production and quality. In this study, the author considers the problem of quality loss for the modified Al-Sultan’s model with k machines in a serial production system based on a single sampling rectifying inspection plan. Taguchi’s symmetric quadratic quality loss function is applied in evaluating the product quality. Then, the author further proposes a modified and integrated economic manufacturing quantity (EMQ) model based on the application of the modified Al-Sultan’s model for obtaining the maximum expected total profit of product per unit of time. The numerical results show that the price of an accepted products sold has the most important effect on both the process means and the expected total profit per unit of time.

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.

Determining the optimum process mean based on quadratic quality loss function and rectifying inspection plan

In 1996, Pulak and Al-Sultan presented a rectifying inspection plan for determining the optimum process mean. However, they did not consider the quality cost for the product within the specification limits and did not point out whether the non-conforming items in the sample of accepted lot is replaced or eliminated from the lot. In this paper, we propose a modified Pulak and Al-Sultan’s model with quadratic quality loss function of product within the specification limits. Assume that the non-conforming items in the sample of accepted lot are replaced by conforming ones. Finally, the numerical results and sensitivity analysis of parameters of modified model and those of Pulak and Al-Sultan are provided for illustration.

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.