Average Outgoing Quality Limit Research Articles

Designing of Variables Double Sampling Plan Under Rectifying Inspection for Consumer Protection

Designing of acceptance sampling plans based on operating characteristics fail to prescribe the corrective action for rejected lots although they guarantee the producer’s and the consumer’s protection at their corresponding quality levels. But, rectification sampling inspection plan suggests 100% inspection for rejected lots and hence, the producer’s risk is reduced and also there is a guarantee to the consumer by restricting upper limit of the maximum expected proportion of non-conforming of the shipping lot. Although the variables single sampling plan for rectifying inspection is available, variables double sampling inspection plan under rectifying inspection has not yet been designed. Hence, in this paper, we design a variables double sampling plan for rectifying inspection indexed by acceptable quality level and average outgoing quality limit to meet the needs of the producer as well as the consumer. A non-linear optimization problem is developed to determine the optimal parameters with minimum average sample number at acceptable quality level for both cases of standard deviation are known and unknown. We investigate the validation and limitation of the proposed plan through the simulation study and industrial application of the proposed plan is also given. It can be confirmed from the investigations on the results that in many situations, variables double sampling plan designed under rectifying inspection is more economical than variables single sampling plan designed with the same conditions in providing the same protection to consumer.

Optimum specification limit coefficient setting based on the smaller-the-better quality characteristics

In this work, the authors propose the application of type I continuous sampling plan (CSP-1 plan) with expected inspection cost, expected replacement cost, expected warranty cost, expected quality loss for conforming product, and expected quality loss for nonconforming product per item. The quality characteristics of product is considered as the normal distribution with smaller-the-better characteristics. The quality loss function of product addresses the quadratic quality loss function. The CSP-1 plan is 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.

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.

Optimum specification limit setting under the larger-the-better quality characteristics

In this paper, the optimal clearance number and sampling frequency of type I continuous sampling plan (CSP-1 plan) and specification limit coefficient of product are determined with the minimum expected total cost per item under the specified average outgoing quality limit (AOQL) protection. The expected total cost per item includes the expected inspection cost, the expected replacement cost, the expected warranty cost, the expected quality loss for conforming product, and the expected quality loss for non-conforming product per item. The quality characteristic of product is considered as the normal distribution with larger-the-better characteristics. The quality loss function of product addresses the quadratic quality loss function. The sensitivity analysis of numerical example will be provided for illustration.

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.

Designing of variables repetitive group sampling plan for consumer protection

Due to the development of modern technology, it is possible to reduce the variation of products quality during the production. However, it is necessary to propose a designing methodology of sampling plans to guarantee the consumers protection in terms of maximum limit of outgoing non-conforming items while protecting the producers a good quality level. Hence, in this paper, we propose the designing methodology of variables repetitive group sampling plan indexed by acceptable quality level and average outgoing quality limit. We develop an optimization model for determining the optimal parameters with minimum average sample number at the acceptable quality level by simultaneously considering two inequalities. The optimal plan parameters are determined for both cases of known and unknown standard deviation. Results show that the proposed plan reduces the required sample size than the existing single sampling plan to provide protection to the consumers in terms of average outgoing quality.

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.

A study on continuous inspection of markov processs with a clearance interval

Dodge’s continuous sampling plan-1 (CSP-1) with clearance interval zero may be inefficient if there is serial correlation between successive units which are Markov dependent and a clearance interval greater than zero is appropriate. For such a situation, the average outgoing quality limit (AOQL) expression has been obtained and, when the serial correlation coefficient of the Markov chain is assumed to be known a priori, it is numerically demonstrated that smaller AOQL values are achieved numerically for values of the clearance interval from 1 to 4, by improving the performance of CSP-1.

A Rectifying Acceptance Sampling Plan Based on the Process Capability Index

The acceptance sampling plan and process capability index (PCI) are critical decision tools for quality control. Recently, numerous research papers have examined the acceptance sampling plan in combination with the PCI. However, most of these papers have not considered the aspect of rectifying inspections. In this paper, we propose a quality cost model of repetitive sampling to develop a rectifying acceptance sampling plan based on the one-sided PCI. This proposed model minimizes the total quality cost (TQC) of sentencing one lot, including inspection cost, internal failure cost, and external failure cost. In addition, sensitivity analysis is conducted to investigate the behavior of relevant parameters against TQC. To demonstrate the advantages of the proposed methodology, a comparison is implemented with the existing rectifying sampling plan in terms of TQC and average outgoing quality limit. This comparison reveals that our proposed methodology exhibits superior performance.

Economic Efficiency of Rectifying AOQL Plans Based on the EWMA Statistic

Abstract Rectifying Average Outgoing Quality Limit (AOQL) acceptance sampling plans that minimize the mean inspection cost per lot of the process average quality were originally designed by Dodge and Romig for inspection by attributes. Plans for inspection by variables were then proposed; such plans may be more economically efficient than the corresponding attribute sampling plans. The new AOQL variable sampling plans, which minimize the mean inspection cost per lot of the process average quality when the remainder of the rejected lots are inspected, are introduced in this article. The new plans are based on the usage of the exponentially weighted moving average statistic, and the economic advantages of the new plans over the existing plans with respect to savings in the cost of the inspection are discussed. The economic efficiency of the new plans is evaluated using cost models that consider differences in both variable and fixed costs. The methods for the calculation of the proposed plans have been implemented in a free software, i.e., the contributed package LTPDvar for the R computing environment.

Optimal CSP-1 boundary scheme based on the estimator of the proportion of conformance for specified in-control process

ABSTRACTSingle-level continuous sampling plan (CSP-1), called contour scheme, is constructed on the average outgoing quality limit () contour. However, for specified in-control process the boundary of feasible continuous sampling scheme is not established in CSP-1. The optimal CSP-1 boundary scheme is established based on the estimator of the proportion of conformance for specified in-control process. The parameters of the boundary scheme are determined by the set of equations constructed with the boundary identical equation and contour identical equation, which will guarantee that the proposed scheme is simultaneously both boundary scheme and contour scheme. The behaviour of the established boundary scheme is discussed and compared with the contour scheme. The optimal CSP-1 boundary scheme can quantitatively control the outgoing quality and tighten the inspection whether the process quality fluctuates towards the deteriorated or the improved direction. For practitioners’ convenience, three tables of the boundary scheme parameters under three quality requirements and three confidence levels are provided. The operating procedure is also presented. A real example is given to verify the effectiveness and feasibility of the proposed boundary scheme.

Rectifying inspection for PAOSQLL scheme based on variable repetitive group sampling plan

The concept of the quality loss derived by Taguchi has been accepted as the evaluation measure of quality instead of the traditional attribute property such as the proportion of non-conforming items. Since the variable single sampling plan having the desired operating characteristics indexed by the quality loss was proposed in 1997, various kinds of sampling plans indexed by the quality loss have been considered. Among them, there are two kinds of rectifying variable single sampling (RVSS) plans indexed by the quality loss. In the RVSS plans, two inspection schemes called the acceptance quality loss limit (AQLL) scheme and the permissible average outgoing surplus quality loss limit (PAOSQLL) scheme have been formulated. Note that the concepts of the AQLL and PAOSQLL schemes in the RVSS plans indexed by the quality loss are equivalent to those of the lot tolerance percent defective (LTPD) and the average outgoing quality limit (AOQL) schemes in the traditional rectifying attribute single sampling plans, respectively. On the other hand, in the sampling plan having the desired operating characteristics, an attribute repetitive group sampling plan was proposed for the purpose of reducing the average sampling number in the inspection. Recently, by applying the repetitive group sampling to the rectifying variable sampling plan for the AQLL scheme, the rectifying variable repetitive group sampling (RVRGS) plan for the AQLL scheme has been considered for the purpose of reducing the average total inspection (ATI). However, the RVRGS plan for the PAOSQLL scheme has not been investigated yet. Accordingly, the RVRGS plan for the PAOSQLL scheme must be investigated to complete the RVRGS plans indexed by the quality loss. In this article, the RVRGS plan for the PAOSQLL scheme is addressed. Then, the design procedure in the RVRGS plan for the PAOSQLL scheme is proposed for the purpose of reducing ATI. Through some numerical investigations, the effectiveness to reduce ATI by the RVRGS plan for the PAOSQLL scheme is confirmed.

On Dodge-Romig Single Sampling Inspection Tables under Average Quality Protection

Objectives: This paper aims at presenting an easy method of designing Single Sampling Plans (SSP) by attributes inspection based on Dodge-Romig method under Average Quality Protection. Methods/Statistical Analysis: A computational algorithm is developed for obtaining the parameters of the SSP, viz., the sample size and the acceptance number. A simple computer programme under the Poisson model for the OC function is developed for the computational algorithm using which the parameters of the SSP for desired levels of Average Outgoing Quality Limit (AOQL). Findings: The sample size and acceptance number constituting the SSP obtained using the procedure described in this paper are found to provide closer values of the desired AOQL and the minimum Average Total Inspection (ATI) than those obtainable from Dodge and Romig. The simple computer programme replaces the huge volumes of tables of Dodge and Romig. The procedure avoids the approximations involved in the original Dodge-Romig method and thus results in better plans. Application/ Improvements: The Single Sampling Plans under average quality protection are applicable in attributes inspection where ever rectification is possible.

Economic efficiency of the AOQL single sampling plans for the inspection by variables

The paper refers to the AOQL (Average Outgoing Quality Limit) single sampling plans when the remainder of the rejected lots is inspected. These rectifying AOQL plans for inspection by variables were created by the author of this paper and published in the Statistical Papers. These new plans were compared with the corresponding Dodge-Romig AOQL plans for inspection by attributes from the economic point of view. Numerical investigations confirm that under the same protection of consumer, the AOQL plans for inspection by variables are in many situations more economical than the corresponding Dodge-Romig AOQL attribute sampling plans. The dependence of the saving of the inspection cost on the input parameters of acceptance sampling (the average outgoing quality limit, the lot size and the process average proportion defective) is analysed in the paper. Moreover, a criterion for deciding if the inspection by variables should be considered instead of the inspection by attributes is suggested in the paper.

Comparison between count of cumulative conforming sampling plans and Dodge–Romig single sampling plan

ABSTRACTIn this research, a new sampling system is introduced based on the concept of count of cumulative conforming control charts (CCC-charts). The proposed method is based on Markov modeling and negative binomial distribution. The proposed sampling system is compared with traditional sampling methods like Dodge–Romig single sampling plan based on lot tolerance percent defective (LTPD) and Dodge–Romig single sampling plan based on average outgoing quality limit (AOQL) and its superiority for larger values of lot sizes and process average is denoted using a comparison study.

Development of an Optimal Design for Conforming Run Length Sampling Methods in the Presence of Inspection Errors

Abstract In this research, a new sampling system was introduced based on the concept of conforming run length. The inspection error was considered in the proposed model as well. This methodology was based on Markov modeling and a negative binomial distribution. The proposed sampling system was compared with classical sampling methods such as the Dodge-Romig single sampling plan based on average outgoing quality limit (AOQL) in the presence of inspection errors. The superiority of the proposed method for larger values of lot sizes and process average was denoted using a comparison study.

Optimum process mean setting with specified average outgoing quality limit protection for variable single sampling plan

The average outgoing quality limit (AOQL) is a major performance evaluation for assuring the quality of product lot. The process mean setting is an important topic for statistical process control. In this paper, the author applies a variable single sampling inspection plan with the AOQL protection on the consumer for determining the optimal process mean and the parameters of sampling plan. The quality characteristic is considered with one-side lower specification limit and it is normally distributed with known standard deviation and unknown mean. The 100% inspection is adopted when the product lot is rejected. The optimum process mean and parameters of inspection plan are simultaneously determined by maximizing the expected total profit per unit under the specified AOQL value. The numerical example and sensitivity analysis of parameters are provided for illustration.

An optimization model for economic design of sampling plans based on conforming run length considering outgoing quality

ABSTRACTIn this article, a new economical acceptance sampling model is proposed based on Taguchi loss function. The objective function of the model consists of inspection cost, scrap cost, and Taguchi loss function including producer loss and consumer loss. The expected total cost includes the loss for an inspected item plus the loss for an accepted item which has not been inspected. Decision-making is based on conforming run length. It is assumed that the quality characteristics follow normal distribution. A numerical example is solved for illustrating application of this model. Sensitivity analysis is proposed for illustrating the effect of some important parameters on the objective function. Finally, we compared the results of the proposed method with classical Dodge–Romig sampling plans tables based on average outgoing quality limit. The results confirmed the superiority of proposed model.

Designing optimum plan parameters for continuous sampling plan of type (CSP-2) through GERT analysis

The main aim of this paper is to evaluate the parameters of Continuous Sampling plan of type CSP-2 through GERT technique. Procedures and tables have been provided to simulate the parameters i and f of CSP-2 for known and given process level which satisfies the requirements of Average Outgoing Quality Limit (AOQL) of CSP-2.

Practitioner advice: Dodge and Romig sampling tables: Revisited, refined, and extended-practitioner advice

ABSTRACTExcel templates together with some VBA code permit great refinements in deriving the sample sizes, n, and acceptance numbers, c, for single sampling plans of the Dodge and Romig (1944, 1959) type that were developed many years ago to achieve optimization via minimum average total inspection (ATI), for ranges of lot sizes, N, and process averages, , classified by two indices defined as lot tolerance percent defective (LTPD) and average outgoing quality limit (AOQL). Two Excel templates are presented here by which optimum single sampling plans are derived for specific values of N and , rather than for ranges of these quantities. The templates also allow for tweaking results to achieve desired properties and provide numerous additional characteristics of the derived sampling plans. While the D & R tables are limited to 8 LTPD values and 13 AOQL values, the templates are unlimited.