Variable Sampling Plan Research Articles

Designing Different Sampling Plans Based on Process Capability Index

Acceptance sampling plan is a method to make decision on either accepting or rejecting a specific lot or more generally to inspect the quality of products that can be used by different methods. Along with this, one suitable measure to improve manufacturing processes is to analyze process capability indices. These indices have many applications in production environments. In this paper, a repetitive group sampling (RGS) plan based on process capability index is introduced for variables inspection. Repetitive group sampling plan is useful when sampling costs are expensive. In this paper, considering constraints related to the risk of consumers and producers, the optimal parameters of developed repetitive group sampling plan are obtained and also a new double sampling model, a multiple dependent state (MDS) sampling plan and a sampling plan for resubmitted lots have been proposed. Finally after the development of variable sampling plan based on the Bayesian approach, a comparison study has been performed between developed repetitive sampling plan and other sampling plans and the results are elaborated.

A sequential sampling plan for exponential distribution

ABSTRACTIn this article, a sequential variable sampling plan is studied. Suppose that the quality of an item in a batch is measured by a random variable with exponential distribution; its parameter is unknown having a gamma prior distribution. Then by using Bayesian approach and considering a Markov decision process, the optimality equations for the minimum total expected cost are formulated. We show that an optimal decision rule will have a control limit structure and monotonicity. A backward induction method is suggested that is a finite algorithm for the numerical solution of the sequential sampling plan.

Variable sampling plan for resubmitted lots based on process capability index and Bayesian approach

Acceptance sampling plans are applied for quality inspection of products. Among the design approaches of sampling plan, the most important one is to use process capability indices in order to improve the quality of manufacturing processes and the quality inspection of products. But, selection of estimators of process capability index and their sampling distribution is very important. Bayesian statistical technique can be used to obtain the sampling distribution. In this paper, a variable sampling plan is developed for resubmitted lots based on process capability index and Bayesian approach. In the proposed sampling plan, lots are inspected several times depending on the quality level of the process. In addition, this paper presents an optimization model for determining the decision parameters of developed sampling plan with regards to the constraints related to the risk of consumer and producer. Two comparison studied have been done including: First, the methods of double sapling plan (DSP), multiple dependent state (MDS) sampling plan, and repetitive group sampling (RGS) plan are elaborated, and also in order to comparing developed sampling plans, an expected number of products as average sample number (ASN) is used for different developed plans; second, a comparison study between Bayesian approach and exact probability distribution is carried out and their results are analyzed. It is observed that the ASN values of MDS sampling plan is less than ASN values of other methods, and also the ASN values of different variable sampling plans based on Bayesian approach is less than ASN values obtained using exact approach.

Repetitive group sampling plan based on the process capability index for the lot acceptance problem

ABSTRACTAn acceptance sampling plan is a method used to make a decision about acceptance or rejection of a product, based on adherence to a standard. Meanwhile, process capability indices (PCIs) have been applied in different manufacturing industries as capability measures based on specified criteria which include process departure from a target, process consistency, process yield and process loss. In this paper, a repetitive group sampling (RGS) plan based on PCI is introduced for variables’ inspection. First, the optimal parameters of the developed RGS plan are obtained considering constraints related to the risk of consumers and producers and also a double sampling plan, a multiple dependent state sampling plan and a sampling plan for resubmitted lots have been designed. Finally, after the development of variable sampling plans based on the Bayesian and exact approach, a comparison study has been performed between the developed RGS plan and other types of sampling plans and the results are elaborated.

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

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.

Proposal of variable sequential sampling plan having desired operating characteristics indexed by quality loss

The proportion of non-conforming items has been traditionally utilised as an evaluation criterion for quality of items. However, the proportion of non-conforming items is not necessarily useful as a proper evaluation criterion for controlling high-quality manufacturing in recent years. Accordingly, in order to achieve further quality improvement and innovation, more careful quality evaluation has been required newly. Then, a concept of quality loss in the Taguchi methods has been devised as a severe criterion of quality evaluation. Hereby, a variable single sampling plan having desired operating characteristics (OCs) indexed by quality loss has been proposed in the area of statistical quality control. By the way, the most economical sampling inspection in the average sample number (ASN) is the sequential sampling plan based on the Wald’s sequential probability ratio test. Then, from the viewpoint of cost reduction, we discuss a variable sequential sampling plan having desired OC indexed by quality loss with the aim of expansion of the utility of variable sampling plan for quality loss. As the result, the design procedure of the sequential sampling plan for satisfying some required design conditions indexed by quality loss is provided. In addition, the effectiveness of the proposed sequential sampling plan is verified through some numerical examples.

Designing of variables quick switching sampling system by considering process loss functions

ABSTRACTThis paper proposes a variables quick switching system where the quality characteristic of interest follows a normal distribution and the quality characteristic is evaluated through a process loss function. Most of the variables sampling plans available in the literature focus only on the fraction non-conforming and those plans do not distinguish between the products that fall within the specification limits. The products that fall within specification limits may not be good if their mean is too away from the target value. So developing a sampling plan by considering process loss is inevitable in these situations. Based on this idea, we develop a variables quick switching system based on the process loss function for the application of the processes requiring low process loss. Tables are also constructed for the selection of parameters of variables quick switching system for given acceptable quality level and limiting quality level. The results are explained with examples.

A modified variables repetitive group sampling plan with the consideration of preceding lots information

Various acceptance sampling plans have been developed for different objectives. A repetitive group sampling (RGS) plan has been shown to be an efficient and easy-to-implement scheme for lot sentencing. However, it does not consider the available information from preceding samples. As a result, it may reduce the sampling efficiency in terms of cost and time. In this study, a modified variables RGS plan is proposed based on the commonly used capability index $$C_{pk}$$ for normally distributed processes with two-sided specification limits and to consider the sample results from preceding lots. The plan parameters for various required quality levels and allowable risks are tabulated for practical applications, and the advantages of the proposed plan is compared with existing variables sampling plans in terms of operating characteristic curve and average sample size.

Rectifying inspection for acceptable quality loss limit based on variable repetitive group sampling plan

It is usually assumed that a quality characteristic in an item obeys a normal distribution in the case that the quality of items is evaluated based on the variable property. Then, the concept of Taguchi’s quality loss has been accepted as the evaluation measure of quality instead of the traditional attribute property such as the proportion of nonconforming items. From this viewpoint, some variable sampling plans indexed by the quality loss have been investigated before now. As a study earliest among them, the variable single sampling plan based on operating characteristics (OC) indexed by the quality loss was considered. On the other hand, the attribute repetitive group sampling plan on OC was proposed for reducing the sampling number in the inspection. Recently, the variable repetitive group sampling (VRGS) plan on OC indexed by the quality loss has been considered. By the way, the rectifying inspection is known as one of the schemes of acceptance sampling inspection. Then, Dodge-Romig single sampling plans are known as the traditional rectifying inspection based on attribute sampling plans. Dodge-Romig rectifying attribute sampling plans provide the lot tolerance percent defective (LTPD) scheme on each lot and the average outgoing quality limit (AOQL) scheme for many lots. Furthermore, the rectifying variable single sampling (RVSS) plan indexed by the quality loss was investigated. In conformity with the traditional rectifying attribute sampling plans for the LTPD and AOQL schemes, the acceptance quality loss limit (AQLL) and specified permissible average outgoing surplus quality loss limit (PAOSQLL) schemes are respectively proposed in the RVSS plans indexed by the quality loss. In this article, we suppose that the quality characteristic in an item obeys a normal distribution. Under this condition, the rectifying variable repetitive group sampling (RVRGS) plan for AQLL is considered for the purpose of reducing the average total inspection (ATI). Specifically, the design procedure for finding out the required sample size and inspection criteria for satisfying the constraint of the quality assurance is derived. Lastly, it is shown that ATI of the RVRGS plan is reduced in comparison with that of the RVSS plan under the same condition.

A New Mixed Variable Lot Size Sampling Plan Based on Process Capability Index

Abstract A new mixed sampling plan with a variable lot size plan is developed in this manuscript using the process capability index. The operating characteristic function of the proposed plan is derived and the plan parameters are determined using the non-linear optimization procedure for symmetric and asymmetric fraction non-conforming cases. It is also shown that the proposed plan is more efficient than existing acceptance sampling plans. Industrial data is presented to explain the application of the proposed plan.

Improved Acceptance Sampling Plan Based on EWMA Statistic

In this article, a variable repetitive sampling plan is proposed based on exponentially weighted moving average (EWMA) statistic assuming that the quality of interest follows the normal distribution. A nonlinear optimization problem is developed and the plan parameters are determined by satisfying the imposed conditions. The plan parameters are determined when the standard deviation is known or unknown. The efficiency of the proposed plan is discussed over the existing variable plan using the EWMA statistic for single sampling. An example is presented to implement the proposed plan in the industry.

A lots-dependent variables sampling plan considering supplier’s process loss and buyer’s stipulated specifications requirement

A well-established scheme and mechanism for deciding product acceptance is perceived as a win-win situation for the long-term supplier–buyer relationship. In this paper, we develop a lots-dependent variables sampling scheme for product acceptance determination. The dependent state is based on the sample information of the process capability index that incorporates the supplier’s process loss and the buyer’s demanded specifications requirement. This main scheme is implemented by a three-rule process that accepts or rejects a related lot conditional on the sample results of past lots. The plan-operational parameters satisfying the desired quality levels and constraining the supplier–buyer risks are determined by a non-linear optimisation model. In performance comparisons, our proposed plan demonstrated higher cost effectiveness and discriminatory power than the traditional variables single sampling plan. Finally, industrial applicability of our recommended sampling plans was investigated in a case study.

Variables Sampling Plan for Resubmitted Lots in a Process with Linear Profiles

Acceptance sampling plans include a sampling scheme and a set of rules for determining whether an inspection lot from a supplier should be accepted or rejected. In some circumstances, the supplier is allowed to resubmit lots for further inspection when the original inspection result is unacceptable. In this study, two variables sampling plans based on the process‐yield index for a process with linear profiles are proposed to deal with lot sentencing. The single sampling plan is a special case of the resubmitted lots sampling plan. The plan parameters are determined using a nonlinear optimization method under the given values of producer's risk, consumer's risk, acceptable quality level, and lot tolerance percent defective. Numerous tables are provided to determine the plan parameters. One real example is used to illustrate our proposed method. Copyright © 2015 John Wiley & Sons, Ltd.

The economic design of variable acceptance sampling plan with rectifying inspection

Purpose – The purpose of this paper is to develop an economic model, which could determine the acceptance sampling plan that minimizes the quality cost for batch manufacturing. Design/methodology/approach – The authors propose a variable sampling plan based on one-sided capability indices for dealing with the quality cost requirement. Findings – The total quality cost is much more sensitive to process capability indices and inspected cost than internal and external failure costs. Research limitations/implications – The experimental data were randomly generated instead of real world ones. Practical implications – The proposed model is specifically designed for manufacturing industries with high sampling cost. Originality/value – The one-sided capability indices were utilized for the first time to be suitable for the purpose.

Designing a variables two-plan sampling system of type TNTVSS-(nT, nN; k) for controlling process fraction nonconforming with unilateral specification limit

This paper proposes a variables two-plan sampling system involving normal and tightened inspections, denoted as TNTVSS-, for controlling process fraction nonconforming with a unilateral specification limit based on one-sided capability indices. The system utilises two single variables sampling plans with different sample sizes and the same critical acceptance value , where and are sample sizes required for tightened inspection and normal inspection, respectively. The tightened inspection plan is used when the quality deteriorates and the normal inspection plan is used when the quality is found to be good. The operating characteristic (OC) function of the proposed sampling system is developed based on the exact sampling distribution. The plan parameters under various settings are determined by solving two non-linear equations simultaneously, which satisfy the required quality levels and allowable risks given by the producer and the consumer. The behaviour of the proposed sampling system in terms of the OC curve and the average sample number are also examined, discussed and compared with the traditional single variables sampling plan.

Chance Single Sampling Plan for Variables

This paper considers the design of single sampling plan for variables when the experimental values are treated as observations on independently and identically distributed normal random variables with fuzzy mean value. The design makes use of Liu's (2008) model IV of Chance Theory. Sampling Plans determined by the sample sizes and acceptance numbers are constructed for situations involving imprecise parameter on using chance theory. The process of determining sample sizes and acceptance threshold values has been carried out on assuming the observed values have hybrid normal distribution. Optimal chance sampling plans for variables are also determined by using minimum angle criterion for different choices of fuzzy risks.

A Sampling Scheme for Resubmitted Lots Based on One-Sided Capability Indices

Acceptance sampling plans provide decision rules for lot acceptance determination based on the required quality levels and allowable risks. In this paper, we develop a variables sampling plan based on the one-sided process capability indices, CPU and CPL, when lot resubmissions are permitted on non-acceptance of the original inspection. The plan parameters are determined by solving two non-linear equations simultaneously and fulfill the two-point condition on the operating characteristic (OC) curve. The OC curve of the proposed plan is derived based on the exact sampling distribution rather than approximation. Moreover, the behavior of the proposed resubmitted sampling plan for various parameters is examined and discussed. For practical purposes, the sample size and critical acceptance value are tabulated for various parameter values. An example is used to demonstrate the implementation of the proposed resubmitted sampling plan.

Optimal Designing of Variables Sampling Plan for Resubmitted Lots

This article proposes a variables sampling plan that can be applied for sampling inspection of resubmitted lots when the quality characteristic of interest follows the normal distribution. Resubmission of lots for inspection is allowed in some situations where the original inspection results are suspected or when the supplier or producer is allowed to opt for resampling as per the provisions of the contract, etc. The advantages of this proposed variables sampling plan over the existing single sampling variables plan are discussed. Tables are also constructed for the selection of optimal parameters of known and unknown standard deviation variables resampling scheme for specified two points on the operating characteristic curve, namely, the acceptable quality level and the limiting quality level along with the producer and consumer's risks. The optimization problem is formulated as a nonlinear programming where the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve.

Computation of optimum reliability acceptance sampling plans in presence of hybrid censoring

The decision regarding acceptance or rejection of a lot of products may be considered through variables acceptance sampling plans based on suitable quality characteristics. A variables sampling plan to determine the acceptability of a lot of products based on the lifetime of the products is called reliability acceptance sampling plan (RASP). This work considers the determination of optimum RASP under cost constraint in the framework of hybrid censoring. Weibull lifetime models are considered for illustrations; however, the proposed methodology can be easily extended to any location-scale family of distributions. The proposed method is based on asymptotic results of the estimators of parameters of lifetime distribution. Hence, a Monte Carlo simulation study is conducted in order to show that the sampling plans meet the specified risks for finite sample size.