Multiple Dependent State Sampling Plan Research Articles

Generalized multiple dependent state sampling plans for coefficient of variation

Sampling plans using the coefficient of variation (CV) attract increasing attention by many authors in the literature due to its importance to measure the product quality. A generalized multiple dependent state (GMDS) sampling plan for accepting a lot is proposed based on the coefficient of variation when a quality characteristic comes from a normal distribution. The optimal plan parameters of the proposed plan are solved by a nonlinear optimization model, which minimizes the sample size required for inspection while satisfying the given producer’s risk and the consumer’s risk at the same time. A comparative study of the proposed GMDS sampling plan over the two existing sampling plans is considered. A real example is given to demonstrate the proposed plan.

A variables-type multiple-dependent-state sampling plan based on the lifetime performance index under a Weibull distribution

Verification and validation of product quality highly affects the success of product design and manufacturing processes as well as the long-term collaboration between buyers and suppliers. Lifetime testing for acceptance is the main bottleneck in verification and validation and often requires considerable time and expense, especially in the current high-product-yield era. To establish a cost-effective and risk-controllable life testing sampling scheme, we propose a variables-type multiple-dependent-state (MDS) sampling plan using the lifetime performance index under a Weibull distribution with Type-II right censoring. The design parameters of the lifetime-capable MDS sampling plan are formulated as optimization models to minimize the required number of testing failures subject to nonlinear constraints for the desired lifetime capability levels and allowable risks regulated by the supplier and buyer. Compared with variable single sampling plans, the plan proposed herein is more cost-effective sampling and has greater discriminatory power. The applicability of the proposed plan is demonstrated through an example.

Variables adjustable multiple dependent state sampling plans with a loss-based capability index

Acceptance sampling plans are a cross-functional quality control instrument for benchmarking compliant standards of incoming as well as outgoing lots. The multiple dependent state (MDS) plan has been proposed and proven to advantage the conventional single sampling plan (SSP). However, the MDS plan presents a contradictory situation: Its performance depreciates as the number of previously considered lots increases. This outcome implies that the greater the number of cumulative lot-sentencing results one intends to include is, the greater the sample size is required for inspection, where a loosened criterion for quality acceptance levels, unfavorably, is introduced as well. Therefore, we proposed a modified MDS plan that depends on the loss-based capability index to accommodate an adjustable mechanism, namely, the adjustable multiple dependent state (AMDS) sampling plan. The AMDS plan allows encompassing not only a greater number of preceding lots in the lot disposition decision but also reducing the sample size required for the inspection and raising the lot-sentencing quality standards to stimulate the supplier attaining with persistently reliable submissions for a long-term supplier-consumer relationship. In comparison to the plans’ performance, our proposed AMDS plans demonstrate superior cost-effectiveness, discriminatory powers, and average run lengths than those of the SSP and MDS sampling plans. Furthermore, we tabulated the plan parameters under numerous conditions and delivered a real industry case to demonstrate its applicability.

Generalized Multiple Dependent State Sampling Plans in Presence of Measurement Data

This article introduces a generalized version of the multiple dependent state sampling plan based on the measurement data, that is, when the quality characteristic is measured in a numerical scale. The conditions of application and the operating procedures of the proposed plan are discussed sequentially. A few important performance measures, such as operating characteristic curve, average total inspection and average sample number, are developed. The advantage of the proposed plan over the multiple dependent state sampling and single sampling plan is demonstrated through numerical example. Finally, one real-life data set is analyzed to illustrate the application of the proposed sampling plan.

A group multiple dependent state sampling plan using truncated life test for the Weibull distribution

Group and conditional sampling methods have been recently developed to apply in industrial environments. Based on the combination of two group and conditional schemes, this article introduces a group multiple dependent state sampling plan for a truncated life test when the lifetime of item follows the Weibull distribution. The proposed plan can be applied when the quality history of process is accessible and a multiple number of items are installed as a group in each tester. The proposed plan has merits which are illustrated via a comparative study over the existing group acceptance sampling plan. Furthermore, a real example is provided.

Determination and economic design of a generalized multiple dependent state sampling plan

In this paper, we have introduced a generalized version of multiple dependent state sampling plan called generalized multiple dependent state sampling plan. The conditions of application and operating procedure of this new plan are also proposed. The performance measures such as the probability of acceptance, average sample number and average total inspection are derived. The optimal parameters are determined based on two points on the operating characteristic curve approach under both fraction non-conforming and fraction non-conformities. The efficiency of proposed plan is also discussed over the existing attribute sampling plans. Finally economic aspect of designing of the proposed plan is discussed.

A new multiple dependent state sampling plan based on the process capability index

We propose a new multiple dependent state sampling plan which comprises the features of existing multiple dependent state sampling plan and repetitive group sampling plan. We develop this new sampling plan for the inspection of measurable quality characteristics. The proposed plan is developed based on the process capability index Cpk , where the quality characteristic under investigation follows the normal distribution with unknown mean and unknown variance. For the practical application of the proposed new sampling plan industries by, tables are constructed to determine the optimal parameters through a non-linear optimization problem. The advantages of this proposed sampling plan are also discussed.

Sampling plans for the zero‐inflated negative binomial distribution in the food industry

AbstractIn this paper, we propose 3 new sampling plans, including resubmitted single sampling plan (RSSP), repetitive group sampling (RGS) plan, and multiple dependent state (MDS) sampling plan to study the zero‐inflated negative binomial distribution in microbiological food safety and quality assurance practices. The unity value approach is used to find optimal plan parameters. The proposed plans are compared with the single sampling plan (SSP). We found that degree of clustering and excess of zeros counts affect the performance of all sampling plans. The MDS plan outperforms the SSP, RSSP, and RGS plans with respect to minimum average sample number in most cases. Both RGS and MDS plans show a comparable performance. The average run length is calculated to evaluate the rejection capability of the plans and signal the deterioration of the quality of lots. An example from 9 Irish abattoirs is used to illustrate the application of the proposed methods.

Sampling plans for the zero-inflated Poisson distribution in the food industry

Zero-inflated models have been used successfully to describe microbial data with excess of zero-counts. Some sampling plans such as single sampling plan (SSP), resubmitted single sampling plan (RSSP) and quick switching system (QSS) have been developed for the zero-inflated Poisson (ZIP) distribution. Two new plans such as repetitive group sampling (RGS) and multiple dependent state (MDS) sampling are proposed to compare their performance with the existing sampling plans. Additionally, we develop double sampling (DS) and sequential sampling plans for the ZIP data. The plan parameters of the sampling plans are determined by using the unity value approach. The MDS sampling plan is more economical than the other sampling plans, including SSP, RSSP, RGS and QSS, in terms of the required sample size and average sample number in most cases. The probability of a zero in the ZIP data affects the sample size required for all sampling plans. Practical guidance for selecting sampling plans under ZIP is also provided.

Determination of a new mixed variable lot-size multiple dependent state sampling plan based on the process capability index

ABSTRACTThis article proposes a new mixed variable lot-size multiple dependent state sampling plan in which the attribute sampling plan can be used in the first stage and the variables multiple dependent state sampling plan based on the process capability index will be used in the second stage for the inspection of measurable quality characteristics. The proposed mixed plan is developed for both symmetric and asymmetric fraction non conforming. The optimal plan parameters can be determined by considering the satisfaction levels of the producer and the consumer simultaneously at an acceptable quality level and a limiting quality level, respectively. The performance of the proposed plan over the mixed single sampling plan based on Cpk and the mixed variable lot size plan based on Cpk with respect to the average sample number is also investigated. Tables are constructed for easy selection of plan parameters for both symmetric and asymmetric fraction non conforming and real world examples are also given for the illustration and practical implementation of the proposed mixed variable lot-size plan.

A variables multiple dependent state sampling plan based on a one-sided capability index

ABSTRACTAcceptance sampling plan has been considered as one of most practical tools for quality assurance applications. While various types of acceptance sampling plans have been developed for different purposes, single acceptance sampling plan is the most popular because it is simple to administrate. However, a new concept called multiple dependent state sampling has gained the attention of scholars in recent years. The underlying principle is that the acceptance of a submitted lot should not only depend on the quality of the current lot but also consider the quality of the preceding lots. This research develops a variables multiple dependent state sampling plan (VMDSSP) for unilateral specification limit based on a one-sided capability index. The operating characteristic (OC) curve is prepared based on the exact sampling distribution. The plan parameters are determined by minimizing the average sample number while satisfying the quality levels demanded by both the producer and the consumer. The performance of the proposed plan is compared with the traditional variables single sampling plan (VSSP) and is examined in a case study.

Developing a variables multiple dependent state sampling plan with simultaneous consideration of process yield and quality loss

Acceptance sampling plans have been utilised predominantly for the inspection of outgoing and incoming lots; these plans provide effective rules to vendors and buyers for making decisions on product acceptance or rejection. Multiple dependent state (MDS) sampling plans have been developed for lot sentencing and are shown to be more efficient than traditional single sampling plans. The decision criteria of MDS sampling plans are based on sample information not only from the current lot but also from preceding lots. In this study, we develop a variables MDS sampling plan for lot sentencing based on the advanced process capability index, which was developed by combining the merits of the yield-based index and loss-based index. The operating characteristic function of the developed plan is derived based on the exact sampling distribution. The determination of plan parameters is formulated as an optimisation model with non-linear constraints, where the objective is to minimise the sample size required for inspection and the constraints are set by the vendor and the buyer to satisfy the desired quality levels and allowable risks. The performance of the developed plan is examined and compared with traditional sampling plans. A step-by-step procedure is provided, and the parameters of the plan under various conditions are tabulated for practical applications.

Designing a multiple dependent state sampling plan based on the coefficient of variation

A multiple dependent state (MDS) sampling plan is developed based on the coefficient of variation of the quality characteristic which follows a normal distribution with unknown mean and variance. The optimal plan parameters of the proposed plan are solved by a nonlinear optimization model, which satisfies the given producer’s risk and consumer’s risk at the same time and minimizes the sample size required for inspection. The advantages of the proposed MDS sampling plan over the existing single sampling plan are discussed. Finally an example is given to illustrate the proposed plan.

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.

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.

Mixed Multiple Dependent State Sampling Plan Using Exponentially Weighted Moving Average

Mixed Multiple Dependent State Sampling Plan Using Exponentially Weighted Moving Average

A Single Sampling Plan Based on Exponentially Weighted Moving Average Model for Linear Profiles

The exponentially weighted moving average (EWMA) model has been successfully used in acceptance sampling plans. The EWMA model provides the quality information of the current lot and the preceding lots. In addition, a multiple dependent state (MDS) sampling plan considers the quality information of the preceding lots. In this study, we present two new sampling plans for linear profiles. One is based on EWMA model with yield index using the single sampling plan, and the other is based on EWMA model with yield index using the MDS sampling plans. The plan parameters are determined by a nonlinear optimization approach. As the smoothing parameter value equals to one, the first proposed plan becomes the traditional single sampling plan. In addition, we compare the proposed plans with the traditional single sampling plan. The results indicate that the MDS sampling plan based on EWMA model with yield index with smaller value of smoothing parameter performs better than the traditional single sampling plan and the single sampling plan based on EWMA model with yield index in terms of the sample size required. One real example is used to illustrate the proposed plan. Copyright © 2015 John Wiley & Sons, Ltd.

A Novel Lot Sentencing Method by Variables Inspection Considering Multiple Dependent State

A good acceptance sampling plan is necessary for quality control, and different acceptance sampling plans have been developed to meet different purposes. Under a multiple dependent state (MDS) sampling plan, the lot disposition is not only based on the current sample from the lot but also on the sample results from preceding lots. This paper aims to develop a variables MDS sampling plan for normally distributed processes with two‐sided specification limits. In the proposed MDS sampling plan, the operating characteristic curve is derived based on the exact sampling distribution. The performance of the proposed plan is investigated and compared with the existing variables single sampling plan. Copyright © 2015 John Wiley & Sons, Ltd.

Design and construction of a variables multiple dependent state sampling plan based on process yield

Acceptance sampling plans can be used in decision making for product quality control. The plans provide decision rules to the producer and the consumer for lot determination. In this paper, a new sampling plan, namely variables multiple dependent state (VMDS), is developed based on the process yield index Spk and utilises the conventional variables single sampling (VSS) plan as a reference plan. The plan parameters are solved by the optimisation problem, in which the objective function is designed to minimise the sample size and the constraints are formulated for satisfying the allowable risks given by the producer and the consumer simultaneously. The results indicate that the proposed VMDS sampling plan can provide the same projections to the producer and the consumer with smaller required sample size which compared to the conventional VSS plan. For practical applications purpose, an example taken from Li-ion battery industry is presented for illustration. [Received 25 August 2014; Revised 23 December 2014; Accepted 15 February 2015]