Repetitive Group Sampling Plan Research Articles

An improved skip-lot sampling scheme with resampling mechanism using an advanced capability index

In today’s competitive market, product quality holds significant importance for consumers, motivating companies to prioritise high-quality product development and enhance their competitiveness. Acceptance sampling plans have proven to be indispensable tools in quality control practices, enabling producers and consumers to protect their interests by establishing evaluation rules for product batches. As defective rates decrease in modern manufacturing, skip-lot sampling plans (SkSP) have emerged as a suitable way for lots exhibiting stable and excellent product quality. Additionally, repetitive group sampling plan (RGSP) offers a cost-effective way to maintain desired protection for both parties, especially in costly or destructive inspection scenarios. Therefore, this study integrates the benefits of process capability indices, SkSP, and RGSP to develop a new variables SkSP with RGSP as its reference plan based on an advanced capability index Cpmk (called Cpmk -based SkSP-RGSP). The proposed plan achieves comparable discriminatory power to traditional sampling plans while significantly reducing the required sample size. Detailed tables of plan parameters are given to facilitate effective implementation for practitioners.

Determination and economic design of repetitive group sampling plan under two parameter Lindley distribution

ABSTRACT A designing procedure of repetitive group sampling plan for assuring mean life under a two-parameter Lindley distribution is proposed, and the optimization model is developed for finding the optimal plan parameters such that the demands of both supplier and buyer are satisfied simultaneously. A real-time data set of ball bearings is used to explain the application of the proposed plan. A comparison between the proposed plan and the single sampling plan is done to reveal the better performance of the proposed plan based on operating characteristic function and average sample number. Applying the proposed plan to provide lifetime assurance reduces the inspection effort and related costs. We discuss the design of the proposed plan with an economic aspect. In addition, the sensitivity of the optimal sampling plans concerning the failure probability and cost parameters is analyzed. Finally, it is evident from the study that the proposed plan will be preferable to a single sampling plan for providing quality assurance with a minimum cost of the inspection.

Formation of Repetitive Group Sampling Plan for Life Tests Based on Percentiles using Odd Frechet Inverse Rayleigh Distribution

Objectives: This paper presents the idea of Repetitive Group Sampling Plans using Odd Frechet Inverse Rayleigh Distribution, when the life test is truncated at a pre-specified time. The main objective of the proposed sampling plan is to minimize the sample size because the analogous inspection time and inspection cost will be reduced. Methods: A truncated life test may be conducted to evaluate the smallest sample size to insure certain percentile lifetime of products. The minimum sample size and its ratio for the specified lifetime percentile were derived for the producer’s risk. The operating characteristic values are also obtained for the proposed sampling plan. The corresponding table values are obtained through Monto Carlo Simulation technique. Findings: The results from the sampling plan developed in this research can easily be adaptable in practical situation with small sample sizes and fewer experimental times and hence the plan yields a better result for reliability sampling plan. Novelty: The work designed and developed with the aim that sampling plan in this paper may be helpful for the engineers and statistical plan developers in the field of statistical quality control especially in attribute reliability sampling plan. The tables are generated which is useful for both producer and consumer. This plan can highly recommendable since the products are randomly sampled and also the procedure for sampling involves less experiment time and with minimum sample size. Keywords: Odd Frechet Inverse Rayleigh Distribution, Percentiles, Repetitive Group Sampling Plan (RGS), Producer’s risk

Construction of acceptance sampling schemes for exponential lifetime products with progressive type II right censoring

Ensuring product quality is crucial for enhancing a company's competitiveness, and product lifetime serves as a vital metric, particularly in the context of electronic goods, for evaluating product quality. To meet quality requirements and mitigate risks for both producers and consumers, thorough examinations of components and final products are necessary. Acceptance sampling plans are commonly employed to achieve these objectives. When assessing product lifetime under non-normal distributions, the lifetime performance index emerges as a valuable and frequently utilized metric. In practical scenarios, lifetime tests may encounter challenges such as the absence of experimenters to observe all product lifetimes and the possibility of accidental product breakage. To address these issues, this study introduces two sampling schemes: a single sampling plan and a repetitive group sampling plan. These plans are specifically designed for exponential lifetime products, utilizing the progressively type II right censored sample as the data type for lifetime testing. The study provides tabulated plan parameters for practical implementation and presents a comparative analysis between the two proposed plans. Furthermore, a practical example is presented to demonstrate the efficacy of the developed sampling plans.

Multiple dependent repetitive group sampling plan for Marshall-Olkin logistic-exponential distribution assuring percentile lifetime with applications

Acceptance sampling plans are commonly utilized for planning, process control, and implementation of industrial data sets. In addition to this, they also provide a solution for process quality control. They could be used for executing a decision for acceptance or rejection of a lot. A good acceptance sampling plan can be formulated depending on the requirements of the project. Usually, the plan should follow a defined lifetime distribution. Hence, the appropriate plan would not only determine the plan parameters but would also be cost and time efficient. In this article, an attribute multiple dependent repetitive group sampling (MDRGS) plan is developed assuming that the lifetime of the product follows the Marshall-Olkin logistic-exponential (MOLE) distribution. The parameters of plan are examined by considering a two-point approach. The suggested plan is contrasted with the single sampling and repeated group sampling plans. Finally, the implementation of the proposed plan is discussed using industrial as well as simulated data sets. It is concluded that the proposed plan reduces the sampling inspection cost and time as compared to existing acceptance sampling plans.

Design of Multiple Deferred State Repetitive Group Sampling Plans for Life Tests based on Generalized Gamma Distribution

Reliability sampling plans is a procedure to determine the acceptance or non-acceptance of the lot(s) of finished products by performing tests on the sampled items. Lifetime of individual items is a quality characteristic that can be treated as a continuous random variable and can be modeled by an appropriate continuous probability distribution. In this article, Multiple Deferred State Repetitive Group Sampling (MDSRGS) Plans for life tests under hybrid censoring with a provision to draw a random sample and to admit a maximum of one failure in the sample is formulated assuming that the lifetime random variable follows a Generalized Gamma (GG) distribution. A methodical procedure for the selection of the plan parameters using mean life criterion with the desired discrimination protecting the interests of the producer and the consumer in terms of the acceptable mean life and unacceptable mean life is evolved.

Economical design of multiple deferred (dependent) state repetitive group sampling plan based on truncated life test under exponentiated half-logistic distribution

The design of a multiple deferred (dependent) state repetitive group sampling plan for exponentiated half-logistic distributed percentile life assurance under time-truncated life test is considered in this article. In this research, tables are provided to choose the design parameters of the proposed plan determined for different percentile ratios using the method of two points on the operating characteristic curve with known shape parameter values. We describe the sampling procedure of the proposed multiple deferred (dependent) state repetitive group sampling plan with real-time data and discuss the effect of misspecification of the shape parameter on lot acceptance probabilities. Based on an economical design of the proposed plan, an optimal plan is determined that satisfies both producer and consumer risks with minimum cost. In addition, the performance of the proposed plan is analyzed and compared with other existing sampling plans under an exponentiated half-logistic lifetime distribution. Finally, conclusions are provided.

Optimal design of multiple dependent state repetitive group sampling plan for Inverse Power Lomax distribution

A sampling plan named as Multiple Dependent State Repetitive Group Sampling (MDSRGS) plan is introduced for a time-truncated life test given that the underlying distribution of the product's lifetime is Inverse Power Lomax distribution (IPLD). The proposed sampling plan is developed with the help of two already developed sampling plans (MDS and RGS). The two-point approach OC function known as the producer's risk and customer's risk is used to determine the parameters of the proposed plan. An optimization method is used for different values of customer's risk and producer's risk, for static values of experiment termination ratio and mean ratio, to find out plan parameters (minimum size of the sample, the number of acceptance and rejection, and the number of successive lots). Tables are created for different known values of shape parameters of Inverse Power Lomax distribution. The efficiency of the proposed MDSRGS plan is examined by conducting a comparative study. To accompany the results, graphs are also used for visualizing the average sample and acceptance probabilities with the specific mean ratio. Two real-life applications are also incorporated to demonstrate the operating procedure of the proposed plan.

An optimal construction of yield-based EWMA repetitive multivariate sampling plan

In this paper, a variable repetitive group sampling (VRGS) plan is proposed based on the exponentially weighted moving average (EWMA) statistic with yield index for inspection of mutually independent and multivariate normally distributed characteristics. Plan parameters are found optimally based on asymptotic distribution of using a non linear optimization. A simulation study indicates that the reported parameters can thoroughly warrant determined risks for finite sample sizes. This work also extends application of the proposed plan to the class of correlated characteristics. The obtained findings show that the proposed plan significantly reduces required average sample number compared to the existing modified VRGS plan, single, double, and multiple dependent state sampling plans with yield-based EWMA statistic. Two industrial examples are presented to illustrate the application of the proposed plan in real world.

A repetitive group sampling plan based on the lifetime performance index under gamma distribution

AbstractAs technology and living standards improve, people are becoming more concerned with the importance of quality. Quality, thus, becomes the key to company competitiveness, and process capability indices (PCIs) are effective means of measuring process performance. Most PCIs have been developed under the assumption that the quality characteristics are normally distributed; however, the lifetime of products generally possesses a non‐normal distribution. A lifetime performance index (LPI) CL has been proposed and used for measuring product lifetime performance. In this high‐quality era, the use of traditional testing methods incurs very high costs, so acceptance sampling plans have been widely used by industry to perform the inspection. This study considers the product lifetime with a gamma distribution and uses the uniformly minimum‐variance unbiased estimator (UMVUE) of the LPI to develop a repetitive group sampling plan (RGSP). For the practical purpose, this study presents a step‐by‐step procedure and tabulates the plan parameters for various combinations of acceptable and rejectable quality levels, producer's and consumer's risks, and shape parameter. Thus, practitioners can easily know the sample size and the corresponding critical values for decision making. This study also uses the results of the proposed plan to compare with the single sampling plan. Lastly, a practical example is used to illustrate how to apply this acceptance sampling plan.

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.

Product Acceptance Determination Based on EWMA Yield Index Using Repetitive and MDS Sampling Schemes

In this manuscript, we present a repetitive group sampling plan and a multiple dependent state sampling plan based on the EWMA (exponentially weighted moving average) yield index for product acceptance. The proposed plans utilize the current and the previous information through EWMA statistic to reach a decision of lot sentencing. A non-linear optimization model is developed to determine the plan parameters of the proposed plans for various specified conditions. The performance of the proposed plans over several existing sampling plans is analyzed, which shows that the proposed plans are efficient in reducing the sample size for lot sentencing. For industrial application, a real example is given to demonstrate the implementation of the proposed plans.

Optimization of Bayesian repetitive group sampling plan for quality determination in Pharmaceutical products and related materials

Sampling plans are extensively used in pharmaceutical industries to test drugs or other related materials to ensure that they are safe and consistent. A sampling plan can help to determine the quality of products, to monitor the goodness of materials and to validate the yields whether it is free from defects or not. If the manufacturing process is precisely aligned, the occurrence of defects will be an unusual occasion and will result in an excess number of zeros (no defects) during the sampling inspection. The Zero Inflated Poisson (ZIP) distribution is studied for the given scenario, which helps the management to take a precise decision about the lot and it can certainly reduce the error rate than the regular Poisson model. The Bayesian methodology is a more appropriate statistical procedure for reaching a good decision if the previous knowledge is available concerning the production process. This article proposed a new design of the Bayesian Repetitive Group Sampling plan based on Zero Inflated Poisson distribution for the quality assurance in pharmaceutical products and related materials. This plan is studied through the Gamma-Zero Inflated Poisson (G-ZIP) model to safeguard both the producer and consumer by minimizing the Average Sample Number. Necessary tables and figures are constructed for the selection of optimal plan parameters and suitable illustrations are provided that are applicable for pharmaceutical industries.

An integrated failure-censored sampling scheme for lifetime-performance verification and validation under a Weibull distribution

Acceptance sampling plans (ASPs), practically providing an economic size of sampling inspection and a definite standard for lot-sentencing determination, have been widely used for the products' quality verification and validation. Simply sentencing the submitted lot according to the inspection of only one group of samples, the single sampling plan (SSP) has an advantage of lot-by-lot simple administration. When encountering costly, destructive, and time-consuming life testing, the SSP’s simplicity, however, comes at the high expense of requiring large-tested samples. To overcome the drawback, the multiple-dependent-state sampling plan (MDSP) and repetitive group sampling plan (RGSP) have been recently developed. The former activates a backtracking mechanism to include valuable information inspected from preceding lots, whereas the latter actuates a resampling mechanism to alleviate psychological skepticism raised from both entities of supplier and buyer. In this paper, an integrated failure-censored sampling scheme (IFCSS), consolidating both advantages gained from the MDSP and the RGSP, is developed based on the Weibull-lifetime performance index. We construct an optimization model to determine the plan criteria under the economical objective. Moreover, we further create a Weibull-lifetime IFCSS web-based app with QR code access for the plan’s easy setup. By comparing with inspection performances, our proposed IFCSS exhibits superior cost-efficiency and discriminating capability than the recently developed MDSP and RGSP. Finally, the Weibull-lifetime IFCSS’s applicability is illustrated by a ceramic-bearing lifetime-testing inspection.

Yield‐based variables repetitive group plan with a critical‐value‐adjusted mechanism

AbstractAcceptance sampling plans are preferably used when sample testing becomes destructive or costly to make reliable lot determination from a reasonable size of samples. Previous decades have seen various sampling strategies developed for specific purposes and the evolution of sampling methods continue to ensure that lot sentencing becomes more efficient and economic. In this study, we proposed a modified variables repetitive group sampling (VRGS) plan integrated with a critical‐value‐adjusted switching mechanism. Such a design provides an adaptive assessment of the varied submitted quality level. The operating characteristic function is derived from the sampling distribution of process yield index Spk, which possesses a one‐to‐one transformation to process yield. By solving the developed nonlinear minimization model, the plan parameters of the proposed method are satisfied with tolerable sampling risks and desirable quality levels simultaneously. Furthermore, by comparing the average sample number (ASN) reduction and discriminatory power with other approaches, the proposed method outperforms conventional methods. Numerical illustrations are provided to show its practicability in real applications.

Developing process-yield-based acceptance sampling plans for AR(1) auto-correlated process

Acceptance sampling plans include a sampling scheme and a set of rules to determine whether an inspection lot from a supplier should be accepted or rejected. This paper aims at developing two acceptance sampling plans by variables inspection, namely a quick switching sampling (QSS) system and the modified repetitive group sampling (Modified-RGS) plan based on the process yield index for the first-order auto-regressive (AR(1)) auto-correlated process. A minimization model is employed to solve the plan parameters. The performance of the proposed sampling plans is investigated and compared with the existing sampling plans through the operating characteristic (OC) curve and the average sample number (ASN) required for inspection. The simulation results confirm the advantages of the proposed plans over existing sampling plans. An example is presented to illustrate the applicability of the proposed plans.

Determination of multiple deferred state repetitive group sampling plan for life time assurance under Birnbaum–Saunders distribution

A designing methodology to determine the optimal multiple deferred state repetitive group sampling plan for assuring Birnbaum–Saunders distributed both mean and median life of the products is proposed in this paper. The operating procedure and the performance measures of the proposed sampling plan are presented in this study. One of the familiar approaches involved in sampling plan determination that is two points on the operating characteristic curve approach is used to select the optimal plan parameters, which has minimum average sample number. Tables are constructed to report the optimal plan parameters for different set of mean or median ratio and shape parameter values of Birnbaum–Saunders distribution. Further, the proposed multiple deferred (dependent) state repetitive group sampling plan is compared with other existing sampling plans using some of the performance measures.

Developing a skip-lot sampling scheme by variables inspection using repetitive sampling as a reference plan

ABSTRACT In today’s manufacturing environment, the rate of defective products has been continuously decreasing; thus, variables sampling plans with process capability indices (PCIs) have been recommended to gather more information about a manufacturing process and reduce required sample sizes for inspection. In particular, skip-lot sampling plan (SkSP) is suitable for a series of lots having stable and excellent product quality. Moreover, the concept of repetitive group sampling (RGS), which can allow the use of less samples to maintain desired protection to producers and consumers, is especially appropriate where inspection or testing is costly or destructive. This study, by incorporating the advantages of PCIs, SkSP, and RGS, constructs a variables SkSP with RGS as the reference plan (called SkSP-RGS) based on one-sided PCIs for products with a unilateral specification limit. The proposed plan reduces the sample size while achieving a similar discriminatory power, compared with a conventional variables single sampling plan (SSP), a RGS plan (RGSP), and a SkSP of type 2 (SkSP-2). Tables of plan parameters are provided for frequently applied quality and risk requirements so that practitioners can easily apply the proposed plan.

An adjustable inspection scheme for lot sentencing based on one-sided capability indices

Acceptance sampling is an extensively used strategy for determining if the quality of a submitted product lots meets the required standards. Several sampling plans were developed based on different strategies to meet this aim and to increase their overall efficiency and flexibility. The repetitive group sampling plan (RGSP) is demonstrated to be an efficient sampling scheme but has its demerits in that the number of times sampled depends on the sampling results and theoretically could be infinite. To overcome this drawback, an adjustable inspection scheme based on one-sided capability indices was developed by setting a limit on total sampling times to the conventional RGSP. The operating characteristic (OC) function and average sample number of the proposed plan are derived based on the exact sampling distribution of unbiased estimators. To determine the plan parameters, an optimization model with non-linear constraints related to quality and risk requirements is formulated, and those under various commonly used settings are tabulated for practical use. The plan's performance is examined, discussed, and compared with alternative conventional plans. Finally, an example is provided to illustrate the applicability of the proposed plan.

Design of Multiple Dependent State Repetitive Group Sampling Plans Based on Exponentiated Exponential Distribution

Abstract This article attempts to design a multiple dependent state repetitive group sampling plan under a hybrid censoring scheme by assuming that the lifetime of the product follows an exponentiated exponential distribution. Exponentiated exponential distribution, an alternative to Weibull and gamma distributions, has found applications in reliability and life testing. Also, an attempt is made to study the efficiency of this plan in comparison with a single sampling plan. The efficiencies of these two kinds of sampling plans are analyzed with respect to sample size and sampling risks. Plan parameters are obtained using binomial probabilities protecting the interests of both producers as well as consumers. The selection of a sampling plan for given requirements is illustrated with a numerical example.