Group Sampling Plan Research Articles

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.

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.

Group Acceptance Sampling Plans for Resubmitted lots for life tests based on Half Logistic Distribution

In this article, a group acceptance sampling plan (GASP) for lot resubmitting is developed to ensure quality of the product lifetime assuming that the product’s lifetime follows the half logistic distribution. The parameters of the GASP are determined by satifying the specified producer’s and consumer’s risks according to the experiment termination time and the number of testers. A comparison between this proposed group sampling and the ordinary group sampling plan is discussed. This proposed plan is justified with an illustration.

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.

Single-stage and two-stage total failure-based group-sampling plans for the Weibull distribution under neutrosophic statistics

If the sample or population has vague, inaccurate, unidentified, deficient, indecisive, or fuzzy data, then the available sampling plans could not be suitable to use for decision-making. In this article, an improved group-sampling plan based on time truncated life tests for Weibull distribution under neutrosophic statistics (NS) has been developed. We developed improved single and double group-sampling plans based on the NS. The proposed design neutrosophic plan parameters are obtained by satisfying both producer’s and consumer’s risks simultaneously under neutrosophic optimization solution. Tables are constructed for the selected shape parameter of Weibull distribution and various combinations of neutrosophic group size. The efficiency of the proposed group-sampling plan under the neutrosophic statistical interval method is also compared with the crisp method grouped sampling plan under classical statistics.

Economic design of repetitive group sampling plan based on truncated life test under exponentiated half logistic distribution

In this paper, we propose repetitive group sampling plan based on time truncated life test under exponentiated half logistic distribution by considering percentile lifetime of the product as its quality characteristic when shape parameter value of exponentiated half logistic distribution is known. In this research, the design parameters are determined for various percentile ratios using the method of two points on the operating characteristic curve. Tables are constructed for various values of shape parameters to choose optimal parameters. The sampling procedure of proposed repetitive group sampling plan is illustrated with real time data and the consequence of misspecification of shape parameter on lot acceptance probability is also investigated. The proposed plan is also compared with single and double sampling plans in terms of discriminating power and average sample number under two other lifetime distributions. Moreover, an economic design of the proposed repetitive group sampling plan is discussed and optimal plan is selected to fulfill both producer’s and consumer’s risks with minimum cost.

Economic design of repetitive group sampling plan based on truncated life test under Birnbaum–Saunders distribution

In this paper, we design the repetitive group sampling plan under Birnbaum–Saunders distribution, since this distribution is considered as an appropriate and flexible distribution to model different types of data particularly lifetime data. In this study, the Birnbaum–Saunders distributed mean lifetime of the product is considered as the quality characteristic where the shape parameter is assumed to be known. For different mean ratios, the design parameters such as sample size, conditional and unconditional acceptance numbers of the proposed repetitive group sampling plan are determined using the approach of two points on the operating characteristic curve. In order to select the optimal parameters, tables are constructed for different values of shape parameter of Birnbaum–Saunders distribution. We explain the implementation of the proposed repetitive group sampling plan with descriptive example as well as using real time data and the effect of misspecification of shape parameter on lot acceptance probability is investigated. In addition, the proposed repetitive group sampling plan is compared with single and double sampling plans in terms of discriminating power and average sample number. An economic design of the proposed repetitive group sampling plan is discussed and optimal plans are determined to satisfy both producer’s and consumer’s risks with minimum cost. Sensitivity of the proposed plan based on failure probability and cost parameters is analyzed in this paper.

Design and development of relational repetitive group sampling plans - (RRGS - 1)

Repetitive Group Sampling Plans are widely used in industries for inspection of lots comprises of components or products. In RGS plans if the sample result does not lead to either acceptance or rejection of the lot then it is discarded and a new sample is drawn and the procedure is continued until the lot is sentenced. However in modern industries if the lots are not accepted based on the few sample results then there may be heavy loss in terms of money, huge cost in terms of sampling inspection, etc. Hence producer may face severe risk during such circumstances. Also customers may lose hope on the producer and the relationship between them may be at stake. The major setback of RGS while implementation is, it is not advantageous when the lot size is small. Hence to offset the disadvantages, new algorithm called as Relational Repetitive Group Sampling is given and new types of Relational Repetitive Group Sampling Plans are developed. It is termed as RRGS Inspection plans and the efficiency measures are derived. Tables are constructed to facilitate quality control engineers.

Optimal designing of multiple deferred (dependent) state repetitive group sampling plan for variables inspection

In this paper, we propose the designing methodology of multiple deferred (dependent) state repetitive group sampling plan for lot sentencing when the quality characteristic of the product follows normal distribution. This sampling plan incorporates the features of two existing sampling plans such as multiple deferred (dependent) state sampling plan and repetitive group sampling plan. Under the proposed sampling plan, the current lot is immediately accepted if it has good quality and rejected if the lot quality is poor. But, the decision on the current lot depends on the decision of the successive/preceding lots and/or additional samples from the current lot when the current lot is of moderate quality. Two-points on the operating characteristic curve approach is used to determine the optimal plan parameters for various combinations of acceptable quality level and limiting quality level. In determination of plan parameters, two cases are considered such as standard deviation is known and unknown. An application of the proposed sampling plan in industries is discussed with real life example. The significance of the proposed plan is explained by a comparative study.

Group Acceptance Sampling Plans for Resubmitted Lots UnderType II Generalized Half Logistic Distribution

In this research article, we build-up a group acceptance sampling plan (GASP) for a resubmitting lot when the lifetime of a product follow the Type II Generalized half-logistic distribution (GHLD). The design parameters of the group acceptance sampling plan for the resubmitted are determined by fixing the experiment termination time and the numbers of testers at the stated producer’s and consumer’s risks both satisfy at the same time. We contrast the proposed GASP with the ordinary group sampling plan and the results are demonstrated with a live data set.

Designing of Repetitive Group Sampling Plan under the Inverse Gaussian Distribution

This study investigates the attributes repetitive group sampling plans based on a truncated life test under the inverse Gaussian distribution with known shape parameter. The sample size and two acceptance numbers are the three design parameters determined for the proposed repetitive group sampling plans for different mean ratios. Tables are constructed to determine the optimal design parameters for different values of shape parameters of the inverse Gaussian model and the results are explained by with examples. Also the effect of misspecification of shape parameters is also discussed.

Implementing new variables RGS plan based on EWMA yield index

This paper develops a new variables repetitive group sampling plan using the exponentially weighted moving average (EWMA) statistic based on the yield index for the submitted lot. The optimal parameters of the proposed plan are determined under three scenarios based on the average sample number. Average sample number (ASN) is minimized to decrease inspection's cost and time by using the optimization problem for the required quality levels and sundry combinations of producer's and consumer's risks. The comparison study is provided to specify the efficiency of the proposed plan. Furthermore, the proposed plan is presented with an example which indicates its applicability in the industry. The proposed plan is compared with the single sampling plan and repetitive group sampling plan based on the yield index. The upshots are tabulated for various quality levels. The obtained outcomes demonstrate that the performance of the proposed sampling plan is more lucrative than the existing sampling plans in terms of ASN.

A modified sampling plan by variables with an adjustable mechanism for lot sentencing

Acceptance sampling has been used as a method of determining if submitted product lots meet required quality standards. Recently, several sampling plans with different strategies have been developed to tackle various types of situations and requirements, and to increase their performance and efficiency. In particular, repetitive group sampling plan (RGSP) has been proposed and proven to be an efficient sampling scheme. However, it has its drawbacks that occur when the sampling is repeated until the lot can be successfully determined as either accepted or rejected; in theory, the number of sampling times might be infinite. Therefore, this paper proposes a modified version of variables RGSP (VRGSP) with an adjustable mechanism for lot sentencing (Adj-VRGSP), i.e., by setting a maximum allowable sampling time. The operating characteristic (OC) and average sample number (ASN) functions of the proposed plan are derived along with the step-by-step operating procedure. The determination of plan parameters is formulated as an optimization model with nonlinear constraints related to quality and risk requirements. Additionally, the performance of the proposed plan is examined, discussed, and compared with that of the conventional sampling plans. An application is also presented as an example illustrating the effectiveness of the proposed plan.

Designing variables sampling plans based on the yield index Spk

The acceptance sampling plan is extensively used as a tool to determine whether the submitted lot should be accepted or rejected. In addition, the index establishes the relationship between manufacturing specification and the actual process performance providing a precise measure on the process yield. In this paper, we develop two variables sampling plans based on the index At first, the procedure of a modified double sampling plan by variables is presented for evaluating the lot or process fraction nonconforming. Then, the modified variables repetitive group sampling (VRGS) plan based on the yield index is implemented. The required parameters of proposed sampling plans are specified by minimizing the average sample number (ASN) and tabulated based on miscellaneous combinations of quality levels and producer's and consumer's risks. In order to specify an appropriate sampling plan based on the smallest value of ASN, proposed VDSP and modified VRGS plan are compared with SSP, RGS plan, SSP based on EWMA yield index, and MDS sampling plan. The comparison of sampling plans indicates that SSP based on EWMA yield index reduces ASN values significantly.

Determination of multiple dependent state repetitive group sampling plan based on the process capability index

In this article, we propose a sampling plan called a multiple dependent state repetitive group sampling plan for variable inspection based on the process capability index Cpk. The proposed sampling plan is applicable for the inspection of normally distributed quality characteristics when both mean and variance are assumed to be unknown. This new plan under variable inspection will be very useful particularly in compliance testing. Tables are also constructed for the determination of optimal parameters for easy selection and implementation of the plan. The optimal parameters can be determined by using the approach of two points on the operating characteristic curve. Symmetric and asymmetric cases based on the fraction nonconforming by the lower and the upper specification limits are also considered. Advantages of the proposed plan are also discussed. It is also shown that the proposed plan outperforms other existing sampling plans under variable inspection.

Improved inspection scheme with a loss-based capability index

Acceptance sampling is a practical quality tool for lot sentencing and is used primarily for incoming or outgoing inspections. The repetitive group sampling plan (RGSP) has been developed and shown to be superior to the traditional single sampling plan. However, RGSP’s lot disposition does not consider the valuable information from preceding lots, which may reduce its discriminatory power and sampling efficiency. Therefore, we propose a modified RGSP for variables inspection using the loss-based capability index. It uses not only the current sample information but also the results of preceding lots to sentence the current lot. The proposed plan’s operating characteristic (OC) function is derived using the estimated index’s exact sampling distribution. An optimization model is formulated to solve the plan parameters by minimizing the average sample number (ASN) required for inspection. The proposed plan’s advantages over the traditional sampling plans in terms of the OC curve and the ASN are addressed. Moreover, plan parameters are tabulated under various conditions and an application example is presented to illustrate its applicability.

An improved sampling plan by variables inspection with consideration of process yield and quality loss

ABSTRACTRepetitive group sampling (RGS) plan, a modified version of single sampling (SS) plan, has been shown to be more efficient than the SS plan for lot sentencing. However, because it does not consider the valuable sample information from preceding lots, that could reduce its sampling efficiency and discriminatory power. Therefore, this study proposes a modified-RGS plan by considering the quality history of preceding lots based on the Cpmk index. Additionally, the mathematical model for the plan parameters is formulated such that the objective function is to minimize the average sample number (ASN), and the required quality levels and risks as specified by producer and consumer are satisfied. The performance of the proposed plan is examined and compared with traditional sampling plans. Finally, an example is presented to illustrate its applicability.

Variable stage-independent double sampling plan with screening for acceptance quality loss limit inspection scheme

The quality loss suggested by Taguchi has been recognised as a new quality evaluation based on variable property instead of the quality evaluation based on traditional attribute property such as the proportion of nonconforming items. Some variable sampling inspection plans in order to assure the quality have been considered. As one of those sampling inspection plans, the single sampling plan with screening (SSPS) has been constructed for acceptance quality loss limit inspection scheme. Further, the repetitive group sampling plan with screening (RGSPS) has been developed for reducing the average total inspection (ATI). Although ATI by RGSPS has successfully been reduced in comparison with ATI by SSPS, RGSPS may sometimes increase the average sampling frequency (ASF) in return for reducing ATI. In this study, the stage-independent double sampling plan with screening (SIDSPS) based on the concept of the acceptance quality loss limit inspection scheme is proposed under the consideration of the trade-off between ATI and ASF. Through some numerical comparisons about ATI and ASF in SSPS, RGSPS, and SIDSPS, the usefulness of SIDSPS proposed in this study is confirmed.

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.