Group Sampling Plan Research Articles

Multiple states repetitive group sampling plans with process loss consideration

We propose a multiple state repetitive group sampling plan by considering the process loss. The optimal plan parameters of the proposed plan are selected such that producer’s risk and consumer’s risk are satisfied simultaneously by minimizing the average sample number. The advantages of the proposed plan over the existing sampling plans are given. Extensive tables are provided for practical applications of the proposed plan. Two real world examples are given for the illustration purpose.

Decision Rule Based on Group Sampling Plan Under the Inverse Gaussian Distribution

This article deals with the group acceptance sampling plan based on truncated life tests when the lifetime of a product follows the inverse Gaussian distribution. The design parameters such as the acceptance number and the number of groups are determined according to the specified number of testers, experiment time, and mean ratio. Tables are presented for different known values of the shape parameter. The misspecification issue of the model parameter is also studied. Some examples are discussed to illustrate the plan under the inverse Gaussian distribution.

A two-stage group sampling plan based on truncated life tests for a M-O extended exponential distribution

In this paper, we considered a two-stage group acceptance sampling plan based on a truncated life tests for a lifetime follows Marshall-Olkin (M-O) extended exponential distribution. The decision on acceptance of lot can be made in the first or second stage according to the number of failures from each group. The design parameters of the proposed plan such as number of groups required and the acceptance number for each of two stages are determined so as to satisfy the consumer’s risk at the specified unreliability when group size and test duration are specified. Single-stage group sampling plans are also considered as special cases of the proposed plan and compared with the proposed plan in terms of the average sample number and the operating characteristics. The results are explained with examples.

A new mixed acceptance sampling plan based on sudden death testing under the Weibull distribution

In this article, a new mixed sampling plan based on the group sampling plan and sudden death testing scheme is proposed by assuming that the lifetime of the product follows the Weibull distribution. The optimal parameters of the proposed plan will be determined such that the producer's risk and consumer's risk are satisfied for specified values of acceptable and limiting quality levels. The proposed plan is compared with the existing group acceptance sampling plan and variable single sampling plan based on sudden death testing. The tables are provided and examples are also given to illustrate the proposed plan.

An efficient inspection scheme for variables based on Taguchi capability index

Acceptance sampling has been one of practical tools for quality assurance applications, which provide a general rule to the producer and the consumer for product acceptance determination. It has been shown that variables sampling plans requires less sampling compared with attributes sampling plans. Thus, variables sampling plans become more attractive and desirable especially when the required quality level is very high or the allowable fraction non-conforming is very small. This paper attempts to develop an efficient and economic sampling scheme, variables repetitive group sampling plan, by incorporating the concept of Taguchi loss function. The OC curve of the proposed plan is derived based on the exact sampling distribution and the plan parameters are determined by minimizing the average sample number with two constraints specified by the producer and the consumer. The efficiency of the proposed variables RGS is examined and also compared with the existing variables single sampling plan in terms of the sample size required for inspection. In addition, tables of the plan parameters for various combinations of entry parameters are provided and an example is presented for illustration.

Two-Stage Improved Group Plans for Burr Type XII Distributions

In this paper, we present two-stage group plan for Burr type XII distribution using lifetime percentile as quality parameter. The plan parameters such as acceptance number and group size are determined by considering producer's risk and consumer's risk at the same time. To find the plan parameters, we fixed the number of testers, experiment time and percentiles ratio. Many useful tables are generated for Burr type XII distribution as well as for log-logistic distribution. Two industrial examples are presented for the illustration of the proposed two-stage group sampling plan. Comparison of proposed plan with single-stage group plan is also discussed. Generally, the proposed two-stage sampling plan needs less number of test items than single-stage group plan does.

Decision rule of repetitive acceptance sampling plans assuring percentile life

In this research, Repetitive Group Sampling (RGS) plans are developed for the Weibull and generalized exponential distributions. To design the proposed plans, the median of a life-time is first used as the quality parameter. Then, a decision-making framework is developed, based on first and second type errors. Next, based on acceptable and limiting quality level criteria, tables are obtained to select the parameters of the proposed decision-making framework. The advantages of the proposed method over single sampling plans are discussed at the end.

Construction of mixed sampling plans indexed through Six Sigma quality levels with repetitive group sampling plan as attribute plan

Six Sigma is a concept, a process, a measurement, a tool, a quality philosophy, a culture and a management strategy for the improvement in the system of an organisation, in order to reduce wastages and increase the profit to the management and satisfaction to the customers. Motorola (1980) first adopted the concept of Six Sigma in their organisation and established that it can produce less than 3.4 defects per million opportunities. Focusing on reduction of defects will result in more profit to the producer and enhanced satisfaction for the consumer. The concept of Six Sigma can be applied in the process of quality control in general and acceptance sampling in particular. In this paper, a new procedure for the construction and selection of mixed sampling plan indexed through Six Sigma quality level having the repetitive group sampling plan as attribute plan is presented. The plans are constructed using SSQL-1 and SSQL-2 as indexing parameters. Tables are constructed for easy selection of the plan.

Group acceptance sampling plans for resubmitted lots under Burr-type XII distributions

In this article, a group acceptance sampling plan (GASP) for lot resubmitting is developed to ensure the quality of product lifetime assuming that the product lifetime follows the Burr-type XII distribution. The parameters of the GASP are determined by satisfying the specified producer's and consumer's risks according to the experiment termination time and the number of testers. A comparison between the proposed group sampling plan and the ordinary group sampling plan shows that the proposed plan requires less sample size. Two examples are used for illustration.

A two-stage group sampling plan based on truncated life tests for a general distribution

A two-stage group acceptance sampling plan based on a truncated life test is proposed, which can be used regardless of the underlying lifetime distribution when multi-item testers are employed. The decision upon lot acceptance can be made in the first or second stage according to the number of failures from each group. The design parameters of the proposed plan such as number of groups required and the acceptance number for each of two stages are determined independently of an underlying lifetime distribution so as to satisfy the consumer's risk at the specified unreliability. Single-stage group sampling plans are also considered as special cases of the proposed plan and compared with the proposed plan in terms of the average sample number and the operating characteristics. Some important distributions are considered to explain the procedure developed here.

Variable repetitive group sampling plans with process loss consideration

Traditionally, most acceptance sampling plans considering the fraction defective do not distinguish among the products that fall within the specification limits. However, products that fall within the specification limits may not be good if their mean is far away from the target. So, developing an acceptance sampling plan with process loss consideration is essential. In this paper, a variable repetitive group sampling plan is proposed to deal with process loss. The design parameters of the proposed plan are tabulated for various combinations of acceptance quality levels. The proposed methodology can be used to determine whether the products meet the desired levels of protection for both producers and consumers.

Certain Results and Tables Relating to QSS-1 with Multiple RGS Plan as Reference Plan

This paper enlarges the concept of Quick Switching System and Multiple Repetitive Group Sampling Plan in to a new procedure for construction and selection of Quick Switching System with Multiple Repetitive Group Sampling Plan as reference plan indexed through Acceptable Quality Level (AQL), Limiting Quality Level (LQL), Indifference Quality Level (IQL) and its operating ratio. Poisson unity values have been tabulated to facilitate the operation and construction of the plan. Illustrations are also provided for selection of plan parameters.

New acceptance sampling plans based on life tests for Birnbaum–Saunders distributions

In this paper, we consider the Birnbaum–Saunders distribution as a life model to develop various acceptance sampling schemes based on the truncated life tests. We develop the double sampling plan and determine the design parameters satisfying both the producer's and consumer's risks simultaneously for the specified reliability levels in terms of the mean ratio to the specified life. We also propose a group sampling plan and determine the parameters by the above-mentioned two-point method. Tables are constructed for the proposed sampling plans and results are explained with examples.

Design of progressively censored group sampling plans for Weibull distributions: An optimization problem

Optimization algorithms provides efficient solutions to many statistical problems. Essentially, the design of sampling plans for lot acceptance purposes is an optimization problem with several constraints, usually related to the quality levels required by the producer and the consumer. An optimal acceptance sampling plan is developed in this paper for the Weibull distribution with unknown scale parameter. The proposed plan combines grouping of items, sudden death testing in each group and progressive group removals, and its decision criterion is based on the uniformly most powerful life test. A mixed integer programming problem is first solved for determining the minimum number of failures required and the corresponding acceptance constant. The optimal number of groups is then obtained by minimizing a balanced estimation of the expected test cost. Excellent approximately optimal solutions are also provided in closed-forms. The sampling plan is considerably flexible and allows to save experimental time and cost. In general, our methodology achieves solutions that are quite robust to small variations in the Weibull shape parameter. A numerical example about a manufacturing process of gyroscopes is included for illustration.

An Improved Group Sampling Plan Based on Time-Truncated Life Tests

In this paper, a new group sampling plan for the lot acceptance is proposed for the time truncated life test, which can be utilized when multi-item testers are implemented. The design parameters are found using the two-point approach such that the producer's and consumer's risks are satisfied simultaneously at the acceptable reliability level and the lot tolerance reliability level, respectively. The case of Weibull distribution is described to illustrate the procedure that can be used when the quality level is expressed by a multiple of the specified life. The advantage of the proposed plan is demonstrated by comparing with the existing plan in terms of the sample size required. The tables are constructed and some examples are given to illustrate the procedure developed here.

A variables repetitive group sampling plan under failure-censored reliability tests for Weibull distribution

We propose a variables repetitive group sampling plan under type-II or failure-censored life testing when the lifetime of a part follows a Weibull distribution with a known shape parameter. The acceptance criteria do not involve unknown scale parameter differently from the existing plans. To determine the design parameters of the proposed plan, the usual approach of using two points on the operating characteristic curve is adopted and an optimization problem is formulated so as to minimize the average number of failures observed. Tables for design parameters are constructed when the quality of parts is represented by the unreliability or the ratio of the mean lifetime to the specified life. It is found that the proposed sampling plan can reduce the sample size significantly than do the single sampling plan.

A Time Truncated Two-Stage Group Sampling Plan for Weibull Distribution

In this paper, a two-stage group sampling plan based on the time truncated life test is proposed for the Weibull distribution. The design parameters such as the number of groups and the acceptance number in each stage are determined by satisfying the producer's and consumer's risks simultaneously when the group size and the test duration are specified. The acceptable reliability level is expressed by the ratio of the true mean life to the specified life. It was demonstrated from the comparison with single-stage group sampling plans that the proposed plan can reduce the average sample number or improve the operating characteristics.

Repetitive group sampling procedure for variables inspection

This paper introduces the concept of repetitive group sampling (RGS) for variables inspection. The repetitive group sampling plan for variables inspection will be useful when testing is costly and destructive. The advantages of the variables RGS plan over variables single sampling plan, variables double sampling plan and attributes RGS plan are discussed. Tables are also constructed for the selection of parameters of known and unknown standard deviation variables repetitive group sampling plan indexed by acceptable quality level and limiting quality level.

Designing of Variables Repetitive Group Sampling Plan Involving Minimum Average Sample Number

This article proposes the variables repetitive group sampling plan where the quality characteristic follows normal distribution or lognormal distribution and has upper or lower specification limit. The problem is formulated as a nonlinear programming problem 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 (AQL) and limiting quality level (LQL) under the operating characteristic curve. Sampling plan tables are constructed for the selection of parameters indexed by AQL and LQL in the cases of known standard deviation and unknown standard deviation. It is shown that the proposed sampling plan significantly reduces the average sample number as compared with the single and double sampling plans.

Two stage conditional repetitive group sampling plan (Short Communication)

This paper enlarges the concept of conditional repetitive group sampling plan. The' operating characteristic and average sample number functions of the generalised plan have been derived by graphical evaluation and review technique. Lastly, Poisson unity values have been tabulated to facilitate the operation and construction of the plan. The plan that provides a quick discrimination of good and bad quality lots, could be used for both the process control and goods acceptance or rejection in various stages of production in defence organisations.