Attribute-variable Inspection Policy for Lots Using Resampling Based on EWMA

A new mixed sampling plan which is a combination of the attribute single sampling plan and variables resampling scheme based on EWMA statistic is proposed in this paper. The operating characteristic function of the proposed plan is derived and the plan parameters are determined such that the probability of acceptance of good lot is larger than the specified producer's confidence level and the bad lot acceptance probability is smaller than the consumer's confidence level. The efficiency and the advantages of the proposed plan are discussed over the existing attribute sampling plan. The extensive tables are provided for industrial applications. The use of tables is discussed with the help of a real-time industrial example.     

Optimal acceptance sampling policy considering Bayesian risks

In this paper, we propose a sampling policy considering Bayesian risks. Various definitions of producer's risk and consumer's risk have been made. Bayesian risks for both producer and consumer are proven to give better information to decision-makers than classical definitions of the risks. So considering the Bayesian risk constraints, we seek to find optimal acceptance sampling policy by minimizing total cost, including the cost of rejecting the batch, the cost of inspection, and the cost of defective items detected during the operation. Proper distributions to construct the objective function of the model are specified. In order to demonstrate the application of the proposed model, we illustrate a numerical example. Furthermore, the results of the sensitivity analysis show that lot size, the cost of inspection, and the cost of one defective item are key factors in sampling policies. The acceptable quality level, the lot tolerance proportion defective, and Bayesian risks also affect the sampling policy, but variations of acceptable quality level and producer Bayesian risks, for values more than a specified value, cause no changes in sampling policy.     

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

This 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 C_pk and the mixed variable lot size plan based on C_pk 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 new sampling plan under the exponential distribution

This article considers a sampling plan when the quality characteristic follows the exponential distribution. We provide the exact approach and propose an approximated approach. In the proposed approximation, a new statistic combined with a Weibull transformation is used for the normal approximation. The plan parameters are obtained through the two-point approach at the acceptable quality level (AQL) and the limiting quality level (LQL). The tables for plan parameters are reported according to various values of the AQL and the LQL when the producer's and the consumer's risks are given. A real example is given to illustrate the proposed approximation approach.     

Optimal designing of skip-lot sampling plan of type SkSP-2 with group acceptance sampling plan as reference plan under Burr-type XII distribution

In this paper, skip-lot sampling plan of type SkSP-2 with group acceptance sampling plans is proposed when the lifetime of the product follows the Burr-type XII distributions. The optimal parameters of the proposed plan are determined when two points on operating characteristics curve namely acceptable quality level and limiting quality level and the number of testers are specified. We also considered the Burr-type XII distribution to find the plan parameters. Several tables are given for practical use. We compare the results of proposed plan with the existing plans. Results are explained using real-world examples.     

A group acceptance sampling plan for truncated life test having Weibull distribution

In this paper, a group acceptance sampling plan for a truncated life test is proposed when a multiple number of items as a group can be tested simultaneously in a tester, assuming that the lifetime of a product follows the Weibull distribution with a known shape parameter. The design parameters such as the number of groups and the acceptance number will be determined by satisfying the producer's and the consumer's risks at the specified quality levels, while the termination time and the number of testers are specified. The results are explained with tables and examples.     

Double and group acceptance sampling plan for truncated life test based on inverse log-logistic distribution

This paper introduces a double and group acceptance sampling plans based on time truncated lifetimes when the lifetime of an item follows the inverse log-logistic (ILL) distribution with known shape parameter. The operating characteristic function and average sample number (ASN) values of the double acceptance sampling inspection plan are provided. The values of the minimum number of groups and operating characteristic function for various quality levels are obtained for a group acceptance sampling inspection plan. A comparative study between single acceptance sampling inspection plan and double acceptance sampling inspection plan is carried out in terms of sample size. One simulated example and four real-life examples are discussed to show the applicability of the proposed double and group acceptance sampling inspection plans for ILL distributed quality parameters.     

Design of a time-truncated double sampling plan for a general life distribution

A double sampling plan based on truncated life tests is proposed and designed under a general life distribution. The design parameters such as sample sizes and acceptance numbers for the first and the second samples are determined so as to minimize the average sample number subject to satisfying the consumer's and producer's risks at the respectively specified quality levels. The resultant tables can be used regardless of the underlying distribution as long as the reliability requirements are specified at two risks. In addition, Gamma and Weibull distributions are particularly considered to report the design parameters according to the quality levels in terms of the mean ratios.     

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.     

Optimal designing of an SkSP-R double sampling plan

In this article, we propose a method of planning and determining the optimum parameters of a SkSP-R skip-lot sampling plan by using the attribute double sampling plan as the reference plan. The SkSP-R plan is a new type of skip-lot sampling plan which has a provision for re-inspecting the submitted lots. The optimal plan parameters of the suggested sampling plan are estimated with the target that the average sample number be minimized and satisfying both the specified producer's as well as the consumer's risks simultaneously. In order to obtain the optimum parameters, tables are also built for different combinations of the acceptable quality level and the limiting quality level in conjunctions with different producer's and consumer's risks. An illustrative example is provided for the implementation of the suggested plan. The advantages of the suggested plan over the existing conventional sampling plans and other existing skip-lot sampling plans are also described.     

Multiple dependent state repetitive sampling plans with or without auxiliary variable

In this article, a new variable acceptance sampling plan has been developed using the multiple dependent state repetitive sampling scheme for the normal distribution. The plan parameters have been determined so as to minimize the average sample number while satisfying the producer's and the consumer's risks under the operating characteristic function. The multiple dependent state repetitive sampling scheme has also been extended to the case of utilizing an auxiliary variable. The proposed sampling plans are compared with the existing sampling plans.     

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

This 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.     

Construction and selection of tightened–normal–tightened variables sampling scheme of type TNTVSS (n 1, n 2; k)

This paper provides tables for the construction and selection of tightened–normal–tightened variables sampling scheme of type TNTVSS (n ₁, n ₂; k). The method of designing the scheme indexed by (AQL, α) and (LQL, β) is indicated. The TNTVSS (n _T , n _N; k) is compared with conventional single sampling plans for variables and with TNT (n ₁, n ₂; c) scheme for attributes, and it is shown that the TNTVSS is more efficient.     

A mixed double sampling plan based on Cpk

Abstract

Acceptance sampling plans are quality tools for the manufacturer and the customer. The ultimate result of reduction of nonconforming items will increase the profit of the manufacturer and enhance the satisfaction of the consumer. In this article, a mixed double sampling plan is proposed in which the attribute double sampling inspection is used in the first stage and a variables sampling plan based on the process capability index C_pk is used in the second stage. The optimal parameters are determined so that the producer’s and the consumer’s risks are to be satisfied with minimum average sample number. The optimal parameters of the proposed plan are estimated using different plan settings using two points on the operating characteristic curve approach. In designing the proposed mixed double sampling plan, we consider the symmetric and asymmetric nonconforming cases under variables inspection. The efficiency of the proposed plan is discussed and compared with the existing sampling plans. Tables are constructed for easy selection of the optimal plan parameters and an industrial example is also included for implementation of the proposed plan.     

An economic reliability test plan: Log-logistic distribution

Sampling plans in which items that are put to test, to collect the life of the items in order to decide upon accepting or rejecting a submitted lot, are called reliability test plans. The basic probability model of the life of the product is specified as the well-known log-logistic distribution with a known shape parameter. For a given producer's risk, sample size, termination number, and waiting time to terminate the test plan are computed. The preferability of the test plan over similar plans existing in the literature is established with respect to cost and time of the experiment.     

Time truncated acceptance sampling plans for generalized exponential distribution

Acceptance sampling plans for generalized exponential distribution when the lifetime experiment is truncated at a pre-determined time are provided in this article. The tables are provided for the minimum sample size required to ensure a certain median life of the experimental unit when the shape parameter is two. The operating characteristic function values of the sampling plans and the associated producer's risks are also presented. It is shown that the tables presented here can be used if instead of median life, other percentile life is chosen as the criterion or if the shape parameter is not two. Examples are provided for illustrative purposes.     

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.     

Designing and selection of two-plan variables scheme indexed by crossover point

In this paper, the scheme of the inspection plan, namely the tightened normal tightened (n_T, n_N; k) is considered and procedures and necessary tables are developed for the selection of the variables sampling scheme, indexed through crossover point (COP). The importance of COP, the properties and advantages of the operating characteristic curve with respect to COP are studied.     

Economic design of quick switching sampling system for assuring Weibull distributed mean life

In this paper, we propose the quick switching sampling system for assuring mean life of a product under time truncated life test where the lifetime of the product follows the Weibull distribution and the mean life is considered as the quality of the product. The optimal parameters of the proposed system are determined using two points on the operating characteristic curve approach for various combinations of consumer's risk and ratio of true mean life time and specified life time. Tables are constructed to determine the optimal parameters for specified acceptable quality level and limiting quality level along with the corresponding probabilities of acceptance. The proposed system is compared with other existing sampling plans under Weibull lifetime model. In addition, an economical design of the proposed system is also discussed.