Developing a variables repetitive group sampling plan based on process capability index C pk with unknown mean and variance

In this paper, variables repetitive group sampling plans are developed based on the process capability index C _pk when the quality characteristic follows a normal distribution with unknown mean and variance. The sampling plan parameters such as the sample size and the acceptance constant are determined to minimize the average sample number. Symmetric and asymmetric cases, in percent defectives due to two specification limits, are dealt with for specified combinations of acceptable quality level and limiting quality level. Tables are provided and examples are given to use proposed plans in practice.     

Repetitive group sampling plan based on the process capability index for the lot acceptance problem

An 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.     

Optimal designing of a new mixed variable lot-size chain sampling plan based on the process capability index

In this paper, a new mixed sampling plan based on the process capability index (PCI) C_pk is proposed and the resultant plan is called mixed variable lot-size chain sampling plan (ChSP). The proposed mixed plan comprises of both attribute and variables inspections. The variable lot-size sampling plan can be used for inspection of attribute quality characteristics and for the inspection of measurable quality characteristics, the variables ChSP based on PCI will be used. We have considered both symmetric and asymmetric fraction non conforming cases for the variables ChSP. Tables are developed for determining the optimal parameters of the proposed mixed plan based on two points on the operating characteristic (OC) approach. In order to construct the tables, the problem is formulated as a non linear programming where the average sample number function is considered as an objective function to be minimized and the lot acceptance probabilities at acceptable quality level and limiting quality level under the OC curve are considered as constraints. The practical implementation of the proposed mixed sampling plan is explained with an illustrative real time example. Advantages of the proposed sampling plan are also discussed in terms of comparison with other existing sampling plans.     

A new mixed chain sampling plan based on the process capability index for product acceptance

This article proposes a new mixed chain sampling plan based on the process capability index C_pk, where the quality characteristic of interest follows the normal distribution with unknown mean and variance. The advantages of this proposed mixed sampling plan are also discussed. Tables are constructed to determine the optimal parameters for practical applications. In order to construct the tables, the problem is formulated as a nonlinear programming 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 and limiting quality level under the operating characteristic curve. The practical application of the proposed mixed sampling plan is explained with an illustrative example. Comparison of the proposed sampling plan is also made with other existing sampling plans.     

Designing of a mixed-chain sampling plan based on the process capability index with chain sampling as the attributes plan

In this article, we propose a new mixed chain sampling plan based on the process capability index C_pk, where the quality characteristic of interest having double specification limits and follows the normal distribution with unknown mean and variance. In the proposed mixed plan, the chain sampling inspection plan is used for the inspection of attribute quality characteristics. The advantages of this proposed mixed sampling plan are also discussed. Tables are constructed to determine the optimal parameters for practical applications by formulating the problem as a non linear programming in which the objective function to be minimized is the average sample number and the constraints are related to lot acceptance probabilities at acceptable quality level and limiting quality level under the operating characteristic curve. The practical application of the proposed mixed sampling plan is explained with an illustrative example. Comparison of the proposed sampling plan is also made with other existing sampling plans.     

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.     

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 a multiple state repetitive group sampling plan based on the coefficient of variation

A multiple state repetitive group sampling (MSRGS) plan is developed on the basis of the coefficient of variation (CV) 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 average sample number required for inspection. The advantages of the proposed MSRGS plan over the existing sampling plans are discussed. Finally an example is given to illustrate the proposed plan.     

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.     

Two-Stage Variables Acceptance Sampling Plans Using Process Loss Functions

In this article, a variable two-stage acceptance sampling plan is developed when the quality characteristic is evaluated through a process loss function. The plan parameters of the proposed plan are determined by using the two-point approach and tabulated according to various quality levels. Two cases are discussed when the process mean lies at the target value and when it does not, respectively. Extensive tables are provided for both cases and the results are explained with examples. The advantage of the proposed plan is compared with the existing variable single acceptance sampling plan using the process loss function.     

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.     

Repetitive variable acceptance sampling plan for one-sided specification

In this paper, a variable repetitive group sampling plans based on one-sided process capability indices is proposed to deal with lot sentencing for one-sided specifications. The parameters of the proposed plans are tabulated for some combinations of acceptance quality levels with commonly used producer's risk and consumer's risk. The efficiency of the proposed plan is compared with the Pearn and Wu [Critical acceptance values and sample sizes of a variables sampling plan for very low fraction of defectives. Omega – Int J Manag Sci. 2006;34(1):90–101] plan in terms of sample size and the power curve. One example is given to illustrate the proposed methodology.     

Exponential families of markov processes -part II: birth- and death processes

A common prior distribution and loss structure are set up to be appropriate for the sorting of batches using sampling inspection by variable and by attribute. Approxi¬mations to the exact optimal sampling plans are derived to gain a better understanding of BAYEsian sampling plans and to compare the plans using variable sampling and attribute sampling. It is assumed that the process quality distribution is normal with a known variance     

Reliability sampling plan for repairable items following general failure process and its statistical analysis

Acceptance sampling plan has become an essential tool in the statistical quality control. Traditionally, most acceptance sampling plans have been developed for non-repairable items. Recently in Cha [Variables acceptance reliability sampling plan for repairable items. Statistics. 2015;49:1141–1156], variables acceptance reliability sampling plan for repairable items has been developed assuming that the failure process follows the non-homogeneous Poisson process (NHPP). In this paper, we assume that the failure process follows a new counting process which is a generalized version of the NHPP. Furthermore, it is shown that the developed sampling plan improves the reliability characteristic of the population of items which have passed the testing procedure. An illustrative example is also provided.     

Optimal design of variable acceptance sampling plans for mixture distribution

ABSTRACT

The paper investigates the design of single and sequential variable acceptance sampling plans for a mixture distribution. Mixture distributions are seen in many practical problems such as life testing experiments of electronic components and clinical trials. The sampling plans for this kind of situations are not well addressed in the literature. We first propose a single sampling plan for a distribution which is a mixture of two exponential distributions. An optimization problem which minimizes the total cost of testing at given producer's and consumer's risks is solved to obtain the plan parameters. Two different sequential sampling plans are also defined and plan parameters are obtained by solving corresponding optimization problems. Finally, a case study, a simulation study and a sensitivity analysis are presented to illustrate our sampling plans.     

Stratified Double Sampling with Continuous Outcomes: Design and Analysis

We provide a method for estimating the sample mean of a continuous outcome in a stratified population using a double sampling scheme. The stratified sample mean is a weighted average of stratum specific means. It is assumed that the fallible and true outcome data are related by a simple linear regression model in each stratum. The optimal stratified double sampling plan, i.e. , the double sampling plan that minimizes the cost of sampling for fixed variances, or alternatively, minimizes the variance for fixed costs, is found and compared to a standard sampling plan. The design parameters are the total sample size and the number of doubly sampled units in each stratum. We show that the optimal double sampling plan is a function of the between-strata and within-strata cost and variance ratios. The efficiency gains, relative to standard sampling plans, under broad set of conditions, are considerable.     

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.     

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.     

A flexible sampling scheme for variables inspection with loss consideration

This article develops a variables sampling scheme for resubmitted lots by incorporating the concept of Taguchi loss function. The probability of lot acceptance is derived based on the exact sampling distribution and two-point condition on operating characteristic curve is used to determine the plan parameters that meet both the producer's and consumer's quality and risk requirements. Moreover, the performance of the proposed variables resubmitted sampling plan is investigated and compared with the classical variables single sampling plan. The results indicate that the developed resubmitted sampling plan can provide the same protection with less inspection when the submitted lot is good enough. Tables of the plan parameters under various conditions are provided and the use of the proposed plan is also illustrated with an example.     

Developing a variables two-plan sampling system for product acceptance determination

In this paper, a variables tightened-normal-tightened (TNT) two-plan sampling system based on the widely used capability index C_pk is developed for product acceptance determination when the quality characteristic of products has two-sided specification limits and follows a normal distribution. The operating procedure and operating characteristic (OC) function of the variables TNT two-plan sampling system, and the conditions for solving plan parameters are provided. The behavior of OC curves for the variables TNT sampling system under various parameters is also studied, and compared with the variables single tightened inspection plan and single normal inspection plan.