Selection of csp-t plans

Various continuous sampling plans have been proposed for monitoring the quality of continuous production processes. The multi-level continuous sampling plan of MIL-STD-1235C (1988) is designated as CSP-T Plan. CSP-T plan is a three-level tightened continuous sampling plan. It requires a switch to 100% inspection, at any level, whenever a nonconforming unit is found. This provides quick rectification in the event of a shift in quality. In this paper certain performance characteristics of CSP-T plan are derived using the approach of Stephens (1979) under the assumption that the production process is in statistical control. For the selection of CSP-T plans, two tables are given. These tables can be used to obtain parameters i (clearance interval) and f (sampling fraction) of the CSP-T plan for given acceptable quality level (AQL) with producer’ risk α=0.05 or the limiting quality level(LQL) with consumer’ risk β=0.10 and the outgoing quality limit(AOQL). Two examples are also given to illustrate the selection of plans from these tables     

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.     

SkSP-R sampling plan based on process capability index

In this paper, we present an optimal designing methodology for the skip-lot sampling plan (SkSP) of type SkSP-R based on the most widely used process capability index (PCI) C_pk. The SkSP-R plan is one of the SkSPs that incorporate the provision of the reinspection concept. In order to design the optimal parameters, we consider both symmetric and asymmetric fraction non conforming cases. Tables are also constructed to determine the optimal parameters by formulating an optimization problem. The advantages of the proposed plan over the existing plan are also discussed. Application of the plan is explained with a real-life example.     

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.     

A new policy for designing acceptance sampling plan based on Bayesian inference in the presence of inspection errors

The purpose of this article is to present a new policy for designing an acceptance sampling plan based on the minimum proportion of the lot that should be inspected in the presence of inspection errors. It is assumed that inspection is not perfect and every defective item cannot be detected with complete certainty. The Bayesian method is used for obtaining the probability distribution function of the number of defective items in the lot. To design this model, two constraints of producer risk and consumer risk are considered during the inspection process by using two specified points on operating characteristic curve. In order to illustrate the application of the proposed model, an example is presented. In addition, a sensitivity analysis is performed to analyze the model performance under different scenarios of process parameters and the results are elaborated. Finally, the efficiency of the proposed model is compared with the sampling method of Spencer and Kevan de Lopez (2017) at the same conditions.     

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.     

Optimal designing of quick switching sampling system assuring percentile life under Weibull distribution

In this paper, designing methodology of quick switching sampling system under Weibull distribution for assuring product lifetime percentile is proposed. An optimization problem is formulated for determining the optimal parameters of the proposed system using two points on the operating characteristic curve approach. The operating procedure and designing methodology of the proposed system are discussed. A comparative study between the proposed system and other existing plans is accomplished in terms of average sample number and the operating characteristic curve is provided for analyzing the behavior of proposed system. In addition, the effect of mis-specification of shape parameter on the proposed sampling system is discussed.     

Optimal design of repetitive group sampling plans for Weibull and gamma distributions with applications and comparison to the Birnbaum–Saunders distribution

In this paper, we propose a multiple deferred state repetitive group sampling plan which is a new sampling plan developed by incorporating the features of both multiple deferred state sampling plan and repetitive group sampling plan, for assuring Weibull or gamma distributed mean life of the products. The quality of the product is represented by the ratio of true mean life and specified mean life of the products. Two points on the operating characteristic curve approach is used to determine the optimal parameters of the proposed plan. The plan parameters are determined by formulating an optimization problem for various combinations of producer's risk and consumer's risk for both distributions. The sensitivity analysis of the proposed plan is discussed. The implementation of the proposed plan is explained using real-life data and simulated data. The proposed plan under Weibull distribution is compared with the existing sampling plans. The average sample number (ASN) of the proposed plan and failure probability of the product are obtained under Weibull, gamma and Birnbaum–Saunders distributions for a specified value of shape parameter and compared with each other. In addition, a comparative study is made between the ASN of the proposed plan under Weibull and gamma distributions.     

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.     

Economic design of acceptance sampling plans for truncated life test using Frechet distribution

In this article designing of acceptance sampling plans for the truncated life test is proposed using economic approach by assuming that the lifetime of a product follows Frechet distribution based on median. The optimal sampling plans to meet the consumer’s confidence level with minimum total cost are designed. Efficiency of the proposed plan is also analyzed.     

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.     

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.     

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.     

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.     

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.     

A double acceptance sampling plan for generalized log-logistic distributions with known shape parameters

A double acceptance sampling plan for the truncated life test is developed assuming that the lifetime of a product follows a generalized log-logistic distribution with known shape parameters. The zero and one failure scheme is mainly considered, where the lot is accepted if no failures are observed from the first sample and it is rejected if two or more failures occur. When there is one failure from the first sample, the second sample is drawn and tested for the same duration as the first sample. The minimum sample sizes of the first and second samples are determined to ensure that the true median life is longer than the given life at the specified consumer’s confidence level. The operating characteristics are analyzed according to various ratios of the true median life to the specified life. The minimum such ratios are also obtained so as to lower the producer’s risk at the specified level. The results are explained with examples.     

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.     

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.