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 sampling plan for one-shot systems considering destructive inspection

Abstract

The paper is concerned with an acceptance sampling problem under destructive inspections for one-shot systems. The systems may fail at random times while they are operating (as the systems are considered to be operating when storage begins), and these failures can only be identified by inspection. Thus, n samples are randomly selected from N one-shot systems for periodic destructive inspection. After storage time T, the N systems are replaced if the number of working systems is less than a pre-specified threshold k. The primary purpose of this study is to determine the optimal number of samples n*, extracted from the N for destructive detection and the optimal acceptance number k*, in the sample under the constraint of the system interval availability, to minimize the expected cost rate. Numerical experiments are studied to investigate the effect of the parameters in sampling inspection on the optimal solutions.     

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

Repetitive 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 C_pmk 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.     

Dodge-Romig AOQL single sampling plans for inspection by variables

Acceptance sampling plans for inspection by variables, which minimize the mean inspection cost per lot of process average quality (assuming that the remainder of rejected lots is inspected), are derived under the condition that the maximum value of the mean fraction defective after sampling inspection, replacing all defective items found by good ones, shall be equal top _L . These plans are tabulated for chosen values of the given parameters, and compared with the Dodge-Romig AOQL attribute sampling plans. From the comparison it follows that under the same protection of consumer the AOQL plans for inspection by variables are in some situations more economical than the corresponding Dodge-Romig plans.     

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.     

Modified chain sampling plans for lot inspection by variables and attributes

The purpose of acceptance sampling is to develop decision rules to accept or reject production lots based on sample data. When testing is destructive or expensive, dependent sampling procedures cumulate results from several preceding lots. This chaining of past lot results reduces the required size of the samples. A large part of these procedures only chain past lot results when defects are found in the current sample. However, such selective use of past lot results only achieves a limited reduction of sample sizes. In this article, a modified approach for chaining past lot results is proposed that is less selective in its use of quality history and, as a result, requires a smaller sample size than the one required for commonly used dependent sampling procedures, such as multiple dependent sampling plans and chain sampling plans of Dodge. The proposed plans are applicable for inspection by attributes and inspection by variables. Several properties of their operating characteristic-curves are derived, and search procedures are given to select such modified chain sampling plans by using the two-point method.     

Economic design of continuous sampling plan under linear inspection cost

The article explores the problem of an economically based type I continuous sampling plan (CSP-1 plan) under linear inspection cost. By assuming that the per unit inspection cost is linearly proportional to the average number of inspections per inspection cycle, and by solving the modified Cassady et al.'s model, we not only have the required level of product quality but also obtain the minimum total expected cost per unit produced.     

Minimum average fraction inspected for continuous sampling plan CSP-1 under inspection error

SUMMARY In this paper, we present a further modification of Endres's method to construct the problem of minimizing the average fraction inspected (AFI) for the continuous sampling plan CSP-1 under inspection error. The measures of average outgoing quality under perfect and imperfect replacement conditions are considered. The formulae for searching the smallest clearance number i for minimizing the AFI for a CSP-1 plan are also provided. The solution procedure of the proposed method is more reliable, clearer and easier than that of Endres.     

Exact calculation of the Dodge-Romig LTPD single sampling plans for inspection by variables

In this paper we shall deal with the acceptance sampling plans when the remainder of rejected lots is inspected. We shall consider two types of LTPD plans- for inspection by variables and for inspection by variables and attributes (all items from the sample are inspected by variables, remainder of rejected lots is inspected by attributes). We shall report on an algorithm allowing the calculation of these plans when the non-central t distribution is used for the operating characteristic. The calculation is considerably difficult, algorithm for non-central t distribution takes several minutes. For the calculation we shall use an original method.     

Design and evaluation of skip-lot sampling inspection plans with double-sampling plan as the reference plan

This paper presents a design for skip-lot sampling inspection plans with the double-sampling plan as the reference plan, so as to reduce the sample size and produce more efficient plans in return for the same sampling effort. The efficiency of the proposed plan compared with that of the conventional double-sampling plan is also discussed. The need for smaller acceptance numbers under the plan is highlighted. Methods of selecting the plan indexed by the acceptable quality level and limiting quality level, and by the acceptable quality level and average outgoing quality level are also presented.     

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.     

An empirical bayes approach to a variables acceptance sampling plan problem

An empirical Bayes approach to a variables acceptance sampling plan problem is presented and an empirical Bayes rule is developed which is shown to be asymptotically optimal under general conditions. The problem considered is one in which the ratio of the costs of accepting defective items and rejecting non-defective items is specified. Sampling costs are not considered and the size of the sample taken from each lot is fixed and constant. The empirical Bayes estimation of the Bayes rule is shown to require the estimation of a conditional probability. An estimator for conditional probabilities of the form needed is derived and shown to have good asymptotic properties.     

A bayesian life test acceptance sampling plan by variables with cost considerations

This paper presents an economic life test acceptance sampling plan using item-censored data in a Bayesian situation. It is assumed that failures in a life test are replaced immediately by new ones. A prior distribution is assigned to the mean lifetime θ for the calculation of the expected total cost. Then the optimum plan is chosen to be the one which minimizes the expected total cost. A direct search method and a dual programming method are introduced, with emphasis on the latter. A numerical example is presented to illustrate the procedure. A sensitivity study is included on the effect of a wrong choice of the prior distribution.     

A new variables sampling plan for normally distributed lots with unknown standard deviation and double specification limits

We deal with single sampling by variables with two-way-protection in case of normally distributed characteristics with unknown variance. Givenp ₁(AQL),p ₂ (LQ) and α, β (risks of errors of the first and the second kind), there are two well-known methods of determining the corresponding sampling plans. Both methods are based on an approximation of the OC. Therefore these plans are only approximations, the true risks α and β are not known exactly. In section II we present a new sampling scheme based on an estimatorp for the percent defectivep. We give an exact formula for the OC. Thus we are able to determine these plans exactly without any approximations.     

ASN-minimax double sampling plans for variables

X be a continuous quality characteristic, with one-sided lower specification limit, having either normal distribution with known σ or exponential distribution. We report on an algorithm allowing the calculation of the so-called ASN-Minimax plan. This plan has minimal maximal average sample size among all double sampling plans for variables that obey the classical two-points-condition on the operating characteristic. We give examples and tables of the ASN-Minimax plans in the normal as well as in the exponential case. Received: March 20, 2000; revised version: January 22, 2001     

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.     

A note on the operating characteristic curve of the known sigma single sampling variables plan

The operating characteristic curves of certain known sigma variables sampling plans may not be satisfactory in that they have a tendency to reject even lots of acceptable quality. This note presents the theory and a method to identify such known sigma variables plans possessing unsatisfactory operating characteristic curves.     

Procedure for the selection of CSP-M one level skip-lot sampling inspection plans that have a single-sampling plan with acceptance number zero as the reference plan

This paper presents a procedure for the selection of CSP-M one-level skip-lot sampling plans, designated as CSP-MSkSP, that have a single-sampling plan with acceptance number zero as the reference plan. The parameters of the plan are determined when two points on the operating characteristic curve are specified, the two points being (p1,) and (p2,), where p1 is the acceptable quality level, is the producer's risk, p2 is the limiting quality level and is the consumer's risk.     

Ranked set sampling for ordered categorical variables

The authors show how ranked set sampling, both balanced and unbalanced, can be extended to ordered categorical variables with the goal of estimating the probabilities of all categories. They use ordinal logistic regression to aid in the ranking of the ordinal variable of interest. They also propose an optimal allocation scheme and methods for implementing it under either perfect or imperfect rankings. Results from a simulation study using data from the third National Health and Nutrition Examination Survey indicate that the use of ordinal logistic regression in ranking leads to substantial gains in precision for estimation of cell probabilities.     

Variables acceptance reliability sampling plan for repairable items

Traditionally, acceptance reliability sampling plans have been developed for non-repairable items. However, the functions required for items become more and more complex and, accordingly, the items are composed of several components and tend to be repairable. In this paper, we consider variables acceptance reliability sampling plan for repairable items. We develop a variables acceptance sampling plan based on the failure and repair data observed during the testing period. It is shown that the developed sampling plan improves the reliability characteristic of the population and that the lifetimes of items before and after the reliability sampling test are stochastically ordered.