The Computation of Multi-Stage Attribute Sampling Plans

For multi-stage fraction-defective sampling by attributes, the current methods for determining sampling plans (1) restrict the range of values of some combination of the input parameters for determining such plans and (2) are generally based on the Poisson approximation to the binomial. This report describes the development of a computational algorithm which allows a continuous range of input parameter values and bases sampling plan computations on the binomial probability distribution. The computerized algorithm has been successfully implemented in an industrial firm and requires only a few seconds or less computer time per sampling plan, depending on the input parameters.     

The Dodge CSP-1 Continuous Sampling Plan Under Inspection Error1

This paper examines the results of Dodge's CSP-1 continuous sampling plan under inspection error. Both type I and II errors are explicitly included. Their effect on the average number of items inspected in a 100% screening sequence, average number of items passed during sampling inspection, average fraction of items inspected, proportion of items passed under sampling, and average outgoing quality are examined. Further, the relationships necessary to determine compensating sampling plans, considering inspection error, which yield the desired actual AOQL, are developed. Use of the compensating plan method is illustrated through an example.     

Multiobjective Decision Analysis for Acceptance Sampling Plans

In recent years there has been increased interest in the design and implementation of economically based sampling plans, especially those which consider a prior distribution of defectives in lots submitted for inspection. Sampling plans which are designed using this prior knowledge are often referred to as Bayesian sampling plans. This paper illustrates an approach to the design of Bayesian sampling plans which considers two criteria. The few previous attempts to design multiobjective Bayesian sampling plans have been based on expected values of the criteria. In this paper the authors present a design methodology which takes into consideration the distribution functions of the criteria after sampling inspection, and the utility function of the 'decision maker'. Illustrative examples of the use of the methodology are given as well as areas for further research.     

Acceptance Sampling Plans with Truncated Life Tests for the Length-Biased Weighted Lomax Distribution

In this paper, we considered the Length-biased weighted Lomax distribution and constructed new acceptance sampling plans (ASPs) where the life test is assumed to be truncated at a pre-assigned time. For the new suggested ASPs, the tables of the minimum samples sizes needed to assert a specific mean life of the test units are obtained. In addition, the values of the corresponding operating characteristic function and the associated producer’s risks are calculated. Analyses of two real data sets are presented to investigate the applicability of the proposed acceptance sampling plans; one data set contains the first failure of 20 small electric carts, and the other data set contains the failure times of the air conditioning system of an airplane. Comparisons are made between the proposed acceptance sampling plans and some existing acceptance sampling plans considered in this study based on the minimum sample sizes. It is observed that the samples sizes based on the proposed acceptance sampling plans are less than their competitors considered in this study. The suggested acceptance sampling plans are recommended for practitioners in the field.     

Evaluating and Implementing 3-Level Acceptance Sampling Plans

There are many situations in which product quality can be described by classifying a product using three or more discrete levels. For example, a food product may be classified as good, marginal, or bad depending on the concentration of harmful microorganisms in the product. In this paper, a generic framework is defined for establishing 3-level acceptance sampling plans. These plans utilize what we refer to as quality value functions. The Operating Characteristic function for these plans is constructed and used to develop an approximate parameter selection method based on the Central Limit Theorem. The results of testing this method using numerical examples are presented. The problem of quality value function selection is also addressed. A detailed example is presented, which includes the implementation of both the parameter and quality value function selection methods.     

Some Acceptance Sampling Plans Based on the Theory of Runs

Some attribute sampling plans are presented based on the theory of runs in which a batch or process is accepted if a run of s successes is observed in a fixed number n of trials. The operating characteristic (OC) and expected number of trials (ENT) curves are given for the plans. Situations are described in which these plans are applicable and comparisons made with possible alternative plans.     

The Determination of Single Sampling Attribute Plans with Given Producer's and Consumer's Risk

The paper gives a survey of solutions to the problem of determining a single sampling plan (n, c) so that P(p ₁) > 1 – α, P(p ₂) ≤ β, and c is as small as possible, where P(p) denotes the operating characteristic, p ₁ < p ₂ and 1 – α > β. Solutions corresponding to Poisson, binomial, and hypergeometric operating characteristics are discussed and compared. Both exact and approximate formulas are given, and the accuracy of the approximations is evaluated by numerical investigations.     

The Compound Hypergeometric Distribution and a System of Single Sampling Inspection Plans Based on Prior Distributions and Costs

The main results of this paper, apart from the limit theorems, were given in two lectures at the University of London, and in a seminar at Imperial College of Science and Technology, London, January 1959. The complete paper was presented for discussion in a meeting at Imperial College in February 1960. The paper reviews present sampling inspection plans for attributes placing particular emphasis on their underlying assumptions. A model is then proposed based upon prior distributions and costs, and optimum sampling plans are derived which minimize the average costs for any prior distribution. Tables and examples are provided.     

Sampling Inspection Plans for Discriminating Between Two Weibull Processes

Four procedures—R ₁, R ₂, R ₃ and R ₄, for choosing the better of two processes, the units from which have life times distributed according to the Weibull distribution were formulated in an earlier paper [1]. The calculation in the use of these procedures and some sampling plans based on them are discussed here. The paper also examines the robustness of these procedures.     

The Average Sample Number for Truncated Single and Double Attributes Acceptance Sampling Plans

In attributes sampling acceptance plans the decision to reject the lot can often be made before inspection of a single sample is completed. In double sampling, the same decision may be possible before inspection of the first sample is completed or, if a second sample is required, before the second sample is completely inspected. Or, in double sampling one may always complete the inspection of the first sample, but if a second sample is required, terminate inspection of the second sample if the lot can be rejected before it is completely inspected. Using two formulas, believed to be new, it is shown how to compute the average sample number under these three hinds of truncation and tables of results for typical sampling plans are given.     

The Design of Economic Acceptance Sampling Plans for a Mixture of Variables and Attributes

A method is developed for determining economical acceptance sampling plans where the characteristics of interest are a mixture of variables and attributes. The method uses a model which has been developed to represent the total expected cost per lot of exercising acceptance sampling. An optimum plan is found by minimizing the expected cost model with respect to the decision variables which are the sample sizes and control limits on the sample means for variables and the sample sizes and acceptance numbers for attributes. Optimization is accomplished using the pattern search.     

Multiattribute Bayesian Acceptance Sampling Plans for Screening and Scrapping Rejected Lots

A general model for multiattribute Bayesian acceptance sampling plans is developed which incorporates the multiattribute utility function of a decision maker in its design. The model accommodates various dispositions of rejected lots such as screening and scrapping. The disposition of rejected lots is shown to have a substantial impact on the solution approach used and on the ease of incorporation of multiattribute utility functions in terms of their measurement complexity, functional form, and parameter estimation. For example, if all attributes are screenable upon rejection, and the prior distributions of lot quality on each attribute are independent, then an optimal multiattribute sampling plan can be obtained simply by solving for an optimal single sampling plan on each attribute independently. A discrete search algorithm, based on pattern search, is also developed and shown to be very effective in obtaining an optimal multiattribute inspection plan when such separability cannot be accomplished.     

On the Determination of Single Sampling Attribute Plans Based upon a Linear Cost Model and a Prior Distribution

The linear cost model previously formalized by Hald [4], [5], [9] is reviewed. Techniques are described which permit easy determination of sampling plans based on that model. The degenerate, the beta, and the two point distributions are considered as prior distributions of p, the process fraction defective. For calculations only standard tables and a desk calculator are required.     

Variables Sampling Plans Based on the Normal Distribution

Sampling Plans are considered which call for the acceptance of a lot of material if both – ks ≥ L and + ks ≤ U, where L and U are the lower and upper specification limits and where and s are the sample mean and standard deviation and k is an appropriate constant. Some errors that need to be corrected in previous work are pointed out in interpretation of the mathematical formulas before plans of the type described can be properly applied. Tables are given for the constant k under two different circumstances. Table II applies when the sum of the proportions defective in the two tails of a normal distribution is to be controlled. Table III applies when each tail is to be controlled below preassigned values, i.e., so that one can say with probability y that the proportion in the lower tail (below L) of accepted lots does not exceed a preassigned value and simultaneously the proportion in the upper tail (above U) does not exceed its preassigned value. The same constants, in Table III, apply when all the defectiveness to be controlled is in one tail.     

Progressively Censored Reliability Sampling Plans for the Weibull Distribution

This article presents progressively censored variable sampling plans for the Weibull distribution. Approximate maximum likelihood estimators are developed for estimating the parameters of interest. In the construction of sampling plans, asymptotic distribution theory is used to determine the sample size and the acceptance constant. Sampling plans are tabulated for selected progressive censoring patterns and specifications, for demonstration and comparison. A Monte Carlo experiment, conducted to investigate the accuracy of the asymptotic normal approximation, has shown that the procedure is sufficiently accurate for practical purposes. An example, based on data reported by Montanari and Cacciari from progressively censored aging tests on XLPE-insulated cable models, is given for illustration.     

Inspection Error Adjustment in the Design of Single Sampling Attributes Plan

This article presents an approach for the design of single sampling attributes plans of given strength when inspection errors are present. The design criterion considered is the specification of two points of the Operating Characteristic curve. The design approach also recommends repeated testing of sampled nonconforming units for conformance in order to reduce the adverse effect of the inspection errors. It is shown that realistic sampling plan parameters can be obtained if the inspection error probabilities are taken into account in the design of sampling plans.     

计量抽样检查在射孔器材抽样检验方案的设计与应用

针对射孔器穿孔深度和穿孔孔径符合正态分布的理论特点,应用不合格品率的计量抽样检查方法设计了射孔器穿孔深度和穿孔孔径的检验方案.通过验证证明了该方法的科学合理性,并通过试验数据说明了该检验方案的实施对于提高产品稳定性方面的贡献和对提高油气井产能的意义.