Procedures and tables for the construction and selection of chain sampling plans ChSP-4A(c1, c2,)r-Part 4

In this part of the series, the notion of average total inspection (ATI) is introduced to ChSP-4A(c1, c2)r plans, minimizing ATI at a given process average, while protection to the consumer is given in terms of average outgoing quality limit and limiting quality level. The procedure is similar to that of Dodge and Roming.     

Procedures and tables for the construction and selection of chain sampling plans ChSP-4A(c1 ,c2 )r-Part 5

SUMMARY This paper presents a design procedure for ChSP-4A(c1,c2)r plans based on Kullback-Leibler information and the minimum sum of risks. A table that gives the values of the parameters n and k indexed by the acceptable quality level (AQL) and limiting quality level (LQL) is presented, from which one can select a plan which gives a desired AQL and LQL when the producer's risk alpha= 0.05 and the consumer's risk beta = 0.10. A concluding remark for this series of five papers is given at the end of this paper.     

Procedures and tables for the construction and selection of chain sampling plans ChSP-4A(c1, c2)r—Part 1

This paper presents procedures and tables for the construction and selection of specific chain sampling plans 4A(c1, c2)r.     

Procedures and tables for the construction and selection of chain sampling plans ChSP-4A(c1,c2)r—Part 2

In this paper an approach for designing chain sampling plans ChSP-4A(c1,c2)r indexed by acceptable quality level and limiting quality level under the conditions of binomial model and a procedure of designing plans for fixed sample sizes minimizing the sum of weighted risks are described.     

Modified tables for the selection of double sampling attribute plan indexed by aql and lql

This paper presents modified tables for the selection of double sampling plans for given Acceptable Qualtiy Level (AQL), producer’s risk (α) Limiting Quality Level (LQL), and consumer’s risk (ß) giving the minimum sum of Average Sample Numbers (ASN) at AQL and LQL under the conditions of the Poisson model for the Operating Characteristic (OC) curve.     

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     

Selection of conditional sampling plans for given AQL and LQL

This paper presents procedures and tables for the selection of conditional sampling plans, viz. conditional double sampling plan, chain-deferred sampling plan, link sampling plan, and ChSP-4A chain sampling plan for given acceptable quality level (AQL), producer's risk, limiting quality level and consumer's risk giving minimum sample size at AQL under the conditions of the Poisson model for the operating characteristic curve.     

Determination of conditional double sampling scheme

In this paper, a new sampling scheme called the 'conditional double sampling scheme' (CDSS) has been proposed. A compact table is presented for the selection of a CDSS indexed by various combinations of entry parameters. Advantages of the CDSS over the single sampling scheme have been discussed. The basis for the construction of the table is given.     

Procedures and tables for the selection of tightened-normal-tightened (TNT-( n ; c 1 , c 2 )) sampling schemes

Procedures for the selection of tightened-normal-tightened (TNT) sampling schemes of type TNT-( n ; c 1 , c 2 ) are presented. It is shown that the TNT scheme provides a smaller sample size than the matched single-sampling plan.     

On equivalence of oc functions of certain conditional sampling plans

In this paper equivalence of operating characteristic ( OC ) functions of certain conditional sampling plans viz., ChSP-4, ChSP~4A, Conditional Double Sampling Plan, Link sampling Plan and Chain Deferred State Sampling Plans have been established. A common procedure to select these plans have been suggested.     

Optimal exact design of double acceptance sampling plans by attributes

The design of double acceptance sampling (AS) plans for attributes based on the operating characteristic curve paradigm is usually addressed by enumeration algorithms. These AS plans may be non optimal regarding the sample size to inspect as they were obtained without the requirement that the constraints at the OC curve controlled points are not violated for minimum Average Sample Number (ASN) scenarios. An approach based on mathematical programming is proposed to systematically design double AS plans for attributes, where the characteristics controlled are modelled by binomial or Poisson distributions. Specifically, Mixed Integer Nonlinear Programming (MINLP) formulations are developed and combined with an enumeration algorithm that allows finding ASN minimax optimal plans. A theoretical result is developed with the purpose of assuring the global optimum design is reached by iteration where a convenient solver is used to find local optima. To validate the algorithm, we compare our results with those of tables commonly used for practical purposes, consider different rates of risk, and setups commonly used in Lot Quality Assurance Plans (LQAS) for health monitoring programmes. Finally, we compare AS plans determined for processes described by binomial and Poisson distributions.     

A generalized procedure for selection of attribute double sampling plan

A compact table, yielding attribute double sampling plan indexed by AQL, AOQL and LQL and double sampling scheme indexed by AQL is presented. Method of selecting the plans are indicated through examples.     

Characterization of MIL-STD-105D double sampling plans using normalized OC curves

A simple method of analyzing the MIL-STD-105D double sampling plans by ‘normalizing the OC curve’ is presented. Among a set of competing double sampling plans, procedures are given to select a particular plan when costs are unknown. Necessary tables are constructed and examples given.     

ASN-minimax double sampling plans by variables for two-sided specification limits when the standard deviation is known

Sampling plans are a useful tool to decide whether large-size lots should be accepted or rejected. In this paper we introduce double sampling plans by variables for a normally distributed characteristic with known standard deviation and two-sided specification limits. These plans fulfill the classical two-points-condition on the operating characteristic (OC) and feature minimal maximal average sample number (ASN).     

Construction and selection of quick switching double sampling system-acceptance number tightening

This paper presents a new sampling inspection system consisting of simple switching rule. The performance of the system is compared with those of other equivalent plans. Necessary tables are constructed and procedures presented for the selection of the sampling system.     

Quick specification of acceptance sampling plans for dependent attribute sampling

Traditionally, fraction-nonconforming is treated as a Bernouilli variable with the attendant assumption of independence in constructing the acceptance sampling plans. This study relaxes the independence assumption in attribute sampling and provides a convenient nomogram to incorporate the effects of dependence into the sampling plans. The nomogram provides convenient answers for a number of questions about sampling with attributes. The study simplifies the procedural details, virtually eliminates the computation and facilitates the rapid scanning and evaluation of alternative solutions.     

The operating characteristic of double sampling plans by variables when the standard deviation is unknown

Summary We deal with double sampling plans by variables for a one-sided specification limit when the quality characteristic is normally distributed with unknown standard deviation. An algorithm is presented that allows to calculate the OC of the sampling plans proposed by Bowker and Goode (1952). We give several examples. Furthermore, it is shown that the algorithm carries over to calculating the OC of the double-stage t-test. The authors wish to thank Yvonne K?llner and Timor Saffary for technical support.     

An inequality for random replacement sampling plans

A sample (X₁ …, X_n) is drawn from a population of size N. Karlin (1974) conjectured that for any function ? in a certain class of real-valued functions on the sample space, ? is at least as large for sampling with replacement as for any other random replacement sampling plan. This conjecture is proved under the assumption that ?     

Interval censored sampling plans for the log-logistic lifetime distribution

The log-logistic distribution is one of the popular distributions in life-testing applications. This article develops an acceptance sampling procedure for the log-logistic lifetime distribution based on grouped data when the shape parameter is given. Both producer and consumer risks are considered to develop the ordinary, approximate and simulated sampling plans. Some of the proposed sampling plans are tabulated; moreover, those three types of sampling plans are compared with each other under the same censoring rates. The use of these tables is illustrated by an example.