Optimal Designing of Variables Chain Sampling Plan by Minimizing the Average Sample Number

S Balamurali,M Usha

doi:10.1155/2013/751807

Abstract

We investigate the optimal designing of chain sampling plan for the application of normally distributed quality characteristics. The chain sampling plan is one of the conditional sampling procedures and this plan under variables inspection will be useful when testing is costly and destructive. The advantages of this proposed variables plan over variables single sampling plan and variables double sampling plan are discussed. Tables are also constructed for the selection of optimal parameters of known and unknown standard deviation variables chain sampling plan for specified two points on the operating characteristic curve, namely, the acceptable quality level and the limiting quality level, along with the producer’s and consumer’s risks. The optimization 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.

Highlights

In recent years process control techniques and offline quality control methods have taken important roles, acceptance sampling procedures remain as a major tool for many practical quality control systems
Variables sampling plans are designed based on two points on the operating characteristic (OC) curve, namely, (p1, 1 − α) and (p2, β), where p1 is called the acceptable quality level (AQL), p2 is the limiting quality level (LQL), α is the producer’s risk, and β is the consumer’s risk
Any well-designed sampling plan must provide at least (1 − α)% probability of acceptance of a lot when the process fraction nonconforming is at acceptable quality levels (AQL) level and the sampling plan must provide not more than β% probability of acceptance if the process fraction nonconforming is at the LQL level

Summary

Introduction

In recent years process control techniques and offline quality control methods have taken important roles, acceptance sampling procedures remain as a major tool for many practical quality control systems. That is, sampling plans are widely used in industries for estimating lot or process characteristics and for determining the disposition of lots. Variable sampling plans constitute one of the major areas of the theory and practice of acceptance sampling. The primary advantage of the variables sampling plan is that the same operating characteristic (OC) curve can be obtained with a smaller sample size than would be required by an attributes sampling plan. A variables acceptance sampling plan would require less sampling. The variables sampling provides more information than the attributes sampling, and the same protection is attained with partly considerable smaller sample size. When destructive testing is employed, variables sampling is useful in reducing the costs of inspection

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