To read this content please select one of the options below:

Investigating design of zero acceptance number single sampling plans with inspection errors

Wichai Chattinnawat (Department of Industrial Engineering, Chiang Mai University, Chiang Mai, Thailand)

International Journal of Quality & Reliability Management

ISSN: 0265-671X

Article publication date: 21 June 2013

688

Abstract

Purpose

This research aims to investigate the differences in designing the zero acceptance number single sampling plans using the apparent fraction of nonconforming and the binomial distribution against the exact convolute compound hypergeometric distribution when both types of inspection errors are present.

Design/methodology/approach

This research presents the derivation and uses the numerical study to compare the calculated probability of acceptance and the minimum sample size when using the present design concept of binomial distribution with true fraction of nonconforming replaced with the apparent one. Under the presences of inspection errors and zero acceptance number, the probability of acceptance is alternatively derived and presented in term of a function of the probability generating function. This research uses numerical method to determine the differences in the probability of acceptance. The computation of the minimum sample sizes are presented along with the numerical results and the comparison.

Findings

When the inspection errors are present, the probability of acceptance is extremely decreased even for 1 percent of inspection errors of Type I (rejecting good product) and Type II (accepting bad product). The binomial apparent nonconforming notions yields an over‐estimation of the probability of acceptance, comparing with the exact convolute compound hypergeometric notion under the zero acceptance single sampling plans especially at low fraction of nonconforming levels, the six sigma quality levels. The differences of the calculated probabilities of acceptance and the minimum sample sizes decrease as the inspection error of Type II increases given a fixed value of Type I error and consumer risk.

Originality/value

This research alternatively presents the mathematical derivation along with numerical study to assert the over‐estimation of the probability of acceptance and the minimum sample size if the existing methodology to design the zero acceptance number single sampling plans is used. This finding will help improve the sampling design strategy of the multistage production system.

Keywords

Citation

Chattinnawat, W. (2013), "Investigating design of zero acceptance number single sampling plans with inspection errors", International Journal of Quality & Reliability Management, Vol. 30 No. 6, pp. 662-674. https://doi.org/10.1108/02656711311325610

Publisher

:

Emerald Group Publishing Limited

Copyright © 2013, Emerald Group Publishing Limited

Related articles