The Effect of Inspector Accuracy on the Type I and Type II Errors of Common Sampling Techniques

Hoag, LaVerne L.; Foote, Bobbie L.; Mount-Campbell, Clark A.

doi:10.1080/00224065.1975.11980691

Cited by 21 publications

(2 citation statements)

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“…If y is modeled as binomial r.v., Hoag and Foote (1975) showed that the Pa will follow the binomial rule with the apparent fraction of nonconforming equals to p(1 2 e 2 ). Next consider case II, the inspection error of Type II (e 2 ) is zero.…”

Section: Single Sampling Plansmentioning

confidence: 99%

“…The "effective" fraction of nonconforming is the function the "true" fraction and the inspection errors of two types (Lavin, 1946;Collins et al, 1973;Case et al, 1975). Hoag and Foote (1975) presented the effects of inspection errors on the sampling plan under both with and without replacement. Govindaraju (2007) adopted the word "apparent" fraction of nonconforming and presented an approach to design the single sampling plans under inspection errors with repeated testing.…”

Section: Introductionmentioning

confidence: 99%

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

Chattinnawat

2013

Int J Qual & Reliability Mgmt

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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.

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Section: Single Sampling Plansmentioning

confidence: 99%