ISSN: 0090-3973
Page Count: 6

On Bounding a Near-Zero Probability When Zero Occurrences Appear in a Sample

Proctor, CH
ConsultantConsultant,NCCT,

Luko, SN
ConsultantConsultant,NCCT,

(Received 5 February 2001; accepted 18 January 2002)

Abstract

In attribute sampling, it is sometimes the case that the investigator will report a “zero response” in the sample. This means that where a specific attribute has been defined, no occurrences having the attribute are observed in the sample. When this event occurs, it may be tempting to report a result of “zero defects” or simply that the attribute was not observed within the sample. It may even be concluded that defects are not to be expected from the process or lot since none were observed in the sample. This paper shows that this reasoning is false and shows how to bound the probability of future occurrence of a defined attribute, under various conditions of sampling, when zero occurrences are exhibited in a sample. Several common scenarios of sampling are considered, including sampling from a process, sampling finite or isolated lots, and sampling from a continuum. In addition, some common sampling problems such as errors of misclassification and autocorrelation are considered.

Keywords:
upper confidence bound, misclassification error, binomial distribution, hypergeometric distribution, Poisson distribution, autocorrelation, beta distribution, beta-binomial distribution, Bayesian analysis

Paper ID: JTE12312J
DOI: 10.1520/JTE12312J
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