Fractional Acceptance Numbers for Lot Quality Assurance

Abstract

Fractional acceptance numbers such as one-quarter fraction nonconforming are used in the acceptance sampling literature. The concept of fractional acceptance number is particularly useful for short-run food manufacturing processes involving a measurable quality characteristic such as the percentage sugar or fat content. Attribute method of inspection is desirable for small sample sizes because of the difficulty in identifying the underlying distribution. Analytical testing of fat content, etc. also involves considerable measurement uncertainty, often up to half of the observed variation. However the distribution of the measurement errors can be fairly well ascertained using past calibration studies. An observed measurement X is classified with certainty as conforming or not for given specification limits only when there are no measurement errors. Measurement error uncertainty results only in an estimated probability of conformance of a unit. The probability of nonconformance of an individual unit based on the error-prone measurement is defined as the 'fractional' nonconforming unit. A new fractional acceptance number sampling plan, which is a mix of attribute and variables methods, is introduced. The operating characteristics of the proposed plan are evaluated using common error distributions and the incomplete beta function. The fractional acceptance numbers also extend to broken acceptance numbers such as 1.6.

Acceptance control and guardbanding for error‐prone individual measurements

“…Measurement errors are seldom negligible, especially for analytical measurements, which are often indirect. Govindaraju and Jones proposed a new fractional acceptance number sampling plan using fractional nonconformance probability measure for an observation given the measurement error distribution. Let Y = X + Z be the measurement error model, where X , Y , Z are the true measurement, the apparent measurement, and the measurement error respectively.…”

“…Govindaraju and Jones proposed a probabilistic measure for quantifying nonconformance after adjusting for measurement uncertainty when the underlying measurement error distribution is known. This fractional nonconformance statistic (FNC) was initially applied for acceptance sampling inspection and was further implemented for short‐run process monitoring by Zhou et al The objective of this work is to employ fractional nonconformance principles to acceptance control charting applications in dairy production.…”