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Producer's and Consumer's Risk When Proportion Defective Is a Random Variable
Author(s) -
Graves Samuel B.,
Ringuest Jeffrey L.
Publication year - 1991
Publication title -
decision sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.238
H-Index - 108
eISSN - 1540-5915
pISSN - 0011-7315
DOI - 10.1111/j.1540-5915.1991.tb00363.x
Subject(s) - mathematics , risk measure , acceptance sampling , range (aeronautics) , measure (data warehouse) , statistics , random variable , econometrics , sample (material) , variable (mathematics) , probability distribution , actuarial science , computer science , economics , sample size determination , data mining , portfolio , mathematical analysis , materials science , chemistry , chromatography , financial economics , composite material
In acceptance sampling, producer's and consumer's risk are traditionally based on assumed fixed values of p , the proportion of the lot which is defective. A more useful definition of producer's risk would be the probability of rejecting a lot in which the proportion defective falls within some range of acceptable values. Similarly, a more useful definition of consumer's risk would be the probability of accepting a lot in which the proportion defective falls within some range of unacceptable values. In this paper, we construct measures of these more useful definitions of risk by assuming that p follows either a uniform or triangular probability distribution. The proposed measure yields consumer's risk values, β', which are smaller than the traditionally computed values by a factor of up to twenty times. The proposed measure of producer's risk, α', gives values smaller than traditional values by a factor of two to four times. Decision makers who adopt the proposed measures may be able to reduce sample sizes substantially while maintaining given risk levels.