MODEL:
! Acceptance sampling: taking one or more samples
at random from a lot, inspecting each of the
items in the sample(s), and deciding on the basis
of inspection results whether to accept or reject
the entire lot. (See Schroeder, Oper. Mgt.) This
Acceptance Sampling model illustrates the effect
of choice of distribution.;
! From a lot of 400 items;
LOTSIZE = 400;
! We take a sample of size 100;
SAMPSIZE = 100;
! Producer considers the lot good if
the lot fraction defective is .0075 or less;
FGOOD = .0075;
! Consumer considers the lot bad if
the lot fraction defective is .025 or more;
FBAD = .025;
! We accept the lot if sample contains 2 or less;
ACCEPTAT = 2;
! The model;
! What is producer risk of rejecting a good lot;
! Using the (exact) hypergeometric distribution;
PGOODH = 1  @PHG( LOTSIZE, LOTSIZE * FGOOD,
SAMPSIZE, ACCEPTAT);
! Using binomial approx. to the hypergeometric;
PGOODB = 1  @PBN( FGOOD, SAMPSIZE, ACCEPTAT);
! Using the Poisson approx. to the binomial;
PGOODP = 1  @PPS( FGOOD * SAMPSIZE, ACCEPTAT);
! Using Normal approximation;
PGOODN =
1  @PSN( (ACCEPTAT + .5  MUG) / SIGMAG);
! where;
MUG = SAMPSIZE * FGOOD;
SIGMAG = ( MUG * ( 1  FGOOD)) ^ .5;
! What is the consumer risk of accepting a bad lot;
! Using the hypergeometric;
PBADH = @PHG( LOTSIZE, LOTSIZE * FBAD,
SAMPSIZE, ACCEPTAT);
! Binomial;
PBADB = @PBN( FBAD, SAMPSIZE, ACCEPTAT);
! Poisson;
PBADP = @PPS( FBAD * SAMPSIZE, ACCEPTAT);
! Using Normal approximation;
PBADN = @PSN( ( ACCEPTAT + .5  MUB) / SIGMAB);
! where;
MUB = SAMPSIZE * FBAD;
SIGMAB = ( MUB * ( 1  FBAD)) ^ .5;
END
