Construction of AOQ curve and calculate AOQL value based on limiting fraction

Source: R/AOQL_grab_A.R

AOQL_grab_A provides the AOQ curve and calculates AOQL value based on limiting fraction of contaminated increments.

AOQL_grab_A(c, r, t, d, N, method, plim)

Arguments

c

acceptance number

r

nurber of primary increments in a grab sample or grab sample size

t

number of grab samples

d

serial correlation of contamination between the primary increments

N

length of the production

method

what sampling method we have applied such as 'systematic' or 'random' selection methods

plim

the upper limit for graphing the fraction nonconforming or proportion of contaminated increments

Value

AOQ curve and AOQL value based on on limiting fraction

Details

Since \(P_{ND}\) is the probability of non-detection, \(p\) is the limiting fraction of contaminated increments and the outgoing contaminated proportion of primary increments is given by \(AOQ\) as the product \(pP_{ND}\). The quantity \(AOQL\) is defined as the maximum proportion of outgoing contaminated primary increments and is given by $$AOQL ={\max_{0\leq p\leq 1}}{pP_{ND}}$$

See also

prob_detect

Examples

  c <-  0
  r <-  25
  t <-  30
  d <-  0.99
  N <-  1e9
  method <- 'systematic'
  plim <- 0.30
  AOQL_grab_A(c, r, t, d, N, method, plim)