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##' \code{\link{AOQL_grab_A}} provides the AOQ curve and calculates AOQL value based on limiting fraction of contaminated increments.
##' @title Construction of AOQ curve and calculate AOQL value based on limiting fraction
##' @param c acceptance number
##' @param r nurber of primary increments in a grab sample or grab sample size
##' @param t number of grab samples
##' @param d serial correlation of contamination between the primary increments
##' @param N length of the production
##' @param method what sampling method we have applied such as \code{'systematic'} or \code{'random'} selection methods
##' @param plim the upper limit for graphing the fraction nonconforming or proportion of contaminated increments
##' @details Since \eqn{P_{ND}} is the probability of non-detection, \eqn{p} is the limiting fraction of contaminated increments and the outgoing contaminated proportion of primary increments is given by \eqn{AOQ} as the product \eqn{pP_{ND}}.
##' The quantity \eqn{AOQL} is defined as the maximum proportion of outgoing contaminated primary increments and is given by \deqn{AOQL ={\max_{0\leq p\leq 1}}{pP_{ND}}}
##' @seealso \link{prob_detect}
##' @return AOQ curve and AOQL value based on on limiting fraction
##' @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)
##' @usage AOQL_grab_A(c, r, t, d, N, method, plim)
##' @export
AOQL_grab_A <- function(c, r, t, d, N, method, plim){
Sampling_scheme <- NULL # Initalizing
P_D <- NULL
p <- seq(1e-05, plim, by = 1e-05)
if (method == "systematic") {
f_spr <- function(t, r, c) {
if (r == 1) {
sprintf("systematic increments sampling (t=%.0f, c=%.0f)", t, c)
} else {
sprintf("systematic grab sampling (t=%.0f, r=%.0f, c=%.0f)", t, r, c)
}
}
} else {
f_spr <- function(t, r, c) {
if (r == 1) {
sprintf("random increments sampling (t=%.0f, c=%.0f)", t, c)
} else {
sprintf("random grab sampling (t=%.0f, r=%.0f, c=%.0f)", t, r, c)
}
}
}
AOQ <- p*(1-prob_detect(c, r, t, d, p, N, method))
Prob_df <- data.frame(p, AOQ)
Prob <- plyr::rename(Prob_df, c(AOQ = f_spr(t, r, c)))
melten.Prob <- reshape2::melt(Prob, id = "p", variable.name = "Sampling_scheme", value.name = "AOQ")
ggplot2::ggplot(melten.Prob) + ggplot2::geom_line(ggplot2::aes(x = p, y = AOQ , group = Sampling_scheme, colour = Sampling_scheme)) +
# ggplot2::ggtitle("AOQ curve based on limiting fraction of contaminated increments") +
ggplot2::ylab(expression(AOQ)) +ggplot2::xlab(expression("limiting fraction (" ~ p*~")"))+
ggplot2::theme_classic() + ggplot2::theme(plot.title = ggplot2::element_text(hjust = 0.5, size = 10), legend.position = c(0.75, 0.50)) + ggthemes::scale_colour_colorblind() +
ggplot2::geom_hline(yintercept=AOQ[which.max(AOQ)],linetype = "dashed")+
ggplot2::annotate("text", x=4*p[which.max(AOQ)], y=AOQ[which.max(AOQ)], label = sprintf("\n AOQL = %0.4f", round(AOQ[which.max(AOQ)], digits = 4)), size=3)
}
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