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#' Variable Sampling Plans
#'
#' Variable sampling plans for known and unknown sigma, evaluated for given
#' parameters.
#'
#'
#' @aliases VSPKnown VSPUnknown
#' @param N the lot size
#' @param n the sample size
#' @param k the acceptability constant
#' @param Pa fraction nonconforming
#' @param Plots logical indicating whether the four plots are required
#' @author Raj Govindaraju with minor editing by Jonathan Godfrey
#' @keywords ~kwd1 ~kwd2
#' @examples
#'
#' VSPKnown(1000, 20,1)
#' VSPUnknown(1000, 20,1)
#'
#' @export
VSPKnown=function(N, n, k, Pa=seq(0, 1, 0.001), Plots=TRUE)
{
zpa = qnorm(Pa)
zp = k+(zpa/sqrt(n))
p=1-pnorm(zp)
OC = Pa
AOQ=(N-n)*p*OC/N
ATI= n*OC+N*(1-OC)
results = list(p=p, OC=OC, n=rep(n,length(p)), AOQ=AOQ, ATI=ATI)
class(results)="AccSampPlan"
if(Plots){
par(mfrow=c(2,2))
plot(results)
}
return(results)
}
#' @export
VSPUnknown=function(N, n, k, Pa=seq(0, 1, .001), Plots=TRUE)
{
zpa = qnorm(Pa)
k1 = sqrt(1+(k*k)/2)
zp = k+(k1*zpa/sqrt(n))
p=1-pnorm(zp)
OC = Pa
AOQ=(N-n)*p*OC/N
ATI= n*OC+N*(1-OC)
results = list(p=p, OC=OC, n=rep(n,length(p)), AOQ=AOQ, ATI=ATI)
class(results)="AccSampPlan"
if(Plots){
par(mfrow=c(2,2))
plot(results)
}
return(results)
}
#' Variable Sampling Plan Design
#'
#' Design the variable sampling plan for given AQL, alpha, LQL, and beta.
#'
#'
#' @param AQL Acceptable quality level
#' @param alpha producer's risk
#' @param LQL Limiting quality level
#' @param beta consumers' risk
#' @author Raj Govindaraju with minor editing by Jonathan Godfrey
#' @keywords ~kwd1 ~kwd2
#' @examples
#'
#' VSPDesign(AQL=0.01, alpha=0.05, LQL=0.04, beta=0.05)
#'
#' @export
VSPDesign =function(AQL, alpha, LQL, beta)
{
zp1=qnorm(1-AQL)
zp2=qnorm(1-LQL)
zpa1=qnorm(1-alpha)
zpa2=qnorm(1-beta)
k =(zp2*zpa1+zp1*zpa2)/(zpa1+zpa2)
n =(zpa1+zpa2)/(zp1-zp2)
n = n*n
n = round(n)
n.unknown=n*(1+(k*k/2))
return(data.frame(k, n, n.unknown))
}
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