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# Computation of EWMA critical values for given ARL (variance monitoring)
sewma.crit <- function(l, L0, df, sigma0=1, cl=NULL, cu=NULL, hs=NULL, s2.on=TRUE, sided="upper", mode="fixed", ur=4, r=40, qm=30) {
mitte <- sqrt( 2/df ) * gamma( (df+1)/2 )/ gamma( df/2 )
if ( is.null(hs) ) {
if ( s2.on ) { hs <- 1 } else { hs <- mitte }
}
cu0 <- cl0 <- 0
if ( l<=0 | l>1 )
stop("l has to be between 0 and 1")
if ( L0<1 )
stop("L0 is too small")
if ( df<1 )
stop("df must be positive")
if ( sigma0<=0 )
stop("sigma0 must be positive")
if ( sided=="Rupper" ) {
if ( is.null(cl) )
stop("set cl")
if ( cl<=0 )
stop("cl must be positive")
cl0 <- cl
if ( hs<cl0 )
stop("hs must not be smaller than cl")
}
if ( sided=="Rlower" ) {
if ( is.null(cu) )
stop("set cu")
if ( cu<sigma0 )
stop(paste("cu must be larger than sigma0 =", sigma0))
cu0 <- cu
if ( hs>cu0 )
stop("hs must not be larger than cu")
}
if ( sided=="two" & mode=="fixed" ) {
if ( is.null(cu) )
stop("set cu")
if ( cu<sigma0 )
stop(paste("cu must be larger than sigma0 =", sigma0))
cu0 <- cu
if ( hs>cu0 )
stop("hs must not be larger than cu")
}
s_squared <- as.numeric(s2.on)
if ( !(s_squared %in% c(0,1)) )
stop("wrong value for s2.on")
ctyp <- pmatch(sided, c("upper", "Rupper", "two", "Rlower")) - 1
if (is.na(ctyp))
stop("invalid ewma type")
ltyp <- pmatch(mode, c("fixed", "unbiased", "eq.tails", "vanilla")) - 1
if ( is.na(ltyp) )
stop("invalid limits type")
if ( r<10 )
stop("r is too small")
if ( qm<10 )
stop("qm is too small")
if ( isTRUE(all.equal(1, l)) ) {
if ( sided=="upper" ) {
cv <- c(0, qchisq( 1-1/L0, df)/df)
}
if ( sided=="Rupper" ) {
cv <- c(0, Inf)
warning("not useful for Shewhart type chart")
}
if ( sided=="Rlower" ) {
cv <- c(qchisq( 1/L0, df)/df, Inf)
}
if ( sided=="two") {
if ( mode=="fixed" ) {
a2 <- 1 - pchisq(df*cu, df)
if ( a2 > 1/L0 ) {
cv <- c(0, Inf)
warning("upper limit too small")
} else {
a1 <- 1/L0 - a2
cv <- c(qchisq(a1, df)/df, cu)
}
}
if ( mode=="unbiased") {
a1 <- 1/(2*L0)
step <- 1/(2*L0)/10
one <- 1
for ( j in 1:8 ) {
for ( i in 1:11 ) {
a1 <- a1 + step*one
k1 <- qchisq(a1, df)
a2 <- 1/L0 - a1
k2 <- qchisq(1-a2, df)
condition <- (k2 - k1)/(log(k2) - log(k1))
if ( (one*condition) > (one*df) ) break
}
step <- step/10
one <- -one
if ( abs(condition - df) < 1e-10 ) break
}
cv <- c(k1, k2)/df
}
if ( mode=="eq.tails" ) {
a <- 1/(2*L0)
cv <- qchisq(c(a, 1-a), df)/df
}
if ( mode=="vanilla" ) {
a <- 1/L0
k2 <- qchisq(1-a, df)
k1 <- 2*df - k2
if ( k1 > 0 ) {
zero <- function(x) ( pchisq( 2*df - qchisq(1-x, df), df) + x ) - 1/L0
a <- uniroot(zero, c(1/(2*L0), 1/L0), tol=1e-12)$root
k2 <- qchisq(1-a, df)
k1 <- 2*df - k2
cv <- c(k1, k2)/df
} else {
cv <- c(0, Inf)
warning("symmetric design not possible")
}
}
}
} else {
cv <- .C("sewma_crit",as.integer(ctyp),as.integer(ltyp),as.double(l),
as.double(L0),as.double(cl0),as.double(cu0),as.double(hs),
as.double(sigma0),as.integer(df),as.integer(r),as.integer(qm),
as.double(ur),as.integer(s_squared),
ans=double(length=2),PACKAGE="spc")$ans
}
names(cv) <- c("cl", "cu")
cv
}
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