attrCUSUM (version 0.1.0)

getAve_Poisson: Compute ATSs and Other Informations on (Zero-Inflated) Poisson CUSUM Chart

Description

Computation of ANSSs, ATSs and other related informations on (zero-inflated) Poisson CUSUM chart.

Usage

getAve_pois(lambda, refv, contl, c.zero = 0, warnl = 0, ds = 1, dl = NULL, di = NULL, maxndec = 7L, maxnumsubI = 6000L)
getAve_zipois(rho, lambda, refv, contl, c.zero = 0, warnl = 0, ds = 1, dl = NULL, di = NULL, maxndec = 7L, maxnumsubI = 6000L)

Arguments

rho

A length-one numeric vector of zero-inflated parameter in [0,1).

lambda

A length-one positive numeric vector of mean.

refv

A reference value of CUSUM statistic.

contl

A control limit in CUSUM control scheme.

c.zero

An initial state of CUSUM statistic (default is 0).

warnl

A warning limit in VSI control scheme (default is 0).

ds

The shorter sampling interval in VSI CUSUM control scheme (default is 1).

dl

The longer sampling interval in VSI CUSUM control scheme.

di

The sampling interval at initial state in VSI CUSUM control scheme.

maxndec

The maximum number of decimal places of refv ($\le$ 7L).

maxnumsubI

The maximum number of sub-intervals in [100,6000] to be used in applying the Markov chain approach.

Value

A list from getAve. See getAve for more information.

Details

getAve_pois and getAve_zipois are wrapper functions of getAve for (zero-inflated) Poisson CUSUM chart.

References

White et al. (1997). POISSON CUSUM VERSUS c CHART FOR DEFECT DATA, Quality Engineering, 9:4, 673-679.

See Also

getAve, getAve_binomial.

Examples

# Example 1: Reproduction of results from White et al. (1997)
tbl <- list()
arglist <- list(list(mu.a = 1, k = 2, h = 2),
                list(mu.a = 4, k = 5, h = 8),
                list(mu.a = 8, k = 10, h = 10),
                list(mu.a = 12, k = 15, h = 11))
deltas <- seq(0, 2.5, 0.5)
for(i in seq_along(arglist)) {
  argument <- arglist[[i]]
  arl <- numeric(length(deltas))
  for(j in seq_along(deltas)) {
    std.a <- sqrt(argument$mu.a)
    arl[j] <- getAve_pois(lambda = argument$mu.a + (std.a * deltas[j]),
                          refv = argument$k,
                          contl = argument$h)$ANSS
  }
  tbl[[i]] <- round(arl, 2)
}
tbl <- data.frame(tbl)
colnames(tbl) <- c("CUSUM(2,2)", "CUSUM(5,8)", "CUSUM(10,10)", "CUSUM(15,11)")
rownames(tbl) <- as.character(deltas)
cat("colnames stand for CUSUM(k,h)\n",
    "rownames stand for delta\n", sep = "")
tbl

# Example 2: ANSS profiles (h in seq(20L))
mu.a <-  4
k  <-  5
h <- seq(20)
ANSSs <- numeric(20)
for(i in seq(ANSSs)) {
  ANSSs[i] <- getAve_pois(lambda = mu.a, refv = k, contl = h[i], c.zero = 0,
                          warnl = 1, ds = 1)$ANSS
}
ANSSs