euklid.ewma.arl {spc}

Compute ARLs of Poisson NCS-EWMA control charts

Description

Computation of the (zero-state) Average Run Length (ARL) at given Poisson mean mu.

Usage

euklid.ewma.arl(gX, gY, kL, kU, mu, y0, r0=0)

Arguments

gX

first and

gY

second integer forming the rational lambda = gX/(gX+gY), lambda mimics the usual EWMA smoothing constant.

kL

lower control limit of the NCS-EWMA control chart, integer.

kU

upper control limit of the NCS-EWMA control chart, integer.

mu

mean value of Poisson distribution.

y0

headstart like value – it is proposed to use the in-control mean.

r0

further element of the headstart – deviating from the default should be done only in case of full understanding of the scheme.

Details

A new idea of applying EWMA smoothing to count data based on integer divison with remainders. It is highly recommended to read the corresponding paper (see below).

Value

Return single value which resemble the ARL.

Author(s)

Sven Knoth

References

A. C. Rakitzis, P. Castagliola, P. E. Maravelakis (2015), A new memory-type monitoring technique for count data, Computers and Industrial Engineering 85, 235-247.

See Also

later.

Examples

# RCM (2015), Table 12, page 243, first NCS column
gX <- 5
gY <- 24
kL <- 16
kU <- 24
mu0 <- 20
#L0 <- euklid.ewma.arl(gX, gY, kL, kU, mu0, mu0)
# should be 1219.2