arlCusum {surveillance} | R Documentation |
Calculates the average run length (ARL) for an upward CUSUM scheme for discrete distributions (i.e. Poisson and binomial) using the Markov chain approach.
arlCusum(h=10, k=3, theta=2.4, distr=c("poisson","binomial"), W=NULL, digits=1, ...)
h |
decision interval |
k |
reference value |
theta |
distribution parameter for the cumulative distribution function (cdf) F, i.e. rate λ for Poisson variates or probability p for binomial variates |
distr |
"poisson" or "binomial"
|
W |
Winsorizing value W for a robust CUSUM,
to get a nonrobust CUSUM set
W > k +h . If NULL , a nonrobust CUSUM is used. |
digits |
k and h are rounded to digits decimal places |
... |
further arguments for the distribution function, i.e. number of trials n
for binomial cdf |
Returns a list with the ARL of the regular (zero-start)
and the fast initial response (FIR)
CUSUM scheme with reference value k
, decision interval h
for
X sim F(theta), where F is the Poisson or binomial cdf
ARL |
one-sided ARL of the regular (zero-start) CUSUM scheme |
FIR.ARL |
one-sided ARL of the FIR CUSUM scheme with head start
frac{h }{2} |
Based on the FORTRAN code of
Hawkins, D. M. (1992). Evaluation of Average Run Lengths of Cumulative Sum Charts for an Arbitrary Data Distribution. Communications in Statistics - Simulation and Computation, 21(4), p. 1001-1020.