View source: R/algo_rogerson.R
findH | R Documentation |
Function to find a decision interval h
* for given reference value k
and desired ARL \gamma
so that the
average run length for a Poisson or Binomial CUSUM with in-control
parameter \theta_0
, reference value k
and is approximately \gamma
,
i.e. \Big| \frac{ARL(h^*) -\gamma}{\gamma} \Big| < \epsilon
,
or larger, i.e.
ARL(h^*) > \gamma
.
findH(ARL0, theta0, s = 1, rel.tol = 0.03, roundK = TRUE,
distr = c("poisson", "binomial"), digits = 1, FIR = FALSE, ...)
hValues(theta0, ARL0, rel.tol=0.02, s = 1, roundK = TRUE, digits = 1,
distr = c("poisson", "binomial"), FIR = FALSE, ...)
ARL0 |
desired in-control ARL |
theta0 |
in-control parameter |
s |
change to detect, see details |
distr |
|
rel.tol |
relative tolerance, i.e. the search for |
digits |
the reference value |
roundK |
passed to |
FIR |
if |
... |
further arguments for the distribution function, i.e. number
of trials |
The out-of-control parameter used to determine the reference value k
is specified as:
\theta_1 = \lambda_0 + s \sqrt{\lambda_0}
for a Poisson variate X \sim Po(\lambda)
\theta_1 = \frac{s \pi_0}{1+(s-1) \pi_0}
for a Binomial variate X \sim Bin(n, \pi)
findH
returns a vector and hValues
returns a matrix with elements
theta0 |
in-control parameter |
h |
decision interval |
k |
reference value |
ARL |
ARL for a CUSUM with parameters |
rel.tol |
corresponds to |
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