scusum.crit {spc} | R Documentation |
Compute decision intervals of CUSUM control charts (variance charts)
Description
omputation of the decision intervals (alarm limits)
for different types of CUSUM control charts (based on the sample
variance S^2
) monitoring normal variance.
Usage
scusum.crit(k, L0, sigma, df, hs=0, sided="upper", mode="eq.tails",
k2=NULL, hs2=0, r=40, qm=30)
Arguments
k |
reference value of the CUSUM control chart. |
L0 |
in-control ARL. |
sigma |
true standard deviation. |
df |
actual degrees of freedom, corresponds to subgroup size (for known mean it is equal to the subgroup size, for unknown mean it is equal to subgroup size minus one. |
hs |
so-called headstart (enables fast initial response). |
sided |
distinguishes between one- and two-sided two-sided CUSUM- |
mode |
only deployed for |
k2 |
in case of a two-sided CUSUM chart for variance the reference value of the lower chart. |
hs2 |
in case of a two-sided CUSUM chart for variance the headstart of the lower chart. |
r |
Dimension of the resulting linear equation system (highest order of the collocation polynomials times number of intervals – see Knoth 2006). |
qm |
Number of quadrature nodes for calculating the collocation definite integrals. |
Details
scusum.crit
ddetermines the decision interval (alarm limit)
for given in-control ARL L0
by applying secant rule and using scusum.arl()
.
Value
Returns a single value which resembles the decision interval h
.
Author(s)
Sven Knoth
References
S. Knoth (2005),
Accurate ARL computation for EWMA-S^2
control charts,
Statistics and Computing 15, 341-352.
S. Knoth (2006),
Computation of the ARL for CUSUM-S^2
schemes,
Computational Statistics & Data Analysis 51, 499-512.
See Also
xcusum.arl
for zero-state ARL computation of CUSUM control charts monitoring normal mean.
Examples
## Knoth (2006)
## compare with Table 1 (p. 507)
k <- 1.46 # sigma1 = 1.5
df <- 1
L0 <- 260.74
h <- scusum.crit(k, L0, 1, df)
h
# original value is 10