spc (version 0.7.1)

scusum.crit: 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)

Value

Returns a single value which resembles the decision interval h.

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-\(S^2\) control charts by choosing "upper" (upper chart), "lower" (lower chart), and "two" (two-sided chart), respectively. Note that for the two-sided chart the parameters "k2" and "h2" have to be set too.

mode

only deployed for sided="two" -- with "eq.tails" two one-sided CUSUM charts (lower and upper) with the same in-control ARL are coupled. With "unbiased" a certain unbiasedness of the ARL function is guaranteed (here, both the lower and the upper control limit are calculated).

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.

Author

Sven Knoth

Details

scusum.crit ddetermines the decision interval (alarm limit) for given in-control ARL L0 by applying secant rule and using scusum.arl().

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