scusums.arl {spc} | R Documentation |
Compute ARLs of CUSUM-Shewhart control charts (variance charts)
Description
Computation of the (zero-state) Average Run Length (ARL)
for different types of CUSUM-Shewhart combo control charts (based on the sample variance
S^2
) monitoring normal variance.
Usage
scusums.arl(k, h, cS, sigma, df, hs=0, sided="upper", k2=NULL,
h2=NULL, hs2=0, r=40, qm=30, version=2)
Arguments
k |
reference value of the CUSUM control chart. |
h |
decision interval (alarm limit, threshold) of the CUSUM control chart. |
cS |
Shewhart limit. |
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- |
k2 |
In case of a two-sided CUSUM chart for variance the reference value of the lower chart. |
h2 |
In case of a two-sided CUSUM chart for variance the decision interval 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. |
version |
Distinguish version numbers (1,2,...). For internal use only. |
Details
scusums.arl
determines the Average Run Length (ARL) by numerically
solving the related ARL integral equation by means of collocation (piecewise Chebyshev polynomials).
Value
Returns a single value which resembles the ARL.
Author(s)
Sven Knoth
References
S. Knoth (2006),
Computation of the ARL for CUSUM-S^2
schemes,
Computational Statistics & Data Analysis 51, 499-512.
See Also
scusum.arl
for zero-state ARL computation of standalone CUSUM control charts for monitoring normal variance.
Examples
## will follow