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.
scusums.arl(k, h, cS, sigma, df, hs=0, sided="upper", k2=NULL,
h2=NULL, hs2=0, r=40, qm=30, version=2)Returns a single value which resembles the ARL.
reference value of the CUSUM control chart.
decision interval (alarm limit, threshold) of the CUSUM control chart.
Shewhart limit.
true standard deviation.
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.
so-called headstart (enables fast initial response).
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.
In case of a two-sided CUSUM chart for variance the reference value of the lower chart.
In case of a two-sided CUSUM chart for variance the decision interval of the lower chart.
In case of a two-sided CUSUM chart for variance the headstart of the lower chart.
Dimension of the resulting linear equation system (highest order of the collocation polynomials times number of intervals -- see Knoth 2006).
Number of quadrature nodes for calculating the collocation definite integrals.
Distinguish version numbers (1,2,...). For internal use only.
Sven Knoth
scusums.arl determines the Average Run Length (ARL) by numerically
solving the related ARL integral equation by means of collocation (piecewise Chebyshev polynomials).
S. Knoth (2006), Computation of the ARL for CUSUM-\(S^2\) schemes, Computational Statistics & Data Analysis 51, 499-512.
scusum.arl for zero-state ARL computation of standalone CUSUM control charts for monitoring normal variance.