Computation of the (zero-state) Average Run Length (ARL) for different types of CUSUM control charts monitoring normal mean.
xtcusum.arl(k, h, df, mu, hs = 0, sided="one", mode="tan", r=30)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.
degrees of freedom -- parameter of the t distribution.
true mean.
so-called headstart (give fast initial response).
distinguish between one- and two-sided CUSUM schemes by choosing "one" and "two", respectively.
number of quadrature nodes, dimension of the resulting linear equation system is equal to r+1.
Controls the type of variables substitution that might improve the numerical performance. Currently, "identity", "sin", "sinh", and "tan" (default) are provided.
Sven Knoth
xtcusum.arl determines the Average Run Length (ARL) by numerically
solving the related ARL integral equation by means of the Nystroem method
based on Gauss-Legendre quadrature.
A. L. Goel, S. M. Wu (1971), Determination of A.R.L. and a contour nomogram for CUSUM charts to control normal mean, Technometrics 13, 221-230.
D. Brook, D. A. Evans (1972), An approach to the probability distribution of cusum run length, Biometrika 59, 539-548.
J. M. Lucas, R. B. Crosier (1982), Fast initial response for cusum quality-control schemes: Give your cusum a headstart, Technometrics 24, 199-205.
L. C. Vance (1986), Average run lengths of cumulative sum control charts for controlling normal means, Journal of Quality Technology 18, 189-193.
K.-H. Waldmann (1986), Bounds for the distribution of the run length of one-sided and two-sided CUSUM quality control schemes, Technometrics 28, 61-67.
R. B. Crosier (1986), A new two-sided cumulative quality control scheme, Technometrics 28, 187-194.
xtewma.arl for zero-state ARL computation of EWMA control charts and xtcusum.arl for the zero-state ARL of CUSUM for normal data.