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)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.
Returns a single value which resembles the ARL.
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.
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