xtcusum.arl: Compute ARLs of CUSUM control charts

Description

Computation of the (zero-state) Average Run Length (ARL) for different types of CUSUM control charts monitoring normal mean.

Usage

xtcusum.arl(k, h, df, mu, hs = 0, sided="one", mode="tan", r=30)

Arguments

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).

sided

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.

mode

Controls the type of variables substitution that might improve the numerical performance. Currently, "identity", "sin", "sinh", and "tan" (default) are provided.

Value

Returns a single value which resembles the ARL.

Details

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.

References

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.

Examples

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