sewma.sf: Compute the survival function of EWMA run length

In spc: Statistical Process Control -- Calculation of ARL and Other Control Chart Performance Measures

Compute the survival function of EWMA run length

Description

Computation of the survival function of the Run Length (RL) for EWMA control charts monitoring normal variance.

Usage

sewma.sf(n, l, cl, cu, sigma, df, hs=1, sided="upper", r=40, qm=30)

Arguments

n	calculate sf up to value n.
l	smoothing parameter lambda of the EWMA control chart.
cl	lower control limit of the EWMA control chart.
cu	upper control limit of the EWMA control chart.
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 EWMA-S^2 control charts by choosing "upper" (upper chart without reflection at cl – the actual value of cl is not used), "Rupper" (upper chart with reflection at cl), "Rlower" (lower chart with reflection at cu), and "two" (two-sided chart), respectively.
r	dimension of the resulting linear equation system (highest order of the collocation polynomials).
qm	number of quadrature nodes for calculating the collocation definite integrals.

Details

The survival function P(L>n) and derived from it also the cdf P(L<=n) and the pmf P(L=n) illustrate the distribution of the EWMA run length. For large n the geometric tail could be exploited. That is, with reasonable large n the complete distribution is characterized. The algorithm is based on Waldmann's survival function iteration procedure and on results in Knoth (2007).

Value

Returns a vector which resembles the survival function up to a certain point.

Author(s)

Sven Knoth

References

S. Knoth (2007), Accurate ARL calculation for EWMA control charts monitoring simultaneously normal mean and variance, Sequential Analysis 26, 251-264.

K.-H. Waldmann (1986), Bounds for the distribution of the run length of geometric moving average charts, Appl. Statist. 35, 151-158.

See Also

sewma.arl for zero-state ARL computation of variance EWMA control charts.

Examples

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spc documentation built on Oct. 24, 2022, 5:07 p.m.