Computation of the survival function of the Run Length (RL) for CUSUM control charts monitoring normal mean.
xcusum.sf(k, h, mu, n, hs=0, sided="one", r=40)Returns a vector which resembles the survival function up to a certain point.
reference value of the CUSUM control chart.
decision interval (alarm limit, threshold) of the CUSUM control chart.
true mean.
calculate sf up to value n.
so-called headstart (enables fast initial response).
distinguishes between one- and two-sided CUSUM control chart by choosing "one" and "two", respectively.
number of quadrature nodes, dimension of the resulting linear equation system is equal to r+1.
Sven Knoth
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 CUSUM 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.
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.
xcusum.q for computation of CUSUM run length quantiles.
## Waldmann (1986), one-sided CUSUM, Table 2
k <- .5
h <- 3
mu <- 0 # corresponds to Waldmann's -0.5
SF <- xcusum.sf(k, h, 0, 1000)
plot(1:length(SF), SF, type="l", xlab="n", ylab="P(L>n)", ylim=c(0,1))
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