xcusum.sf {spc}

Compute the survival function of CUSUM run length

Description

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

Usage

xcusum.sf(k, h, mu, n, hs=0, sided="one", r=40)

Arguments

k

reference value of the CUSUM control chart.

h

decision interval (alarm limit, threshold) of the CUSUM control chart.

mu

true mean.

n

calculate sf up to value n.

hs

so-called headstart (enables fast initial response).

sided

distinguishes between one- and two-sided CUSUM control chart by choosing "one" and "two", respectively.

r

number of quadrature nodes, dimension of the resulting linear equation system is equal to r+1.

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 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.

Value

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

Author(s)

Sven Knoth

References

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.

See Also

xcusum.q for computation of CUSUM run length quantiles.

Examples

## 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))
#