xcusum.q {spc}

Compute RL quantiles of CUSUM control charts

Description

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

Usage

xcusum.q(k, h, mu, alpha, 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.

alpha

quantile level.

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

Instead of the popular ARL (Average Run Length) quantiles of the CUSUM stopping time (Run Length) are determined. The algorithm is based on Waldmann's survival function iteration procedure.

Value

Returns a single value which resembles the RL quantile of order q.

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.arl for zero-state ARL computation of CUSUM control charts.

Examples

## Waldmann (1986), one-sided CUSUM, Table 2
## original values are 345, 82, 9

XCUSUM.Q <- Vectorize("xcusum.q", "alpha")
k <- .5
h <- 3
mu <- 0 # corresponds to Waldmann's -0.5
a.list <- c(.95, .5, .05)
rl.quantiles <- ceiling(XCUSUM.Q(k, h, mu, a.list))
cbind(a.list, rl.quantiles)