simulation {CautiousLearning}

Estimation errors and conditional run-length simulation

Description

Function ruv simulates the standardized estimation errors at the starting of the monitoring phase (see Section 2.3 of Capizzi and Masarotto (2019)).

Function rcrl simulates, under different in-control or out-control scenarios, the conditional run-length given the standardized estimation errors. When openMP is supported, computation can be distribuited on multiple cores. See omp.

Usage

ruv(n, m)

rcrl(n, chart, u, v, tau, delta, omega, maxrl = 1000000L)

Arguments

n

number of simulated values.

m

number of in-control observations available at the starting of the monitoring phase.

chart

list with the same elements as those returned by x.cl, ewma.cl and cusum.cl.

u, v

values of the estimation errors (scalars).

tau, delta, omega

when i<tau, observations are distributed as N(mu,sigma^2) random variables; when i>=tau, observations are distributed as N(mu+delta*sigma, (omega*sigma)^2) random variables.

maxrl

run-length are truncated at i=maxrl.

Value

ruv

numeric matrix of dimension nx2.

rcrl

integer vector of length n.

Author(s)

Giovanna Capizzi and Guido Masarotto

References

Capizzi, G. and Masarotto, G. (2019) "Guaranteed In-Control Control Chart Performance with Cautious Parameter Learning", accepted for publication in Journal of Quality Technology, a copy of the paper can be obtained from the authors.

Examples

ruv(5, 100)
## EWMA control chart (nominal ARL=500, 
## initial estimates based on 100 in-control observations)
chart <- list(chart = "EWMA",
              lambda = 0.2,
              limit = c(Linf=3.187, Delta=0.427, A=1.5, B=50, m=100))
rcrl(10, chart, 2, 1, 50, 2, 1)