shroArlPfaCed: ARL, PFA and CED of Shiryayev-Roberts procedure

In mistat: Data Sets, Functions and Examples from the Book: "Modern Industrial Statistics" by Kenett, Zacks and Amberti

ARL, PFA and CED of Shiryayev-Roberts procedure

Description

Average Run Length, the Probability of False Alarm and the Conditional Expected Delay, given that the alarm is given after the change-point for Normal and Poisson cases

Usage

shroArlPfaCedNorm(mean0 = 0, mean1 = NA, sd = 1, n = 10, 
                  delta = 1, tau = NA, N = 100, limit = 10000, 
                  seed = NA, w = 19, printSummary = TRUE)
                  
shroArlPfaCedPois(lambda0 = 10, lambda1 = NA, delta = 1, 
                  tau = NA, N = 100, limit = 10000, seed = NA, 
                  w = 19, printSummary = TRUE)

Arguments

mean0	value of the mean of a normal distributed process
mean1	optional value of the mean after a shift in a normal process, ignored if delta is not NA
sd	standard deviation of a normal distributed process
n	sample size
lambda0	mean of a Poisson distributed process
lambda1	optional value of the mean after a shift in a Poisson process, ignored if delta is not NA
delta	value of the shift from mean0 or lambda0, set to NA if the alternative specification with mean1 or lambda1 is needed
tau	location of the point of change in the process parameter mean0 or lambda0, if NA simulation is perfomed without any shift: mean1, lambda1 and delta are ignored
N	the number of replicates
limit	safety parameter, stop rule for procedures with very long ARL
seed	a single value, interpreted as an integer. If specified make the simulation replicable.
w	Shiryayev-Roberts statistics used as the stopping threshold
printSummary	logical, if TRUE print a summary of the Shiryayev-Roberts ARL, PFA and CED

Value

a list with elements:

rls	a numeric vector representing the Run Length of the simulation
statistics	a numeric vector with summary statistics
run	a list of length N elements each of which has single numeric elements violationLower, violationUpper and rl

Author(s)

Daniele Amberti

References

Kenett, R., Zacks, S. with contributions by Amberti, D. Modern Industrial Statistics: with applications in R, MINITAB and JMP. Wiley.

Examples

shroArlPfaCedNorm(mean0=10, 
                  sd=3, 
                  n=5, 
                  delta=0.5, 
                  tau=10, 
                  w=99, 
                  seed=123)
                  
shroArlPfaCedPois(lambda0=5, 
                  delta=0.5, 
                  tau=10, 
                  w=99, 
                  seed=123)

shroArlPfaCedNorm(mean0=15, 
                  sd=3, 
                  n=5, 
                  delta=0.5, 
                  tau=NA, 
                  w=99, 
                  seed=123)

mistat documentation built on March 7, 2023, 6:43 p.m.